MMP as sub-category of two-tier PR–some basis for doubt

In yesterday’s review of the German election outcome, I used the extended Seat Product Model (SPM) formula for two-tier PR systems. I have done this many times, and Rein Taagepera and I (in our 2017 book, Votes from Seats) do explicitly include mixed-member proportional (MMP) in the category of two-tier PR systems.

However, there is one problem with that characterization. All other two-tier PR systems that I can think of entail a single vote, which is then used both for allocating seats in the basic tier and pooled across districts for national (or sometimes regional) compensation.

MMP, of course, usually entails two votes–a nominal (candidate) vote used only in the basic tier, and a second, party-list, vote used for determining overall proportionality. (In MMP, the basic tier is a “nominal tier” because the vote there is cast for a candidate, and the district winner earns the seat solely on votes cast for him or her by name.) This two-vote feature is a complex feature of MMP that is actually emphasized in my more recent coauthored book, Party Personnel Strategies, but which I may have tended to underplay in my comparative work on modeling the effects of electoral systems on party systems. Of course, by being two-tier, it is already a non-simple system, as Taagepera and I define that term. But we also say that two-tier PR, including MMP, is as simple as an electoral system can be and still be included in the complex category (see p. 263 and 299 of Votes from Seats).

Maybe that is not an accurate statement for two-vote MMP. Our definition of simple (pp. 31-36) concentrates on two features: (1) all seats allocated within districts, and (2) adherence to the rank-size principle, such that the largest party gets the first seat in a district, and remaining seats are allocated in a way that respects their relative sizes (i.e., by any of the common PR formulas). We further say that for simple PR, “the vote for candidate and for party is one act” (p. 35). This latter condition still holds for any two-tier list-PR system, because there is a list vote that applies both for allocating seats within a district, and also for the “complex” feature of the supra-district compensation mechanism. Obviously, however, MMP as used in Germany violates the principle that “the vote for candidate and for party is one act.” So maybe it is not “simple enough” to qualify as an almost-simple complex system. (Yes, that was a complex statement, but that’s kind of the point.)

If MMP were to tend to produce a party system more fragmented than expected from the extended SPM, it might be due to the “second” vote, i.e., the list vote. To test this, one could aggregate all the nominal votes and use them as the notional list votes in a simulated compensation. (This is how MMP in Germany worked in 1949, albeit with compensation only at state level. It is also how MMP now works in Lesotho.) The aggregation of basic-tier votes should work better from the standpoint of modeling the party system impact of the key features of a given MMP system–the size of the basic tier and the share of seats in the compensation tier.

The catch in all this is that, of course, till quite recently German MMP was under-fragmented, according to the SPM, despite using a separate list vote. Thus the issue did not arise. The New Zealand MMP system also has matched expectations well, after the first three post-reform elections were over-fragmented relative to model prediction. The graph below shows the relationship over time between the expectations of the SPM and the observed values of effective number of seat-winning parties (NS) in both Germany and New Zealand. For the latter country, it includes the pre-reform FPTP system. In the case of Germany, it plots NS alternately, with the CDU and CSU considered separately. As I noted in the previous discussion, I believe the “correct” procedure, for this purpose, is to count the “Union” as one party, but both are included here for the sake of transparency. In both panels, the dashed mostly horizontal line is the output of the extended SPM for the countries’ respective MMP systems1; it will change level only when the electoral system changes. (For New Zealand, the solid horizontal line is the expectation under the FPTP system in use before 1996.)

The German party system from 1953 through 2005 was clearly fitting quite poorly, due to how under-fragmented it was for the electoral system in use. The old CDU/CSU and SPD were just too strong and overwhelmed the considerable permissiveness of the electoral rules.2 So clearly the question I am raising here–whether the two-vote feature of MMP means it should not be modeled just like any (other) two-tier PR system–is moot for those years. However, perhaps it has become an issue in recent German elections, including 2021. The underlying feature of voter behavior pushing the actual NS to have risen to well above “expectation” would be the greater tendency of voters towards giving their two votes to different parties. At least that would be the cause in 2021, given that we saw in the previous post that the basic tier produced almost exactly the degree of fragmentation that the SPM says to expect. It is the compensation tier that pushed it above expectation, and the problem here (from a modeling perspective) is that the formula implicitly assumes the votes being used in the compensation mechanism are the same votes being cast and turned into seats in the basic (nominal) tier. But with two votes, they are not, and with more voters splitting tickets, the assumption becomes more and more untenable.

The previous planting on this matter emphasized that the SPM is actually performing well, even in this most recent, and quite fragmented, election. I am not trying to undermine that obviously crucial point! However, the marked rise in NS since 2009–excepting 2013 when the FDP failed to clear the threshold–may suggest that the model’s assumption that the two votes are pretty similar could be problematic.

Maybe two-vote MMP is more complex after all than its characterization as a two-tier PR system–the simplest form of complex electoral system–implies. In fact, maybe I should stop referring to MMP as a sub-category of two-tier PR. Yet for various reasons, it is a convenient way to conceptualize the system, and as yesterday’s discussion of the recent German election showed, it does work quite well nonetheless. It could be based on a flawed premise, however, and the more voters cast their nominal and list votes differently, the more that flaw becomes apparent.

A work in progress… in other words (fair warning), more such nerdy posts on this topic are likely coming.

Notes

1. The “expected NS” line for Germany takes the tier ratio to be 0.5, even though as I argued in the previous entry, we really should use the actual share of compensation seats in the final allocation. This would have only minimal impact in the elections before 2013; in 2021, it makes a difference in “expected” NS of 0.36.

2. Partly this is due to the 5% list-vote threshold, which is not a factor in the version of the SPM I am using. In Votes from Seats, we develop an alternate model based only on a legal threshold. For a 5% threshold, regardless of other features, it predicts NS=3.08. This would be somewhat better for much of the earlier period in Germany. In fact, from 1953 through 2002, mean observed NS=2.57. In the book we show that the SPM based only on mean district magnitude and assembly size–plus for two-tier PR, tier ratio–generally performs better than the threshold model even though the former ignores the impact of any legal threshold. This is not the place to get into why that might be, or why the threshold might have “worked” strongly to limit the party system in Germany for most of the postwar period, but the permissiveness of a large assembly and large compensation tier is having more impact in recent times. It is an interesting question, however! For New Zealand, either model actually works well for the simple reason that they just happen to arrive at almost identical predictions (3.08 vs. 3.00), and that for the entire MMP era so far, mean NS has been 3.14.

The Germany 2021 result and the electoral system

The German general election of 2021 has resulted in a situation in which neither major party can form a government without either the other, or more likely, a coalition that takes in both the liberal FDP and the Greens. With the largest party, the social-democratic SPD, under 30% of seats, it is an unusually fragmented result compared to most German elections. Naturally, this being Fruits & Votes, attention turns to how much more fragmented this outcome is than expected, given the electoral system. The answer may be a bit of a surprise: not all that much. I expected this outcome to be a significant miss for the Seat Product Model (SPM). But it is really not that far off.

For a two-tier PR system, of which Germany’s MMP can be thought of as a subtype, we need to use the extended version of the SPM developed in Votes from Seats.

NS = 2.5t(MSB)1/6,

where NS is the effective number of seat-winning parties (here, meaning the expected NS), M is the mean district magnitude of the basic tier, SB is the total number of seats in the basic tier, and t is the “tier ratio” defined as the share of the total number of assembly seats allocated in the compensatory tier. For Germany, basic-tier M=1 and SB=299. The tier ratio could be coded as 0.5, because the initial design of the system is that there are 299 list tier seats, allocated to bring the result in line with the overall party-list vote percentages of each party that clears the threshold. However, in Germany the electoral law provides that the list tier can be expanded further to the extent needed to reach overall proportionality. Thus t is not fixed; we should probably use the ratio that the final results are based on, as NS would necessarily be lower if only 299 list seats had been available. In the final result, the Bundestag will have 735 seats, meaning 436 list seats, which gives us a tier ratio of t=436/735=0.593. Plug all this into the formula, and you get:

NS = 2.50.5932991/6=1.72*2.59=4.45.

Now, what was the actual NS in the final result? We have to ask ourselves whether to count to two Christian “Union” parties, the CDU and the CSU, as one party or two. The answer really depends on the question being asked. They are separate parties, with distinct organization, and they bargain separately over portfolios and policy when they are negotiating a coalition with another party. However, for purposes of the SPM, I firmly believe that when two or more parties in a bloc do not compete against each other (or, alternatively, do so only within lists over which votes are pooled for seat-allocation1), they should be treated as one. The SPM does not “care” whether candidates of the bloc in question are branded as CSU (as they are in Bavaria) or as CDU (the rest of Germany). It simple estimates the effective number of “agents of the electorate” given the electoral rules. In terms of national politics, these are the same “agent”–they always enter government together or go into opposition together, and they jointly nominate a leader to be their Chancellor candidate.

Taking the CDU/CSU as a “party” for this purpose, we get actual NS =4.84 in the 2021 election. So, given an expectation of 4.45, the actual outcome is just over 8.75% higher than expected. That is nothing too extraordinary. For comparison purposes, we can just take the ratio of actual NS to expected NS. Here are some elections in the dataset used for Votes from Seats that are in the same range of over-fragmentation as Germany 2021:

      country   year   simple   Ns   exp_Ns   ratio 
     Barbados   1981        1    1.87   1.735597   1.077439  
       Norway   1965        1    3.51   3.255616   1.078137  
    Sri Lanka   1970        1    2.49   2.307612   1.079037  
Dominican Rep   1990        1    3.05   2.810847   1.085082  
     Trinidad   2002        1    1.98   1.824064   1.085488  
      Iceland   1963        0    3.33   3.060313   1.088124  
       Israel   1961        1    5.37   4.932424   1.088714  
     Trinidad   2001        1       2   1.824064   1.096452  
     Trinidad   2000        1       2   1.824064   1.096452  
      Iceland   1999        0    3.45   3.146183   1.096567  
      Denmark   1950        0    3.98   3.624933   1.097951  
     

(The table indicates as ‘simple’ those with a single tier; others are two-tier.)

The ratio variable has a mean of 1.021 in the full dataset and a standard deviation of 0.359. Its 75th percentile is 1.224 (and 25th is 0.745). So the German election of 2021 is actually very well explained by this method. The degree of fragmentation we saw in this election is not too surprising. It is about what should be expected with MMP consisting of 299 nominal-tier M=1 seats and a very generous and flexible compensation tier.

As an aside, if we used the initial tier size (299, so t=0.5) in the formula, we would get an “expected” NS=4.09. This would mean a ratio of 1.183, still short of the 75th percentile of the 584 elections included in the book’s main statistical test. Here is the company it would be keeping in that neighborhood:

            country   year   simple   Ns   exp_Ns   ratio 
            Germany   2009        0    4.83   4.121066   1.172027  
St. Kitts and Nevis   2000        1    1.75   1.491301   1.173472  
         Luxembourg   2009        1    3.63   3.077289    1.17961  
             Canada   2004        1    3.03   2.560218   1.183493  
            Denmark   1998        0    4.71   3.965222   1.187828  
          Venezuela   1963        0    4.32    3.63006   1.190063  
        Korea South   1988        0    3.55   2.981969   1.190488  
     Czech Republic   2010        1    4.51   3.767128   1.197199  
            Iceland   1991        0    3.77   3.146183   1.198277  

This would put the German 2021 election about as “over-fragmented” as the Canadian election of 2004. In other words, still not a big deal. If we count the two “Union” parties separately, obviously the degree of over-fragmentation goes up considerably. As I have said already, I think for this purpose counting them as one is the correct decision.2

As far as size of the largest seat-winning party is concerned, the SPD has 206 seats, for 28.03%. The SPM would predict, given expected NS=4.45, that the largest should have 32.6% (240 seats out of 735); that’s a ratio of 0.860 (which is a slightly bigger miss than the NS ratio of 1.088, the reciprocal of which would be 0.919). It is worth pausing on this for a bit. Polling before the election said the largest party might be only on a quarter of the votes. This was accurate, as the SPD won 25.7%. The advantage ratio (%seats/%votes) is 1.09, which is rather high for an electoral system that promises as near-perfect proportionality as Germany’s current system does, with its compensation for overhangs (cases in which a party has won more nominal-tier seats in a state than its list votes would have entitled it to). This bonus is a result of a rather high below-threshold vote. Not as high in 2013, of course, when two parties (FDP and AfD) narrowly missed the nationwide 5% threshold. But still considerably high, at 8.6% combined for all parties that failed to win a seat.

It is also worth asking whether the logic behind the extended SPM for two-tier systems holds for this German election. The formula says that the basic tier produces an initial allocation of seats consistent with the SPM for simple systems, and then inflates it based on the size of the compensation tier. So we can ask what the effective number of seat-winning parties is in the basic tier alone. It should be NS =(MSB)1/6= 2991/6= 2.59. In fact, the basic-tier NS in this election was 2.51 (as before, taking CSU/CSU as one party). The ratio of 0.969 is a pretty trivial miss. We should expect the largest party to have won 0.490 of these seats (about 146). Actually the Union parties, which together won the most single-seat districts, won 143 (0.478). Thus Germany’s MMP system, in the 2021 election, actually did produce a basic-tier (nominal-tier) party system pretty much just like it should, given 299 seats and M=1 plurality, and then augmented this through a large compensatory national tier. The actual inflator is a factor of 1.93=4.84/2.51, rather than the expected 1.72=2.50.593. Had it been 1.72 instead, the final effective number of seat-winning parties would have been 4.32, about “half a party” less than in reality, implying almost exactly one third of seats to the SPD instead of just 28%.

This surprised me (pleasantly, of course). When I saw that the Greens and AfD each had won 16 seats in the nominal tier, I thought that was too many! But in fact, it works out. Maybe sometimes even I think Duverger had a law, or something. But given 299 single-seat districts, this is pretty much in line with expectations.

The outcome is interesting in the many ways that it serves as a primer on details of the electoral system. Here I mean not only the substantial expansion of the Bundestag from 598 to 735 seats, due to the way the compensation mechanism works, but also the thresholds. One of the best known features of the German electoral system is the 5% nationwide threshold. But of course, the threshold is more complex than that. It is 5% of the national party-list vote or three single-seat wins, except if a party is an ethnic-minority party. All these provisions were on display. For instance, the Linke (Left) party fell below the 5.0% threshold, yet is represented at full proportionality. That is because it won three individual mandates, thus fulfilling the “or” clause of the threshold. There was a point on election night when it looked as if the Linke might hold only two single-seat districts. In that case, with less than 5% of the list votes nationwide, it would have held only those seats as its total. By winning three, it is entitled under the law to full proportional compensation, and as a result it was awarded 36 list seats. Then, for the first time in a very long time, an ethnic party has won a seat. The South Schleswig Voters’ Association (SSW), which had not contested federal elections in decades, ran in this one and was able to win a single (list) seat, because as a representative of the Danish and Frisian minorities, it is exempt from the usual threshold provisions, as long as its votes are sufficient to qualify it for a seat when the threshold is ignored. Its 0.1% of the national vote was good enough. The SSW has had some renewed success in state elections in Schleswig-Holstein recently, and now it has scored a seat in the federal parliament for the first time since 1949. In 1949, the MMP system was a bit different, in that the 5% threshold was determined state-by-state, rather than nationwide. If the threshold had been state-by-state in this election, one other party would have earned seats. The Free Voters won around 7.5% of party-list votes in Bavaria. However, they managed only 2.9% nationwide (and no district seat), so they are shut out.

Now attention turns to what the coalition will be. Two options are on the table: SPD+Greens+FDP (“traffic light”) or CDU/CSU+Greens+FDP (“Jamaica”). The possibility of a broad left coalition has been ruled out by the election results: SPD+Green+Linke is not a majority. It was never likely anyway; the SPD and Greens did not spend recent years convincing voters they were safe options near the center of German politics to team up with the far left. Nonetheless, had it been mathematically possible the SPD might have used it as leverage against the FDP. My guess is that the traffic light coalition will form. Despite some serious policy differences between the FDP and the other two, it would be a government made up of the winners of the election, as these three parties all gained votes compared to 2017. On the other hand, one led by the CDU/CSU would be led by a pretty big loser, even though it is mathematically possible and the Greens seem to have been positioning for it over the last several years.3 Following the election, the DW live blog has been reporting on comments by various prominent CDU and CSU politicians that could be interpreted as saying the bloc needs some time in opposition, after the disappointing result. I suspect this is the view that will prevail, and after a lot of intense and difficult bargaining, Germany will be led by a traffic light coalition for the first time.

____

Notes

1. Here I am thinking of cases like Chile, where alliance lists contain candidates of different parties, but for purposes of how the electoral system assigns seats between competing teams of candidates, we should count the alliances, not the component parties. The same condition applies in Brazil and Finland, only there it is essentially impossible to aggregate to a meaningful national alliance category because the combinations of parties are not always the same across districts. In Chile, and also in the FPTP case of India–as well as in the current case of Germany–there is no such problem, as the alliances are nationwide in scope and consistent across districts.

2. For the record, counting them separately yields NS=5.51 in this election, which would put the ratio just barely above the 75th percentile.

3.To be clear, they are much happier working with the SPD, but what I mean is that their positioning for the possibility of a coalition with the CDU/CSU should make finding common ground with the FDP easier than it otherwise would have been.

What electoral system should Canada have?

Once again, Canadians have voted as if they had a proportional representation (PR) electoral system, but obtained almost exactly the party system they should be expected to get, given the first-past-the-post (FPTP) system that they actually use.

If voters are voting as if they had PR already, why not just give them PR? Of course, it does not work that way, as the decision to adopt a new electoral system is rarely separable from party politics. Nonetheless, it is worth asking what electoral system the country should have, based on how voters are actually voting. They certainly are not playing the game as if it were FPTP. Even though it is.

To get at an answer to this question, we can start with the average value of the effective number of vote-earning parties over recent elections. (For those just tuning in or needing a refresher, the effective number of parties is a size-weighted count, where each party’s “weight” in the calculation is its own size–we square the vote (or seat) share of each party, sum up the squares, and take the reciprocal. If there were four equal size parties, the effective number would be 4.00. If there are four parties of varying sizes, the effective number will be smaller than four. For instance, if the four have percentages of 40%, 35%, 20%, and 5%, the effective number would be 3.08.) From the effective number, we can work backwards through the Seat Product Model (SPM) to determine what electoral system best fits the distribution of parties’ votes that Canadians have actually been providing. The SPM lets us estimate party system outputs based on a country’s mean district magnitude (number of seats elected per district (riding)) and assembly size. As noted above, Canada currently tends to have a distribution of seats among parties in the House of Commons consistent with what the SPM expects from a district magnitude of 1 and a House size of 338. The puzzle is that it does not have a distribution of votes consistent with the SPM. Instead, its distribution of votes across parties looks more like we would expect from a PR system. But what sort of PR system? That is the question the following calculations aim to answer.

Over the past eight elections, going back to 2000, the mean effective number of vote-earning parties (dubbed NV in systematic notation) has been 3.70. During this time, it has ranged from a low of 3.33 (2015 when Justin Trudeau won his first, and so far only, majority government) to a high of 3.87 (the second Conservative minority government of the period under leadership of Stephen Harper). In 2019 it was 3.79 and in 2021 it was very slightly higher (3.84, based on nearly complete results). Even the lowest value of this period is not very “two party” despite the use of FPTP, an electoral system allegedly favorable to two-party systems. (I say allegedly, because given FPTP with a House of 338 seats, we actually should expect NV=3.04, according to the SPM. In other words, a “two-party system” is not really what the current electoral system should deliver. Nonetheless, it would not be expected to be associated with as fragmented a voting outcome as Canadians typically deliver.)

How to get from actual voting output to the PR system Canadians act as if they already had

The SPM derives its expectation for NV via a phantom quantity called the number of “pertinent” vote-earning parties. This is posited in Shugart and Taagepera (2017), Votes from Seats, to be the number of parties winning at least one seat, plus one. It is theoretically expected, and empirically verifiable, that the effective number of seat-winning parties (NS) tends to equal the actual number of seat winning parties (NS0, with the 0 in the subscript indicating it is the unweighted, raw, count), raised to the exponent, 2/3. That is, NS=NS02/3. The same relationship logically would hold for votes, meaning NV=NV02/3, where NV0 is the aforementioned number of pertinent vote-earning parties. We can’t measure this directly, but we take it to be NV0=NS0+1, “strivers equal winners, plus one.” In Votes from Seats we show that this assumption works for estimating the impact of electoral systems on NV.

Thus we start with the recently observed mean NV=3.7. From that we can estimate what the number of pertinent parties would be: given NV=NV02/3, we must also have NV0=NV3/2. So NV0=3.73/2 = 7.12. This number by itself is not so interesting, but it makes all the remaining steps of answering our question possible.

Our expected number of seat-winning parties from a situation in which we know NV=3.7 works out to be 6.12 (which we might as well just round and call 6). We get that as follows. First, NS0=NV0-1: the number of pertinent vote-earning parties, minus one. We already estimated the pertinent vote-earning parties to be 7, so we have an estimated average of 6 parties winning at least one seat. This is realistic for current Canadian politics, as recently five parties have been winning seats (Liberal, Conservative, NDP, BQ, and since 2011, Greens). With PR, the PPC likely would win a few seats on current strength, and the Greens probably would continue to do so, assuming they either recover from their current doldrums (especially once PR were adopted) or that any legal threshold would not be applied nationally and thus even their 2.3% showing in the 2021 election would not lock them out of parliament. (In 2021, Greens still got 9.6% in PEI, 5.3% in BC and 5.2% in New Brunswick, for example (per Elections Canada).)

If we have an expected number of seat-winning parties, based actual mean NV, that is equal to six, what would be the seat product (MS) that would be expected? Once again, the seat product is the mean district magnitude (M), times the assembly size (S). Given M=1 (single-seat districts) and S=338, Canada’s current seat product is 338. Based on one of the formulas comprising the SPM, a seat product of 338 should be expected to result in an effective number of seat-winning parties (NS) of 2.64 and effective number of vote-earning parties (NV) of 3.04. It is working out pretty close to that for seats (average NS=2.8). Yet voters are voting more like they had a PR system given the average over recent elections of NV=3.7.

One of the formulas of the SPM, which like all of those referenced here, is empirically accurate on a worldwide sample of election results, predicts that NS0=(MS)1/4. Thus if we have an expected value of seat-winning parties of around 6, as expected from NV=3.7, we can simply raise it to the power, 4, to get what the seat product is expected to be: MS=64=1296. In other words, based on how Canadian voters are actually voting, it is as if their country had an electoral system whose seat product is around 1300, rather than the actual 338. For a comparative referent, this hypothetical PR system would be quite close to the model of PR used in Norway.1

Any electoral system’s mean district magnitude is M=(MS)/S,so taking a House of 338 seats,2 our hypothetical PR system has M=1300/338=3.85. That is, based on how Canadian voters are actually voting, it is as if their country had an electoral system whose mean district magnitude is around 3.85. Comparatively, this is quite close to the Irish PR system’s mean magnitude (but it should be noted that Ireland has a seat product of closer to 600, due to a much smaller assembly).

So there we have it. The mean district magnitude that would be most consistent with Canada’s current vote fragmentation would be just under 4, given the existing size of the House of Commons.

If Canada adopted a PR system with a seat product of 1300, its expected effective number of seat-winning parties (NS) would rise to 3.30, and its expected largest party would have, on average, 40.8% of the seats, or 138. (This is based on two other predictive formulas within the SPM: NS=(MS)1/6 and s1=(MS)–1/8, where s1 is the seat share of the largest party.)

A largest party with 138 seats (as an average expectation) would then require another party or parties with at least 32 seats to have a majority coalition, or a parliamentary majority supporting a minority government. The NDP would reach this easily under our hypothetical PR system, given it can win around 25 seats on under 18% of the votes under FPTP (and 44 seats on just under 20% as recently as 2015).

The Bloc Quebecois also would be available as a partner, presumably for a minority government, with which to develop budgets and other policy, thereby preventing the NDP from being able to hold the Liberal Party “hostage” to its demands. The BQ won 32 seats in 2019 and 33 in 2021. However, because it is a regionally concentrated party, we should entertain the possibility that it might do worse under PR than under FPTP, which rewards parties with concentrated votes. The only way to estimate how it would do might be to run the SPM within the province.

Estimating Quebec outcomes under PR

Quebec has 78 seats total, such that 33 seats is equivalent to 42% of the province’s seats. On Quebec’s current seat product (78) its largest party should win 45 seats (58%). So it is actually doing worse than expected under FPTP!

If the province had a mean district magnitude of 3.85, its seat product would be 300, for which the expected largest party size would be 49%, or 38 seats. In other words, when the BQ is the largest party in Quebec, it could do a little better on the very moderate form of PR being suggested here than it currently is doing under FPTP. (Suppose the model of PR had a mean magnitude of 9 instead, then we’d expect the largest provincial seat winner to have 44.1%, or 34 seats, or roughly what it has won in the last two elections. Only if the mean M is 16 or higher do we expect the largest party in Quebec—often the BQ—to have fewer than 32 of 78 seats. Obviously, in 2011 when the BQ fell all the way to 23.4% within the province, PR would have saved many of their seats when FPTP resulted in their having only 4 of 75 in that election. In 2015 they did even worse in votes—19.3%, third place—but much better in seats, with 10 of 78. Under the PR model being considered here, it is unlikely they would not have won at least 10 seats, which is 12.8%, on that provincial share of the vote.)

Do Canadians actually ‘want’ a still more proportional system than this?
It is possible we should use a higher NV as reflective of what Canadians would vote for if they really had a PR system. I have been using the actual mean NV of recent elections under FPTP, which has been around 3.7. But in the final CBC polling aggregate prior to the 2021 election, the implied NV was 4.12. It dropped by almost “half a party” from the final aggregate3 to the actual result either because some voters defected late from the NDP, Greens, and PPC, or because the polls simply overestimated the smaller parties. If we use 4.12 as our starting point, and run the above calculations, we’d end up with an estimated average of 7.4 parties winning at least one seat. Maybe this implies that the Maverick Party (western emulators of the BQ’s success as a regional party) might win a seat, and occasionally yet some other party. In any case, this would imply a seat product of 2939, for a mean M of 8.7. The largest party would be expected to have only 36.8% of the seats with such an electoral system, or about 125.

How to use this information when thinking about electoral reform

I would advise, as the way to think about this, that we start with what we’d like the parliamentary party system to look like. I am guessing most Canadians would think a largest party with only around 125 seats would be an overly drastic change, despite the fact that they are currently telling pollsters, in effect, that this is the party system they are voting for as of the weekend before the election!

The expected parliamentary party system from an average M around 4, yielding a largest party averaging just over 40% of the seats (around 138) is thus probably more palatable. Nonetheless, armed with the information in this post, drawn from the Seat Product Model, we could start with a desirable average share of the largest party, and work back to what seat product it implies: MS=s1–8, and then (assuming 338 seats in the House), derive the implied district magnitude from M=(MS)/S. Or one can start with how Canadians are actually voting, as I did above–or from how we think they would (or should) vote, using MS=[(NV3/2)–1]4, and followed by M=(MS)/S.

Whichever value of the seat product, MS, one arrives at based on the assumptions about the end state one is hoping to achieve, remember that we’d then expect the seat share of the largest party to be s1=(MS)–1/8. As we have seen here, that would tend to be around 40% if mean magnitude were just under 4. This implies a typical largest party of around 138 seats.4

But herein lies the rub. If you tell the Liberal Party we have this nifty new electoral system that will cut your seats by about 20 off your recent results, they probably will not jump at the offer. The parties that would benefit the most are the Conservatives (twice in a row having won more votes than the Liberals but fewer seats), NDP, and smaller parties, including apparently (based on above calculations) the BQ. But this isn’t a coalition likely to actually come together in favor of enacting PR. Thus FPTP is likely to stick around a while yet. But that’s no reason not to be thinking of what PR system would best suit Canadian voters, given that they have been voting for a while as if they already had a PR system.

_______

Notes

General note: At the time of writing, a few ridings remained uncalled. Thus the seat numbers mentioned above, based on who is leading these close ridings, could change slightly. Any such changes would not alter the overall conclusions.

1. More precisely, it would be almost identical in seat product to the Norwegian system from 1977 to 1985, after which point a small national compensation tier was added to make it more proportional.

2. I will assume electoral reform does not come with a change in the already almost perfect S for the population, based on the cube root law of assembly size, S=P1/3, where P is population, which for Canada is currently around 38 million. This suggests an “optimal” number of seats of about 336.

3. This is based on the Poll Tracker final aggregate having vote shares of 0.315, 0.310, 0.191, 0.070, 0.0680, 0.035 for the six main parties (and 0.011 for “other”).

4. I am deliberately not going into specific electoral system designs in this post. I am stopping at the seat product, implicitly assuming a simple (single-tier) districted PR system, meaning one with no regional or national compensation (“top up” seats). Arriving at a seat product to produce the desired party system should be the first step. Then one can get into the important finer details. If it is a two-tier system–including the possibility of mixed-member proportional (MMP)–one can generate its parameters by using the result of the calculations as the system’s “effective seat product,” and take it from there.

Canada 2021: Another good night for the Seat Product Model, and another case of anomalous FPTP

The 2021 Canadian federal election turned out almost the same as the 2019 election. Maybe voters just really do not want to entrust Justin Trudeau with another majority government, as he led from 2015 to 2019. The early election, called in an effort to turn the Liberal plurality into a Liberal majority, really changed almost nothing in the balance among parties.

The result in terms of the elected House of Commons is strikingly close to what we expect from the Seat Product Model (SPM). Just as it was in 2019. The predictive formulas of the SPM suggest that when your electoral system is FPTP and there are 338 total seats, the largest one should win 48.3% of the seats, or about 163. They further suggest that the effective number of seat-winning parties (NS) of around 2.64. In the actual result–with five districts still to be called–the largest party, the Liberals, has won or is leading in 159, or 47.0%., and NS=2.78. These results are hardly different from expected. They also are hardly different from 2019, when the Liberals won 157 seats; in that election we had NS=2.79.

While the parliamentary balance will be almost what the SPM expects, the voters continue to vote as if there were a proportional system in place. The largest party again has only around a third of the votes, and the effective number of vote-earning parties (NV) is around 3.8. For a FPTP system in a House the size of Canada’s, we should expect NV=3.04. Once again, the fragmentation of the vote continues to be considerably greater than expected.

Another bit of continuity from 2019 is the anomalous nature of FPTP in the current Canadian party votes distribution. For the second election in a row, the Conservative Party has won more votes than the Liberals, but will be second in seats. The votes margin between the two parties was about the same in the two elections, even though both parties declined a little bit in votes in 2021 compared to 2019. Moreover, as also has happened in 2019 (and several times before that), the third largest party in votes will have considerably fewer seats than the party with the fourth highest vote share nationwide. The NDP won 17.7% of the vote and 25 seats (7.4%), while the Bloc Quebecois, which runs only in Quebec, won 7.8% of vote and 33 seats (9.8%).

The Green Party and the People’s Party (PPC) more or less traded places in votes: Greens fell from 6.5% in 2019 to 2.3%, while the PPC increase from 1.6% to 5.0%. But the Greens’ seats fell only from 3 to 2, while the PPC remained at zero.

So, as in 2019, the 2021 election produced a good night for the Seat Product Model in terms of the all-important party balance in the elected House of Commons. However, once again, Canadians are not voting as if they still had FPTP. They are continuing to vote for smaller parties at a rate higher than expected–and not only in districts such parties might have a chance to win–and this is pushing down the vote share of the major parties and pushing up the overall fragmentation of the vote, relative to expectations for the very FPTP system the country actually uses.

It is worth adding that the virtual stasis at the national level masks some considerable swings at provincial level. Éric Grenier, at The Writ, has a table of swings in each province, and a discussion of what it might mean for the parties’ electoral coalitions. A particularly interesting point is that the Conservatives’ gains in Atlantic Canada and Quebec, balanced by vote loss in Alberta and other parts of the west, mirrors the old Progressive Conservative vs. Reform split. Current leader Erin O’Toole’s efforts to reposition the party towards the center may explain these regional swings.

In a follow up, I will explore what this tendency towards vote fragmentation implies for the sort of electoral system that would suit how Canadians actually are voting.

Below are the CBC screen shots of election results for 2021 and 2019. As of Thursday afternoon, there remain a few ridings uncalled. I may update the view for 2021 once they have all been called.

Why 1.59√Ns?

In the previous planting, I showed that there is a systematic relationship under FPTP parliamentary systems of the mean district-level effective number of vote-earning parties (NV) to the nationwide effective number of seat-winning parties (NS). Specifically,

NV =1.59√NS .

But why? I noticed this about a year after the publication of Votes from Seats (2017) while working on a paper for a conference in October, 2018, honoring the career of Richard Johnston, to which I was most honored to have been invited. The paper will be a chapter in the conference volume (currently in revision), coauthored with Cory Struthers.

In VfrS Rein Taagepera and I derived NV =1.59S1/12. And as explained in yesterday’s planting, it is simply a matter of algebraic transformation to get from expressing of NV in terms of assembly size (S) to its expression in terms of NS. But perhaps the discovery of this connection points the way towards a logic underlying how the nationwide party system gets reflected in the average district under FPTP. In the paper draft, we have an explanation that I will quote below. It is on to something, I am sure, but it remains imperfect; perhaps readers of this post can help improve it. But first a little set-up is needed.

To state clearly the question posed in the title above, why would the average district-level effective number of vote-winning parties in a FPTP system tend be equal to the square root of the nationwide effective number of seat-winning parties, multiplied by 1.59?

We can deal with the 1.59 first. It is simply 22/3, which should be the effective number of vote-earning party in an “isolated” district; that is, one that is not “embedded” in a national electoral system consisting of other seats elected in other districts (this idea of embedded districts is the key theme of Chapter 10 of VfrS). The underlying equation for NV, applicable to any simple districted electoral system, starts with the premise that there is a number of “pertinent” parties that can be expressed as the (observed or expected) actual (i.e., not ‘effective’) number of seat-winning parties, plus one. That is, the number of parties winning at least one seat in the district, augmented by one close loser. For M=1 (as under FPTP), we obviously have one seat winning party, and then one additional close loser, for two “pertinent” parties. Thus with M=1 it is the same as the “M+1 rule” previously noted by Reed and Cox, but Taagepera and I (in Ch. 7 of our 2017 book) replace it with an “N+1″ rule, and find it works to help understand the effective number of vote-earning parties both nationwide and at district level. Raising this number of pertinent vote-earning parties to an exponent (explained in the book) gets one to NV (nationwide) or NV (district-level). When M=1, the number of pertinent parties is by definition two, and for reasons shown by Taagepera in his 2007 book, the effective number of seat-winning parties tends to be the actual number of seat-winning parties, raised to the exponent, 2/3. The same relationship between actual and effective should work for votes, where we need the “pertinent” number only because “actual number of parties winning at least one vote” is a useless concept. Hence the first component of the equation, 22/3=1.5874.

As for the second component of the equation, S1/12, it is also an algebraic transformation of the formula for the exponent on the quantity defined as the number of seat-winning parties, plus one. At the district level, if M>1, the exponent is itself mathematically complex, but the principle is it takes into account the impact of extra-district politics on any given district, via the assembly size. The total size of the assembly has a bigger impact the smaller the district is, relative to the entire assembly. Of course, if M=1, that maximizes the impact of national politics for any given S –meaning the impact of politics playing out in other districts on the district of interest. And the larger S is, given all districts of M=1, the more such extra-district impact our district of interest experiences. With all districts being M=1, the exponent reduces to the simple 1/12 on assembly size (shown in Shugart and Taagepera, 2017: 170). Then, as explained yesterday we can express NV in terms of NS via the Seat Product Model. It should be possible to verify NV =1.59√NS empirically; indeed, we find it works empirically. I showed a plot as the second figure in yesterday’s post, but here is another view that does not add in the Indian national alliances as I did in yesterday’s. This one shows only Canada, Britain, and several smaller FPTP parliamentary systems. The Canadian election mean values are shown as open squares, and several of them are labelled. (As with the previous post’s graphs, the individual districts are also shown as the small light gray dots).

It is striking how well the Canadian elections, especially those with the highest nationwide effective number of seat-winning parties (e.g., 1962, 2006, and 2008) conform to the model, indicated with the diagonal line. But can we derive an explanation for why it works? Following is an extended quotation from the draft paper (complete with footnotes from the original) that attempts to answer that question:

Equation 4 [in the paper, i.e. NV =1.59√NS ] captures the relationship between the two levels as follows: If an additional party wins representation in the national parliament, thus increasing nationwide NS to some degree, then this new party has some probabilistic chance of inflating the district-level voting outcome as well. It may not inflate district-level voting fragmentation everywhere (so the exponent on NS is not 1), but it will not inflate it only in the few districts it wins (which would make the exponent near 0 for the average district in the whole country). A party with no seats obviously contributes nothing to NS, but as a party wins more seats, it contributes more.[1] According to Equation 4, as a party emerges as capable of winning more seats, it tends also to obtain more votes in the average district.

As Johnston and Cutler (2009: 94) put it, voters’ “judgements of a party’s viability may hinge on its ability to win seats.” Our logical model quantitively captures precisely this notion of “viability” of parties as players on the national scene through its square root of NS component. Most of the time, viability requires winning seats. For a new party, this might mean the expectation that it will win seats in the current election. Thus our idea is that the more voters see a given party as viable (likely to win representation somewhere), the more they are likely to vote for it.[2] This increased tendency to vote for viable national parties is predicated on voters being more tuned in to the national contest than they are concerned over the outcome in their own district, which might even be a “sideshow” (Johnston and Cutler 2009: 94). Thus the approach starts with the national party system, and projects downward, rather than the conventional approach of starting with district-level coordination and projecting upward.

[Paragraph on the origin of 22/3 =1.5874 skipped, given I already explained it above as stemming from the number of pertinent parties when M=1.3]

Thus the two terms of the right-hand side of Equation 4 express a district component (two locally pertinent parties) and a nationwide one (how many seat-winning parties are there effectively in the parliament being elected?) Note, again, that only the latter component can vary (with the size of the assembly, per Equation 2, or with a given election’s national politics), while the district component is always the same because there is always just one seat to be fought over. Consider some hypothetical cases as illustration. Suppose there are exactly two evenly balanced parties in parliament (NS =2.00), these contribute 1.41=√2 to a district’s N’V, while the district’s essential tendency towards two pertinent parties contributes 1.59=22/3. Multiply the two together and get 1.59*1.41=2.25. That extra “0.25” thus implies some voting for either local politicians (perhaps independents) not affiliated with the two national seat-winning parties or for national parties that are expected to win few or no seats.[4] On the other hand, suppose the nationwide NS is close to three, such as the 3.03 observed in Canada in 2004. The formula suggests the national seat-winning outcome contributes √3.03=1.74 at the district level; multiply this by our usual 1.59, for a predicted value of N’V =2.77. […] this is almost precisely what the actual average value of N’V was in 2004.[5]


[1] The formula for the index, the effective number, squares each party’s seat share. Thus larger parties contribute more to the final calculation.

[2] Likely the key effect is earlier in the sequence of events in which voters decide the party is viable. For instance, parties themselves decide they want to be “national” and so they recruit candidates, raise funds, have leaders visit, etc., even for districts where they may not win. Breaking out these steps is beyond the scope of this paper, but would be essential for a more detailed understanding of the process captured by our logic. 

[3] Because the actual number of vote-earning parties (or independent candidates) is a useless quantity, inasmuch as it may include tiny vanity parties that are of no political consequence.

[4] A party having one or two seats in a large parliament makes little difference to NS. However, having just one seat may make some voters perceive the party a somehow “viable” in the national policy debate—for instance the Green parties of Canada and the UK.

[5] The actual average was 2.71.

Small national parties in Canada in the 2021 election and the connection of district voting to national outcomes

One of the notable trends in polling leading up to the Canadian election of 20 September is the increasing vote share of the Peoples Party of Canada (PPC). At the same time, polls have captured a steady decline of the Green Party as the campaign reaches its end. These two small parties’ trends in national support appear to be happening in all regions of the country, albeit to different degrees (see the graphs at the previous link). That is, while these parties have different levels of support regionally, their trends are not principally regional. Rather, all regions seem to be moving together. This will be a key theme of this post–that politics is fundamentally national, notwithstanding real difference in regional strengths1 and the use of an electoral system in which all seat winning is very local (in each of 338 single-seat districts or “ridings”).

The PPC is a “populist” party of the right. It seems that the Conservatives’ attempt to position themselves closer to the median voter during this campaign has provoked some backlash on the party’s right flank, with increasing numbers of these voters telling pollsters they will vote PPC.

At The Writ, Éric Grenier offers a look into what the polls say about the type of voter turning to the PPC, and whether they might cost the Conservatives seats. The PPC vote share ranges widely across pollsters but in the CBC Poll Tracker (also maintained by Grenier) it currently averages 6.7%. This would be quite a strikingly high figure for a party that is not favored to win even one seat and probably very unlikely to win more than one.2 The Poll Tracker shows a stronger surge in the Prairies region than elsewhere (3.6% on 14 Aug. just before the election was called to 10.9% when I checked on 19 Sept.) and Alberta (4.6% to 9.0% now), but it is being picked up in polling in all regions (for example, from 2.2% to 4.4% in Quebec and 2.9% to 6.1% in Atlantic Canada).

What I wish I knew: Is a voter more likely to vote PPC if he or she perceives that the party is likely to win at least one seat? This question is central to the “all politics is national” model developed in Shugart & Taagepera (2017) Votes from Seats, in chapter 10. We do not mean “all” to be taken literally. Of course, regional and local political factors matter. We mean that one can model the average district’s effective number of parties based on the national electoral system. More to the point, we argue that the way to think of how party systems form under FPTP (or any simple districted system) is not to think in terms of local “coordination” that then somehow gets projected up to a national party system, but rather that the national electoral system shapes the national party system, which then sets the baseline competition in the district contests.

If the PPC or Greens are perceived as likely to have a voice in parliament–and perhaps especially if the parliament is unlikely to have a majority party– voters who like what a small party proposes may be more inclined to support it, even though few voters live in a district where it has any chance of winning locally. Below I will show two graphs, each based on a mathematical model, showing a relationship of local votes to national seats. The first is based on the total available seats–the assembly size–while the second will be based on the seat outcome, specifically the nationwide effective number of seat-winning parties. The formula derived in the book for the connection to assembly size states the following for FPTP systems (every district with magnitude, M=1, and plurality rule):

NV=1.59S1/12,

where NV is the mean district-level effective number of vote-earning parties and S is the assembly size. Please see the book for derivation and justification. It may seem utterly nuts, but yes, the mean district’s votes distribution in FPTP systems can be predicted when we know only how many districts there are (i.e., the total number of seats). In the book (Fig. 10.2 on p. 156) we show that this sparse model accurately tracks the trend in the data across a wide range of FPTP countries, particularly if they are parliamentary. Here is what that figure looks like:

Of course, individual election averages (shown by diamonds) vary around the trend (the line, representing the above equation), and individual districts (the smear of heavily “jittered” gray dots) have a wide variation within any given election. But there is indeed a pattern whereby larger assemblies tend to be associated more fragmented district voting than is the case when assembly size is smaller. At S=338, Canada has a relatively large assembly (which happens to be almost precisely the size it “should be,” per the cube root law of assembly size).

The model for NV under FPTP is premised on the notion that voters are less attuned to the likely outcome in their own district than they are to the national scene. There is thus a systematic relationship between the national electoral system and the average district’s votes distribution.

Moreover, by combining the known relationship between the national electoral system and the national party system, we can see there should be a direct connection of the district vote distribution to the national distribution of seats. The Seat Product Model (SPM) states that:

NS=(MS)1/6,

where NS is the nationwide effective number of seat-winning parties. For FPTP, this reduces to NS=S1/6, because M=1. In terms of a FPTP system, this basically just means that because there are more districts overall, there is room for more parties, because local variation in strengths is, all else equal, likelier to allow a small party to have a local plurality in one of 400 seats than in one of 100. So, more seats available in the assembly (and thus more districts), more parties winning seats. The model, shown above, connecting district-level votes (NV) to the assembly size (S) then suggests that the more such seat-winning opportunities the assembly affords for small parties, the more local voters are likely to give their vote for such parties, pushing NV up. The process probably works something like this: Voters are aware that some small parties might win one or more seats somewhere, providing these parties a voice in parliament, and hence are likelier to support small parties to some degree regardless of their local viability. It is national viability that counts. “All politics is national.” The posited connection would be more convincing if it could be made with election-specific seat outcomes rather than with the total number of available seats. We can do that! Given the SPM for the national seat distribution (summarized in NS) based on assembly size, and the model for district-level votes distribution (NV), also based on assembly size, we can connect NV to NS algebraically:

NV=1.59NS1/2.

(Note that this comes about because if NS=S1/6, then S=NS6, giving us NV=1.59(NS6)1/12, in which we multiply the exponents in the final term of the equation to get the exponent, 1/2, which is also the square root. A full discussion and test of this formula may be found in my forthcoming chapter with Cory Struthers in an volume in honor of Richard Johnston being edited by Amanda Bittner, Scott Matthews, and Stuart Soroka. Johnston’s tour de force, The Canadian Party System likewise emphasizes that voters think more in terms of national politic than their local contest.)

Here is how this graph looks:

This again shows elections with diamonds and individual districts in small gray dots. The diagonal line is the preceding equation. It most definitely fits well. Note that it even fits India if we base the nationwide party system on the alliances (shown by squares), as we should, given that they and not the many parties are the nationwide actors, whereas each alliance is represented by a given component party in each district. (The graph also shows India if we use individual parties in the calculation of NS, which is useful because it makes clear just how well India, in the era of competing alliances, follows the S model–the one in the first graph. It obviously would not fit the NS model if we did not use the alliances, but again, it is the alliances that it should track with if the model is correct in its grounding district-level vote outcomes in the national balance of seats among the national political forces–parties elsewhere, including Canada, but alliances in India.)4

By implication, this connection of district-level NV to national NS may arise because voters have some estimate of how the national parliament is going to look when they decide whether or not to support a party other than one of the two leading national parties. For instance, a voter wavering between the NDP and the Liberals might be more likely to support the NDP if she estimates that there will be no majority, thereby allowing a smaller party like the NDP to be more influential than if one of the big parties has a majority on its own.

A vote for a much smaller party, like the PPC, might be simply expressive–“sending a message” to the Conservatives that they are not sufficiently right wing or populist. For a purely expressive voter, the national seat outcome may be irrelevant. Such a voter simply wants to register a protest. There still might be a connection to expected national votes: If such a voter thinks the PPC can get 7% he might be likelier to vote for it than if it’s only 3%.3 If, however, the connection runs through thinking about the national parliament, and whether one’s party will have voice there, it should help the party win votes around the country if its potential voters perceive that it will win one or more seats–in other words, that it is viable somewhere. I hope there is some polling data that I can find some day that allows us to get at this question, as it would connect the aggregate outcome demonstrated here with individual-level voter behavior. As the Canadian 2021 campaign has developed, it would be an especially good test of the model’s underlying individual-voter premise, given the surge of a small national party that is probably not likely to have a voice in the House of Commons. (But maybe its voters believe it will! They might even turn out to be correct.)

I do not, however, currently know if any polling or voter surveys exist to get at these questions. Such a survey ideally would ask the respondent how many seats they believe the various parties will get in the election. This would allow a rough construction of voter-expected effective number of seat-winning parties even though no voter actually has to know what that concept means or how to calculate it for the premise of the model to work. Minimally, as noted, it would at least be useful to know if voters choosing a small party think that party will indeed get one or more seats.

I have so far focused on the PPC in the Canadian 2021 election, as a possible example of a wider phenomena connecting local voting to the (expected) national seat outcome. A similar logic on the left side of politics should apply for the Green Party. Does its perceived viability for seats in parliament affect the tendency of voters to vote for it outside the specific districts where it is locally viable? The very big wrinkle this time around for the Greens, however, is that the party is struggling mightily, with an ongoing conflict between its leader and much of the rest of the party. It is currently projected to win no more than two seats, and perhaps none. It might be expected to retain the former leader’s seat in British Columbia, but even that may be in jeopardy with the national party in such disarray.

It is even questionable whether the Green Party still meets the criteria of a “national” party this time around; I do not (yet) have a really precise working definition of how many districts the party must be present in to qualify as “national.” The Green Party has not fielded a candidate in about a quarter of the ridings nationwide. Grenier has reviewed the 86 Green-less constituencies and whether their absence could affect outcomes among the contesting parties. Obviously the connection between expected seat winning nationally and obtaining votes in contests around the country is broken in any district in which there is no candidate running for the party. No candidate, no possibility of the local voters augmenting the party’s aggregate vote total. In any case, the party has dropped in national polls from 5.4% on 14 August to 3.2% now.

Further emphasizing now the Greens may not be a “national” party in this election is the campaign behavior of the leader. The CBC recently noted that the leader, Annamie Paul, is not exactly campaigning like the leader of a national party:

Asked why she hasn’t campaigned in more ridings, Paul acknowledged Friday that some candidates may want her to steer clear. She has campaigned outside of her home riding of Toronto Centre twice so far — once in a neighbouring riding and then Monday, in P.E.I.

Candidates distancing themselves from the leader is not normally a good sign for a party, particularly in a parliamentary system. “All politics is national,” after all. As explained in Votes from Seats (ch. 10), the impact of national politics on local voting is likely enhanced by parties bringing resources into districts to “show the flag” even where they are not likely to win a seat. (The PPC leader is certainly doing this.) If your leader remains mostly ensconced in her own district, the party is not deploying what is normally one of its best resources–the leader making the case for her party.

Nonetheless, it still might matter for the party’s ability to get votes, even in ridings it surely will not win, whether its potential voters believe it is viable for seat-winning somewhere. The good news for the party–and there is little of that–is that the province where it currently holds two seats, BC, is one of those where its polling has declined least: 7.0% on 14 August to 6.3% now. So, politics is still at least a bit more regional for the Greens than for other “national” parties, perhaps.

In conclusion, the district-level extension of the Seat Product Model states that in FPTP systems, district-level effective number of vote-earning parties can be predicted from the national electoral system–specifically, the assembly size. By further extension (in the aforementioned chapter I am working on with Struthers for the volume honoring Johnston), it should also be tied to the nationwide effective number of seat-winning parties, and to voter perceptions in the campaign as to how parties are doing at the national level. The result would be that voters are more likely to vote for even a small party under FPTP to the extent that they expect it to have a voice in parliament, and to the extent that the parliament may not have a majority party. The Canadian 2021 election, with a surging small party (the PPC) and another one declining (the Greens) offers an excellent case study of the phenomenon that is behind these models.

___________

Notes:

1. Obviously, things are different for an explicitly regional party (one that does not present candidates outside its region) like the Bloc Quebecois, which I will leave aside for this current discussion.

2. Perhaps it has some chance of winning the leader’s riding of Beauce (in Quebec), but as Grenier notes in a post the day before the election:

There’s nothing about Bernier’s Beauce riding that makes it particularly open to a party that has been courting the anti-vaxxer, anti-vaccine mandates and anti-lockdowns crowd. It’s hard to know where in the country that crowd would be big enough to elect a PPC MP.

He does also note that one poll, by EKOS, has put the party second in Alberta, albeit with only 20% of the vote. Maybe they could get a local surge somewhere and pick up a seat there.

3. Indeed, it might seem that we could make a similar algebraic connection. The Seat Product Model expects national effective number of vote-earning parties to be NV=[(MS)1/4 +1]2/3. This is confirmed in Votes from Seats. However, this can’t easily be expressed in terms of just S (even for FPTP, where the term for M drops out) and therefore is complicated to connect to the NV formula. In any case, the theoretical argument works better from seats–that voters key on the expected outcome of the election, which is a distribution of seats in parliament and whether one or another party has a majority or not. These outcomes are summarized in the effective number of seat-winning parties.

4. This graph is a version of the one that will be shown in the previouysly mentioned Shugart & Struthers chapter.

Party Personnel Strategies is published

Just received: My copy of Party Personnel Strategies: Electoral Systems and Committee Assignments.

A preview of most of Chapter 1 is available for free at Google Books. More details, including the table of contents, can be viewed at the book’s Oxford University Press page.

The back cover has the short summary, as well as some very kind words from other scholars:

The country cases covered in the book, each with its own chapter, are Germany, Japan, Israel, Portugal, Britain, and New Zealand. The research design leverages the electoral-system changes in Japan and New Zealand.

The book develops two “models” of party personnel practices, tested on the patterns of assignment of a party’s legislators to committees, broken down into three categories: high policy, public goods, and distributive. Under the expertise model, parties are assumed to want to harness the perceived expertise of their individual members by assigning them to committees with matching policy functions. We assume all parties in parliamentary democracies would like to achieve such matches, but, depending on features of the electoral system, they may have to trade off fulfilling the expertise model in order to assign according to an electoral–constituency model. Within the expertise model, there are also a series of issue ownership premises, under which parties of the center-right are expected to match experts to high policy and parties of the center-left to public goods (even if they do not expertise-match in other categories). As expected under our theory, the more that an electoral system makes seat-maximization depend on the geographic location of votes (as with FPTP) or on candidate’s personal votes (or both, as with Japan’s former SNTV), the more the electoral–constituency model dominates over the expertise model.

Although not the book’s central theme, a key subtext is that we now probably can take the question mark off of “best of both worlds” regarding the impact of mixed-member electoral systems, at least for the proportional (MMP) variant used in Germany and post-reform New Zealand. These systems show the highest reliance on the expertise model while simultaneously also fulfilling key premises of the electoral–constituency model.

The project was a long time in development. The book arrives thirteen and a half years after the original “central team” (me, Krauss, and Pekkanen) obtained the news that our NSF grant proposal was going to be funded. It was a complex collaboration, involving scholars specializing on each of the cases, who led the data collection and answered many a question we had. The book could never have seen the light of day without their effort. Nor could have been written without the addition to the author team of Matthew Bergman (originally the project’s research assistant, and central data manager, as well as the originator of our issue-ownership premises) and Cory Struthers (who brought new ideas about distributive policy to the author team, and was my first UC Davis Ph.D. student, not counting one who originally started at UCSD before I moved). We also benefitted from numerous other research assistants and the work of several undergraduate students at Davis, who are named individually in the preface.

As foreshadowed previously at this blog, the book is dedicated to one of the most important scholars ever of comparative legislatures, Gerhard Loewenberg, of blessed memory.

Datasets used in the book will soon be made public. They are not quite ready yet (pending review of a planned journal article that will introduce them to the wider public), but I will post a notification when they are available.

Israel government update and the likelihood of a 2021b election

It has been some time since I did an update on the election and government-formation process in Israel, 2021 (or, as I called it, 2021a, giving away my expectation that a 2021b was likely). The election was on 23 March, and as all readers likely know, it was the fourth election since an early call of elections was legislated at the end of 2018.

Since the March election, the government-formation process has been playing out in its usual manner. President Reuven Rivlin received recommendations from party leaders about who should be tasked to form a government. As expected, no candidate had recommendations from parties totaling 61 or more seats, but incumbent PM Benjamin Netanyahu (Likud) had more than opposition leader Yair Lapid (Yesh Atid), so he got the first nod. As everyone pretty much understood would happen, Netanyahu failed to cobble together a government. Arguably he did not even try very hard, “negotiating” mainly through press statements trying to shame leaders of small right-wing parties to rejoin his bloc. So, again as expected, Lapid received the mandate to try. And he most certainly has been trying hard. But as I write this he has one week remaining before his time expires.* If Lapid’s mandate expires with no government to present to the Knesset, there is a period in which any Knesset member can be nominated to be the PM via 61 signatures from members of the Knesset. However, with two blocs (using the term loosely) having both failed to win 61 seats, such a path to a government is highly unlikely to work.

The attempt to strike an agreement with Yamina, whose head Naftali Bennett would have gone first as PM, with Lapid taking over after a year (based on the same Basic Law amendments that the aborted Netanyahu–Gantz rotation was to follow), seemed close to fruition as the second week of May began. It would have been a strange government, given Bennett’s party won only 7 seats to Lapid’s 17, and because it would span nearly the entire Israeli political spectrum, including one Arab party (most likely as an outside supporter to a minority government, not as a full cabinet partner). Then once Hamas decided to escalate ongoing tensions in Jerusalem (including over things such as those I was writing about a decade ago) by firing their terrorist rockets directly at the capital city on Jerusalem Day, the ensuing war led Bennett to get cold feet and abandon a plan that apparently was all but final. On the other hand, he apparently also never quite ruled out returning to the plan. For instance, he never said in front of cameras that the deal was off, and there was a letter on 20 May from major activists in Yamina calling for the party to avoid another election and back an anti-Bibi government. Just today Bennett has supposedly told Likud he will return to talking with Lapid about forming a government if Netanyahu can’t form one (which he can’t).

So the “change” government remains a possibility even now (given the cessation of hostilities after 11 days) and may remain so right up until Lapid’s mandate expires. Frankly, it was always uphill to to form this proposed government, and would be a challenge for it to last if it did form. Yet it is the only current option, aside from another election later this year. Bennett has claimed numerous times that he will do everything he can to prevent another election. He has claimed a lot of things, so no one really can claim to know what he will do. (This is sometimes a good negotiating tactic, although it seems to have failed badly for Bennett, and in any case it is a terrible trait in a governing partner.) Although it is easy to mock Bennett for his flip-flops, we should acknowledge that he is in a genuinely difficult place. He has spent the last several years carving out a niche for his party to the right of Likud on security matters, so he can’t appear too eager to form a government with left-wing parties and reliant on Arab support. Thus even if he has intended all along to back such a government–and who knows–he and his no. 2, Ayalet Shaked, would need to make a good show of “leaving no stone unturned to form a nationalist government” before signing up to a deal with Lapid and Labor, Meretz, and Ra’am.

The bottom line is that the election produced a genuine stalemate. Even if Yamina sides with Netanyahu, that is not a majority without Ra’am, the Islamist party that broke off from the Joint List and has a pragmatic leader, Mansour Abbas, who seeks to be relevant in Israeli politics (unlike the Joint List itself). Such a government would also need the Religious Zionist list, which has said repeatedly it opposes any cooperation with Ra’am. The parties we are talking about here for a potential right-wing government are Likud (30 seats), the Haredi parties–Shas (9) and UTJ (7)–Yamina (7), plus Religious Zionist (6). These reach only 59 seats, hence the need for Ra’am (4) to back it; and, yes, Ra’am is certainly a right wing party within Arab Israeli politics, particularly on matters of social/religious policy. There is also New Hope (6), the party formed by Gideon Sa’ar and other Likud defectors. Obviously, if they joined, it would obviate the need to have the backing of Ra’am. However, Sa’ar has said over and over that he will not back Netanyahu. The entire reason his party formed was to offer an option for Likud without Bibi. While one should never rule anything out, and reports occasionally circulate that he is talking with Bibi, he looks like he just might mean it when he says no.

The “change” government would be Lapid (17), Blue and White (8), Labor (7), Yisrael Beiteinu (7), Meretz (6) New Hope (6), plus 6** from Yamina. Together, that “bloc” of left and right parties would have 58 seats, hence the inability to form a government without backing of Ra’am (who remains “brave” in evidently being willing to do a deal despite the violence of recent weeks). If Yamina is really out of this group, then that leaves it on only 51 seats, ten seats short. Yes, the two Arab lists just happen to combine for 10 seats, but it is highly unlikely that the Joint List is going to be part of such a government. And it is just as unlikely that the either or both Haredi parties are going to defect from the Bibi bloc to lend Lapid a hand.

I concluded my preview of the last election by saying, ” I don’t see a government being formed from this mess… the safe call is continuing deadlock and a 2021b election being necessary.” While that almost proved too pessimistic as of early May, and maybe yet will be shown to be the wrong call, it still could end up that way.

Finally, because this is Fruits and Votes, I want to highlight just how crazy the fragmentation was in the 2021(a) election. Throughout the three elections of 2019-20 the party system had reached a period of being almost exactly as fragmented as expected for its electoral system, as emphasized in my chapter in the Oxford Handbook of Israeli Politics and Society. In my post-election blog post, I even called the 2019a election “a totally normal election” based on the effective number of seat-winning parties being just over five and the largest party having 29% of the seats. These are almost precisely what we expect from the Seat Product Model (SPM) for such a high seat product (120-seat assembly elected in a single district). The indicators stayed in that general range for the next two elections. But check out the disruption of that trend in 2021! This graph is an updated version of the plots in the Handbook chapter (also a version of this was shown in the just-linked earlier post following 2019a).

The plots, for four party-system indicators, show lines for observed values over time with the expected values from the SPM marked by the horizontal solid line in each plot. The dashed line marks the mean for the entire period, through 2021a. Vertical lines mark changes in electoral-system features other than the district magnitude and assembly size–specifically formula changes or threshold increases.

Look at those spikes in the plots of the top row! The number of seat-winning lists (not parties, per se, given that many lists actually are alliances of two or more parties) jumped to 13, and the effective number to 8.52, almost as high as in 1999 (8.69). In 1999, a key reason for the spike was the directly elected PM, which freed voters to vote sincerely rather than for their preferred PM party in Knesset elections. In 2021, it is a product of the breakup of Blue and White (which happened as soon as the “unity” government was formed), the breakaway New Hope, the split of the Labor-Meretz list that contested the 2020 election, and Ra’am splitting from the (Dis)Joint List.

In the bottom row at left we see the corresponding collapse in the size of the largest party, although not quite to the depths reached a few times previously. In the lower right, we see a new record for lowest deviation from proportionality, thanks to no parties just missing the threshold (as happened in 2019a spectacularly and to a lesser degree in the subsequent election).

If there is a 2021b, will the fragmentation again be this high? The number of seat-winning lists could very well turn downward again as some parties re-enter pre-election pacts. On the other hand, as long as the Bibi-or-no cleavage continues to cross-cut all the others, it is entirely possible that fragmentation will remain “unnaturally” high. Barring Bennett and Lapid getting back together in the next week, we will find out later this year. And if that happens, then in the meantime, Bibi would continue benefitting from the stalemate.

______

* By coincidence, Rivlin’s successor as president will be elected by the Knesset the same day Lapid’s current mandate to form a government expires.

** Yamina won 7 seats but one of the party’s MKs has said he will not support the government that was being negotiated with Lapid. Today he said his position has not changed.

Presidentialization is still a thing

With the second impeachment of Donald Trump, we can say that one piece of good news is that Samuels and Shugart (2010) are still right. In our book, Presidents, Parties, and Prime Ministers, one of our claims is that parties in presidential systems face a severe dilemma: On the one hand, they need leaders who can win a separate popular election. On the other hand, the leaders selected for that purpose may not always share the goals of the party, but the party is basically stuck with the president, given the fixed term. While impeachment and removal are usually available under constitutional provisions, it is almost an iron law that parties do not vote to impeach their own president.

On 13 January, and in the wake of the insurrection of 6 Jan., this theory was put to a severe stress test. In fact, the day before the impeachment vote, it looked like the dam had broken and there would be many defectors from the Republican Party, who would join with Democrats and vote to impeach. The biggest blow was Liz Cheney, with the no. 3 position in the GOP House leadership, announcing she would vote to impeach. That seemed like it could give cover to others who wanted to break with the president after his reprehensible actions the week before. The New York Times reported that Kevin McCarthy, the minority leader, “and other party leaders have decided not to formally lobby Republicans to vote “no”.” Moreover, according to the same report, the Republican Senate leader, Mitch McConnell believed Trump had committed impeachable offenses.

Yet, in the end, there were only ten defectors. While this is the highest number of Representatives from a president’s own party to have joined an impeachment vote in US history (all four such votes), it is only about 5% of the total number of party members in the House. Normally, we would think of 95% unity as pretty high, and thus the case of Trump’s impeachment conforms, so far, to the theory: the president’s party does not vote in favor of a process that could lead to removal of its own leader, the president.

By contrast, the book shows that for about a third of prime ministers in parliamentary systems the manner in which they leave office is due to their own party replacing them between elections. Fundamentally, prime ministers do not have fixed terms and are agents of their own parties. Presidents, on the other hand, typically cease to be agents of their parties upon being nominated and especially upon winning the presidential election. This is the key argument of the book: “Presidentialization” effectively reverses the principal–agent relationship, as party members have strong electoral and other incentives to follow the lead of the president whose term does not depend on their ongoing support.

Presidents’ parties may not always support the president’s legislative initiatives (although in most cases, they follow the big ones, even when such initiatives deviate from normal party priorities–see Chapter 8 of the book), but they do usually hold the ranks together when it comes to a co-partisan president’s continued tenure in office. Apparently, even after incitement to insurrection over refusal to accept a lost reelection bid, and even with only a week to go in the term.

In connection with the above argument, some have asked what about Richard Nixon? Had he not resigned, it would have been a bipartisan impeachment and removal. This is probably correct. We also have other cases in our dataset of presidents who resigned for one reason or another. Obviously, in these cases, we are unable to observe an impeachment vote, so they are outside our theory. We can thank Nixon and others for sparing their parties the need to violate an iron law!

More seriously, there is probably, theoretically, some floor of presidential approval below which the dynamic changes. I do not claim to know where that floor is, but Nixon probably breached it when his approval hovered near 20% at the end. Given the small N problem, this remains entirely speculative. The logic might be something about tipping points of support in the party member’s own constituencies, as opposed to a parliamentary party, which typically has a more collective leadership that looks out for swing voters who determine its ability to retain executive control in future elections. And in multiparty systems, this modelling would get even more complex. Lots of PMs lose office due to coalition collapse. Presidents rarely go out that way. There is the case of Dilma Rousseff in Brazil (2016), but it conforms to the theory: her party voted 0-10 in the Senate against conviction. Ultimately, her problem was that her party had only 10 of the 81 seats! (They had also voted 0-60 against impeachment in the Chamber of 513 total members.) There was also the case of Park Geun-hye in South Korea in 2016, where some unknown number of members of her party may have voted to impeach. The reason it is unknown is the vote is secret. If the logic of members not dumping a co-partisan president is tied to electoral incentives (fates of legislators tied to that of the president), then a secret vote would break that. In the book we also mention the case of Raúl Cubas Grau in Paraguay (1999), forced out during an impeachment vote by his own Colorado Party. In this case, the party held a super-majority, and could do it alone without fear of electoral blowback. We discuss some other cases with splits in a party. The bottom line is that there is nothing routine about impeachment, and the calculation of president’s co-partisans is usually that it is unwise to break with the leader who won your own voters’ support in the most recent election. Trump’s case would be the only one I am aware of in which the most recent presidential election was one he had lost, but we still saw a very high degree of overlap between vote for House GOP winners and votes for the president, meaning that a break is essentially saying to voters, sorry, you voted for a crook, so let us set things straight for you.

So 13 January may not have been a good day for American democracy, but it was a good day for comparative institutional political science.

In Memory of Gerhard Loewenberg

The following is the text of a memorial lecture I gave for Dr. Gerhard Loewenberg on the occasion of his first yarzheit. I delivered it remotely on behalf of Beth Israel Congregation in Ann Arbor; I explain how it came about in the lecture itself. The following text includes some paragraphs that I had to skip in the live session (viewable on YouTube) due to time constraints.

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Comparative Legislatures: Or What America and Israel can learn from Germany

The legislature is the single most important institution of a democratic political system. Yet legislatures are puzzling in terms of how they are able to function, and they tend to be disliked, even reviled, by democratic publics everywhere. Professor Gerhard Loewenberg dedicated his professional life to advancing the comparative analysis of legislatures, and in his last book, published in 2011 (other than his highly engaging memoir from 2012), he wrote about how puzzling the legislative institution is.

On the one hand, he wrote, a legislature consists of technically equal representatives. Each one, upon being seated after having won an election, has the same status as any other. Every one has just one vote on any matter that comes before the chamber for decision. A legislature is a collective body, comprised of equal individual legislators. Yet, as we know from some of the most important studies of social science, collective decision-making is difficult and prone to failure—unless some institution or leader within the legislature is endowed with authority to set the agenda, control members’ speaking time, and otherwise manage the proceedings. Of course, as soon as someone has been given power to do these tasks, by definition the legislators are no longer equal. Some of them have been awarded additional power over the others, some will not be able to speak as much as they wish, and various rules will limit the admissibility of amendments to bills that legislators may hope to advance. 

Moreover, given the complexity of decision making for a modern society, no one legislator can possibly be knowledgeable about all the issues that come before the body demanding a decision. So, legislative chambers establish committees and other means of having some legislators specialize in one set of policies while others specialize in different topics. Again, this changes them from formally equal to at least potentially having outsized influence over specific policies. For instance, members of the agriculture committee acquire more knowledge and procedural advantage than their colleagues over policy related to food supply and farm subsidies, while members of the health committee acquire more knowledge and procedural advantage over policies in that topic. And so on.

These organizational questions—agenda control and committee structure—are among the topics that have fascinated researchers in comparative legislative studies. They are also presumably the key to why voters tend to hold legislative institutions in such disdain. Crafting legislation is something of a dark art, out of the view of most voters. And when they tune in to C-Span or equivalent elsewhere, they may like what they seen even less than they’d imagined. They will often see a mostly empty chamber, or an endless series of procedural measures that make no sense to outsiders. It is all quite “mystifying” as Jerry said in his book, On Legislatures: The Puzzle of Representation

Yet without an elected legislature, you have no democracy. Actual democracies vary in whether they have two legislative chambers or one, whether they have an elected presidency or a ceremonial one (or none at all or even a monarch), and in whether courts can overturn legislation on various grounds. But no country would be called a democracy without having at least one chamber of a legislature elected by the citizens. The legislature is the one political institution that has the greatest claim on being able to represent a microcosm of citizen preferences and interests, and advancing majority rule, the central democratic principle. How much an actual legislature fulfills this central mission is quite variable, as I shall get into in more detail later. But no one can deny the absolute centrality of a legislature, and its representative function, to democracy. 

Given the importance of legislatures to democracy, then understanding these institutions is central to understanding how democracy works, and how representation and democratic policy-making can be improved. It was for the purpose of advancing such understanding that Jerry Loewenberg not only devoted his own career, but also established an entire sub-field and an important journal, Legislative Studies Quarterly, in political science devoted to the study of legislatures around the world. 

**

In my remarks this evening, I want to use the cases mentioned in my title—the USA, Israel, and Germany—as examples of what we can learn when we compare legislatures in different countries to one another. Because it is Chanukah, which celebrates an earlier recovery of Jewish national and cultural autonomy in our ancient homeland, this season is an especially appropriate time to reflect on the institutions that maintain the Jewish people’s newly recovered sovereignty in recent times. Moreover, Chanukah is all about bringing light into the darkest of times, as well as a season when Messianic yearnings have long been heightened in our tradition. It may seem strange to say so, especially to my political-scientist friends tuning in, but I see the study of democratic institutions, and especially the promotion of reforms to improve their performance on behalf of a nation, in quasi-Messianic terms. That is, democracy as a set of institutions for governance may be flawed, because they are human-devised. It may even be “the worst of all forms of government, except for all the others” than have been tried from time to time, as Churchill famously remarked. A major theme of Jewish tradition is establishing the Kingdom of Heaven—or more specifically, of offering a challenge to governments that fail to serve the broad interests of the community, including its cultural minorities, over which they claim the right to rule. Until the Kingdom of Heaven is established some day—and whether or not it is anyway meaningful to you that it might be some day—improving democracy is an essential task for our time. Democracy in Israel and the United States has been enduring some dark times of late. It is my hope that comparative legislative studies can shed some light on how democracy works, and how it can be improved. A tikkun, a repair, is in order for democracy. How can learning about different democracies help us think about making government work better? This is my rather lofty ambition for today’s remarks.

**

I will focus mainly on the comparison of the US and Israel, as the two counties’ legislative structures are about as different as any two can be. I will then ask if there might be a middle ground between the extremes represented by the American and Israeli cases. And the answer may be surprising—it is the German case. Or perhaps not so surprising, given that we are here to reflect on the contributions of Gerhard Loewenberg, who emigrated from Germany with his family before the Nazi takeover, and who returned to do research on the Bundestag in the decade-and-a-half following the establishment of the postwar Federal Republic of Germany.

But before I go into the substantive topic, I want to say a little about myself and specifically how I came to be honored with the invitation to give this memorial address.

My own field is indeed comparative legislatures, although until completing a book that will be out in the spring of 2021, most of my research has not been on the internal organization of legislatures, but rather on two aspects of how legislatures are related to the wider political system: (1) the electoral system, defined as the set of rules determining how candidates become legislators; and (2) how legislatures relate to the executive, i.e., either a prime minister or an elected president (or sometimes, as in France and Poland or the pre-war Weimar Republic of Germany, both) and the cabinet. 

My forthcoming book, entitled Party Personnel, is about committees of legislatures—the German and Israeli cases (but not the US) are among the cases included; the book also analyzes the committee systems of Portugal, Japan, Britain, and New Zealand. I am the lead author, and my coauthors and I ask how the electoral system shapes the ways in which individual legislators are assigned to one committee or another. The process of assigning legislators to specific committees is, in all these cases, managed by political party organizations within the legislature.

For instance, political parties might assign their legislators according to expertise developed in their pre-legislative careers (their occupational background). Or the assignments might be made according to their ability to draw votes from a district the party needs to win (assuming the electoral system consists of large number of districts where specific local candidates run, which is not always the case, as we’ll see). These two possible motivations for parties are often in tension! Those legislators who are best at winning additional votes beyond what some “generic” party nominee might win in a local district contest may be only loosely correlated—if at all—with those who have the policy expertise from their prior occupation (lawyer, healthcare worker, teacher, farmer, etc.). And the electoral system is one of the key things shaping which criteria loom largest in a party’s decision about committee assignments. Or so we say in Party Personnel.

Only recently did I purchase a used copy of Dr. Loewenberg’s first book, Parliament in the German System, published in 1967. I was amazed when I began reading it to see how much it foreshadows the kind of questions that motivate my forthcoming book. For instance, in Table 20 of the book we find a summary of the percentage of legislators who come from various occupational backgrounds—lawyers, teachers, business owners, etc.–and it is comparative. It shows not only the figures for the German Bundestag that had been elected in 1957, but also comparable summaries for the UK, France, and Italy. It tracks, for the Bundestag and by political party, the percentage who serve on occupationally related committees (i.e., where their parties are taking advantage of members’ policy expertise) and their tendency to speak in the Bundestag on matters in their speciality vs. as generalists. All this sort of thing is in our Party Personnel book, for more recent German election years and various elections in seven other countries—but we have it a lot easier, thanks to rather bigger computer data processing power than existed over fifty years ago! It is really amazing to me how far ahead of his time Jerry was in thinking about these issues of how different legislatures and political parties make use of expertise in the legislative process. Moreover, the table is itself such a work of art; I just love these fold-out pages. I normally see them in atlases or books with panoramic photos, but the presentation of statistics in this manner is such a sight to behold!

**

Table 20 of Gerhard Loewenberg, Parliament in the German Political System (Cornell University Press, 1967)

When my coauthors and I were finishing up the draft of our book to submit to a publisher for review, we got the news of Jerry’s passing. Because it is a book on comparative legislatures, and because the path the book seeks to advance is grounded firmly in Jerry’s contributions to the field, my coauthors and I immediately made the decision to dedicate our book to his memory.

**

But that still does not explain why I am here, speaking at a memorial hosted by Beth Israel Congregation in Ann Arbor, when I myself am in California. For that, I have Rabbi Nadav Caine to thank. And, strangely enough, the pandemic, or more precisely how the pandemic has changed Jewish community. Rabbi Caine was our rabbi back in San Diego; we have known each other for about a dozen years. One Friday night a few months ago, my wife and I played the YouTube recording of the Beth Israel Shabbat evening service, to reconnect with Rabbi Caine and his family, leading the Shabbat service from their home. And at the section where the Rabbi reads the names of those being remembered, I heard… Gerhard Loewenberg. Could it be? It must be. And so I emailed Rabbi Caine after Shabbat. And he told me about Jerry’s daughter, Deborah, being part of the Ann Arbor community. And so, here we are together, thanks to Zoom!

***

I now want to turn to the substantive application of some of the lessons of comparative legislative studies—the case-study section, so to speak. I want to start by sketching some of the key differences between the US and Israeli cases. Then I will bring in the German case a little later. I will mention a few other countries along the way. Hey, it is all about comparative legislatures, after all, so we need to compare, and try to learn from, the experiences of different countries! 

As I said at the start, there are few pairs of long-term democracies that illustrate the extreme poles of legislative and broader institutional design than do the US and Israel.

First of all, the US is, of course, a presidential system, whereas Israel is parliamentary. As the work of comparative legislative scholarship has long recognized, this basic difference in how the executive functions creates fundamental differences in the role of the legislature. Put simply, the most important role of a legislature in a parliamentary system is to produce—and maintain in office or dismiss—the executive. By definition, the prime minister and executive cabinet in a parliamentary system must have the support of a majority of legislators—or at least not the active opposition of a majority. If the majority wants a different prime minister and cabinet, it can act to replace them, or in most cases, an early election can be called.

(The Israeli case has recently taken this to yet greater extreme, having had three elections between April 2019, and March, 2020. As we speak, it seems likely there will be an election in March, 2021, or perhaps June. The term of a Knesset is nominally four years, but it’s looking like four elections in a period of about two years! While this is obviously not an ideal situation, I hope to convince you that it is not so bad. Instead of imposing a government supported by less than a majority of the voters—as the 2016 US presidential election did—it requires the politicians to have the backing of representatives of a majority of the voters and, when political conditions prevent smooth governance, to go back to the public to renew or revise their consent to govern.)

In contrast to the parliamentary model used in Israel and most of Europe, in a presidential system, by definition the head of the government is elected separately. Legislators in presidential systems have no role in choosing the head of government, and also are unable to depose the head before the end of the constitutional term, absent a process that requires more than a simple majority (as the Trump impeachment process served to demonstrate). 

So this—the executive type—is the first major difference between the American and Israeli legislatures.

A second fundamental difference is that the US Congress is, of course, bicameral. House and Senate. Not only are there these two chambers, but they are equally powerful and elected in very different manners. Israel is unicameral. Because it is unicameral and parliamentary, the only national voting choice Israeli voters make is when they are called to the polls to elect a new Knesset.

The third fundamental difference is in how the legislatures are elected—the electoral system. Here I will take the US House and the Israeli Knesset as the first point of comparison, and then bring in the US Senate afterwards. The electoral systems for the House and the Knesset are diametrically opposed in their institutional design: In the US House, every member is elected as the sole representative of his or her district. There are thus as many districts as there are members—435. (Which, by the way, is awfully small to represent a country this large, but I’ll leave that aside.)

However, in Israel there are no districts. Or more accurately, there is one district. All 120 members are elected nationwide. Whereas a US House member is the candidate who wins the most votes in a local district, the Knesset is elected according to proportional representation. Israeli voters do not vote for candidates at all. They vote for a party list. Each list is composed of candidates nominated by the party, and given a priority ranking—what political scientists call a “closed list.” (Other types of list–“open” or “flexible” allow voters to favor one or more candidates within a party’s list.)

So given the closed lists used in Israeli elections, suppose a given list has earned 10% of the votes, Then it will win approximately 12 of the 120 seats, and the winners will be the first 12 candidates on its list. There is a threshold, currently 3.25% of the votes. A list that gets less than that will have no seats. But any list that clears 3.25% will be represented. This is a system designed so as to make room for a lot of parties, and lo and behold, it does! 

In fact, based on predictive models developed in one of my earlier books, we should expect Israel’s Knesset to have about 11 lists with representation, and the largest one to have about 30% of the seats, which would be 36 seats. Thirty six happens to be just one more than the number the two most popular lists tied for in April, 2019. But in elections since then, and in many over the last two decades, the leading list has had even fewer seats—sometimes not even 30 seats (which is 25%). That’s a pretty small leading party—not even half the total number of seats needed to comprise a governing majority!

Note that I have been using “list” and “party” more or less interchangeably. Nonetheless, when talking about Israeli elections and Knesset politics, these terms are distinct. Often there are lists that are presented by alliances of two or more parties. For instance, the Joint List consists of four distinct parties representing Arab citizens of Israel, the Yamina is a list of various ultra-nationalist and Religious Zionist parties, and Blue and White contested the last several elections as an alliance of three distinct centrist parties.

The key is that the electoral system works by allocating seats proportionally to lists, and is designed so as to allow many such lists to win. The most recent election, for example, resulted in just 8 lists getting seats, somewhat lower than the typical 10-12. However, the number of parties is greater, and sometimes partners in elections break up and operate separately in the Knesset. In fact, this is what happened when Benny Gantz signed his coalition deal with Benjamin Netanyahu. Gantz’s list from the election, Blue and White, split, and his election partner, Yair Lapid, became the leader of an opposition party while Gantz became part of the government. 

**

One of the most important things to understand of all this is that, (1) under the Israeli electoral system, a vote cast anywhere in the country has the same weight as a vote cast anywhere else, and (2), whatever percentage of votes a list gets, that is its (approximate) percentage of seats in the next Knesset. 

In the US, by stark contrast, most districts are “safe” for one party or the other. Thus only those voters who happen to live in districts that are closely contested really participate in determining whether control of the House will shift from one party to the other. In the US Senate, of course, there is even more variation across the country in the de-facto value of a vote. California gets the same number of Senators as Wyoming, despite about a 70:1 difference in the states’ populations. And only a few states might determine whether control of this chamber of the national legislature might shift in an election—such as the flips of the seats in Arizona and Colorado this past November, and we’ll all be watching what voters in Georgia do in early January. 

So let’s pull it all together. In the US, voters elect a president and two chambers of congress separately. It is thus often the case that one of these three is held by a different party than at least one of the others, as has been the case since the 2018 election and was also the case for all but the first two years of Obama’s presidency. In the US, votes are aggregated only in local House districts or for the Senate in states of greatly varying population, rather than nationally. There are only two parties of any consequence, so one will have a majority in one or both chambers, and one will have the presidency, but again, no necessary partisan alignment across these institutions. And elections occur at fixed intervals, so if they can’t work together, we get gridlock instead of the Israeli recourse to an early election.

In Israel, there is only one national elected institution—the legislature. There are many parties, and the contest for votes and seats is fully nationwide. The prime minister and cabinet are products of bargaining among parties after an election to determine who can form a coalition capable of holding majority support in the Knesset. The cabinet might fall early, before the next scheduled election, if one or more parties decide not to continue working with their partners. And there can be an early election.

In the Israeli system, there is no local representation, except that a party might choose to place a former mayor or someone else with a local connection somewhere on their list (something they do rather rarely). Unlike in the US, Members of the Knesset have no local base in the sense of a place where voters have chosen them as an individual representative. 

***

For all the reasons just sketched, these two systems are as extreme as they can be in terms of what legislators represent and how they relate to the executive. The question thus might arise of whether it is possible to split the difference between these extremes. I will focus on just one dimension here—how the legislators are elected.

As I pointed out earlier, in the US, every legislator is elected in a unique district. That means, his or her election depends only on voters in one geographic subset of the country—435 different ones in the case of the House. (And each state in the case of the Senate.) By contrast, in Israel, they are elected in one national district, and on closed party or alliance lists.

Each of these has some basic advantages and some disadvantages. On the one hand, the US system makes life difficult for minor parties. Now, here I need to take a little excursus and interject something that even many of my political science colleagues get wrong! We have something called “Duverger’s law”, although calling it a “law” is a sure way to trigger me!!! 

I will try to spare you my long screed against it, but here is the short version. The famous French sociologist, Maurice Duverger, pointed out in the early 1950s that it is hard for parties other than two major ones to win seats when each member is elected by plurality (winner take all) in single-seat districts. This he called the “mechanical effect” because it concerns how the electoral system works to assign seats. And if it is hard for them to win seats, they don’t get many votes—voters don’t want to “waste” their votes on parties that can’t win. This is the so called psychological effect, also known as strategic voting or “lesser of two evils” voting.

The logic is sensible, but it is overstated. It certainly is not a law in the scientific sense (Duverger himself never claimed it was—he just said it was close to being a “true sociological law”). And it certainly is not a law in the sense of a binding constraint on voters or political elites. Nor should we expect it to be. In work that I have done with Rein Taagepera, we show that when there are a lot of districts—even ones electing just a single member, as in the US—there is a theoretical reason to expect parties beyond the top two to win some of those seats and to get significant vote percentages, even to the point of receiving votes in districts where they finish in a distant third place and thus are unable to win locally. And, empirically, this is true in other countries using the single-seat winner-take-all rules—Canada is multiparty, for instance. In the last Canadian election, the Liberal Party won only 33% of the votes and it was overrepresented, due to the non-proportional electoral system. But because it has 46% of the seats, short of a majority, it must take account of the views of other parties in order to govern.

The UK also has multiparty politics, albeit a lesser degree than in Canada. In 2010, a two-party coalition government formed, and after 2017, Theresa May’s government was in a minority in the House of Commons, because of the success of some smaller parties in winning seats.

So the US is a real outlier in having a rigid two-party system even given its electoral system, and even given Duverger’s so-called law. We should have more space in our congressional elections for Greens and Libertarians, and others, even without changing how members are elected. Nonetheless, it is true that it is much harder to get multiparty politics and minority representation using our electoral system than it would be if we used proportional representation.

Additionally, local representation really matters in US elections. It probably matters less than it used to, because voters are much more likely to vote straight party tickets nowadays than they were back in the 1970s and 1980s. (In those days, many districts had Democratic House members but the voters therein had favored Nixon or Reagan for president). Even with stronger party-line voting, we still see House members advertising what they have done on behalf of local communities and Senators emphasizing issues of concern to their states. They are local representatives even as they are also partisan actors. And this is a good thing! Local concerns that cross ideological and party lines need attention from policymakers as much as national policy challenges do.

So the US system makes it hard for minor parties to prosper, which is in many respects disadvantageous, particularly as the parties have become more distinct ideologically (“polarization”) in recent decades. But the US system offers local representation, which is in many respects advantageous.

In the Israeli case, there is certainly no problem with small parties getting seats! In fact, almost anyone—even a strong advocate for proportional representation and coalition governance like myself—would say in Israel the fragmentation of the choices into many small parties goes too far. It makes the formation of governments with a clear agenda for national policy challenges exceedingly difficult, and recently has resulted in three elections within eleven months because of the difficult interparty bargaining.

Yet a very big advantage of the Israeli system is that votes cast anywhere in the country contribute to the seat totals for their preferred parties (as long as they get at least 3.25% of the overall vote). So voters are equal, and the weight of my vote does not depend on the preferences of people who happen to live near me, as is the case in so much of the US where we might live in a safe state or district for one party and thus be essentially ignored at election time (even in presidential elections, given the electoral college). 

And a very big disadvantage of the Israeli system is the absence of local representation. Now, of course, Israel is a much smaller country than the US. But there are still are significant differences across the territory in terms of local infrastructural or other needs, and these do not get represented well in the legislative process for a very basic reason: no legislator in Israel is in any way accountable to local voters. The closed-list system means that they win solely based on their rank on the list, and how well their party performs in the nationwide vote.

So, I asked earlier whether it might be possible to combine the advantages of these two systems without taking in the disadvantages. Yes! Enter the German system.

In Germany, the members of the Bundestag are elected in what electoral-system terminology refers to as “two tiers”. There is one tier that consists of single-seat districts, thus resembling the American system (or those of Canada and Britain) in which a legislator is elected upon winning a plurality of votes in a geographically defined district. This election method comprises about half the seats in the Bundestag. 

The rest are elected in another tier from party lists, thus resembling the Israeli system. Each voters has two votes—one for a local representative (winner take all in their district) and one for a party list. The party list vote is more important for the overall composition of the legislature, but the separate district vote ensures candidates pay attention to a local area, have an incentive to become visible to voters and—crucially–that even a party that loses the local contest will tend to nurture support at the district level.

The way the two tiers are inter-related in the electoral law ensures that the overall balance of parties in the Bundestag is almost perfectly proportional to their nationwide vote shares—just as in Israel. There is a 5% threshold (thus somewhat higher than Israel’s). Under this arrangement, a party’s total number of seats is a mix of however many seats it won in the district tier, plus a number from its list needed to reach its proportional share of the total. Small parties often have only list seats, as they may not have any local wins. (I am glossing over some details here, but this is the general picture.)

The German system, often called mixed-member proportional (MMP), thus ensures that a vote cast anywhere in the territory is just as valuable as one cast anywhere else, in terms of contributing to the overall balance of partisan forces in the national legislature. In this sense, it is like Israel’s system and very unlike the US system. 

At the same time, it also ensures local representation, like the US system but very unlike Israel’s. 

(As an aside, I want to add that about 25 years ago New Zealand changed from single-seat plurality elections to MMP, modeled on Germany’s system. It has been a smashing success for their democracy. So electoral system reform is both possible, and beneficial. An example we could follow.)

Taking the two features together, Germany has coalition governments (as does New Zealand now), but not involving as many small and otherwise incompatible parties as we see in Israel’s coalitions. Germany also has local accountability that really matters. My own research and that of others confirms that members spend time in their districts, and often come from local roots including prior electoral offices or other ties to their communities. And, as we show in the Party Personnel book, committee assignments in the Bundestag are allocated according to a logic by which parties take advantage of expertise (occupational background), but crucially also to take advantage of local variations in party support and policy demands. (We also see this balance of representation criteria having emerged in NZ since they changed to a German-inspired MMP system.)

It has obviously worked quite well, in that Germany in the postwar period developed one of the most robust democracies and probably the strongest legislature in Europe. In fact, the development of that legislature was one of the recurring themes in Jerry’s career, from his very first book (in 1967, as I mentioned earlier) right up to his last publication, which was a remarkable essay published in a German journal (but in English) in 2018, reflecting on the choices made by both the Allied powers and the new German political class that laid the groundwork for the Bundestag’s development.

(Before I close out the section on Germany, I want to note that Germany is a federation of states, like the US, and it has a bicameral parliament. The other chamber, the Bundesrat, is a great model that Americans could learn from! Its members are chosen by state governments, and it has a veto on on legislation that directly affects the states, instead of on all national policy like the US Senate. It therefore deftly balances the state-interest and national-interest tensions inherent in federalism.)

****

Legislatures, as Gerhard Loewenberg showed us, are puzzling institutions. In democracies, they consist of formally equal individual representatives who somehow must organize themselves to make collective decisions on behalf of the citizens they represent. They are essential to democratic governance, yet the very procedures that they devise in order to function make them mysterious to the average voter, who is quite likely to associate the body with the worst features of politics.

We can learn a lot from comparing legislatures in different countries, as Gerhard Loewenberg’s long and distinguished career taught us. Both the US and Israel, as well as other countries, can learn from the German experience of how to balance seemingly contradictory goals of legislative and electoral institutional design. While there will never be a perfectly functioning democratic legislature for the simple reason that societies and the people who comprise them are complex, a process of scholarly and public enquiry into how different systems work can bring us towards a better understanding of how to make democracy work better, both in our own country and elsewhere.

Chag sameach; Chodesh tov. Happy Hanukkah, and a good new month. And may Dr. Gerhard Loewenberg’s memory be a blessing and an inspiration. 

“Effective Seat Product” for two-tier PR (including MMP) and MMM

The seat product for a simple electoral system is its assembly size (S) times its mean district magnitude (M) (Taagepera 2007). From this product, MS, the various formulas of the Seat Product Model (SPM) allow us to estimate the effective number of parties, size of the largest, disproportionality, and other election indicators. For each output tested in Shugart and Taagepera (2017), Votes from Seats, we find that the SPM explains about 60% of the variance. This means that these two institutional inputs (M and S) alone account for three fifths of the cross-national differences in party system indicators, while leaving plenty for country-specific or election-specific factors to explain as well (i.e., the other 40% of the variance).

The SPM, based on the simple seat product, is fine if you have a single-tier electoral system. (In the book, we show it works reasonably well, at least on seat outputs, in “complex” but still single-tier systems like AV in Australia, majority-plurality in France, and STV in Ireland.) But what about systems with complex districting, such as two-tier PR? For these systems, Shugart and Taagepera (2017) propose an “extended seat product model”. This takes into account the basic-tier size and average district magnitude as well as the percentage of the entire assembly that is allocated in an upper tier, assumed to be compensatory. For estimating the expected effective number of seat-winning parties (NS), the extended SPM formula (Shugart and Taagepera, 2017: 263) is:

NS=2.5t(MB)1/6,

where MB is the basic-tier seat product, defined as the number of seats allocated in the basic tier (i.e., assembly size, minus seats in the upper tier), and t is the tier ratio, i.e., the share of all assembly seats allocated in the upper tier. If the electoral system is simple (single tier), the equation reduces to the “regular” seat product model, in which MS=MB and t=0.

(Added note: in the book we use MSB to refer to what I am calling here MB. No good reason for the change, other than blogger laziness.)

We show in the book that the extended seat product is reasonably accurate for two-tier PR, including mixed-member proportional (MMP). We also show that the logic on which it is based checks out, in that the basic tier NS (i.e., before taking account of the upper tier) is well explained by (MB)1/6, while the multiplier term, 2.5t, captures on average how much the compensation mechanism increases NS. Perhaps most importantly of all, the extended seat product model’s prediction is closer to actually observed nationwide NS, on average, than would be an estimate of NS derived from the simple seat product. In other words, for a two-tier system, do not just take the basic-tier mean M and multiply by S and expect it to work!

While the extended seat product works quite well for two-tier PR (including MMP), it is not convenient if one wants to scale such systems along with simple systems. For instance, as I did in my recent planting on polling errors. For this we need an “effective seat product” that exists on the same scale as the simple seat product, but is consistent with the effect of the two-tier system on the effective number of parties (or other outputs).

We did not attempt to develop such an effective seat product in Shugart and Taagepera (2017), but it is pretty straightforward how to do it. And if we can do this, we can also derive an “effective magnitude” of such systems. In this way, we can have a ready indicator of what simple (hypothetical) design comes closest to expressing the impact of the (actual) complex design on the party system.

The derivation of effective seat product is pretty simple, actually. Just take, for the system parameters, the predicted effective number of seat-winning parties, NS, and raise it to the power, 6. That is, if NS=(MS)1/6, it must be that MS=NS6. (Taagepera 2007 proposes something similar, but based on actual output, rather than expected, as there was not to be a form of the seat product model for two-tier systems for almost another decade, till an initial proposal by Li and Shugart (2016).)

Once we do this, we can arrive at effective seat products for all these systems. Examples of resulting values are approximately 5,000 for Germany (MMP) in 2009 and 6,600 for Denmark (two-tier PR) in 2007. How do these compare to simple systems? There are actual few simple systems with these seat products in this range. This might be a feature of two-tier PR (of which MMP could be considered a subtype), as it allows a system to have a low or moderate basic-tier district magnitude combined with a high degree of overall proportionality (and small-party permissiveness). The only simple, single-tier, systems with similar seat products are Poland (5,161), with the next highest being Brazil (9,747) and Netherlands before 1956 (10,000). The implication here is that Germany and Denmark have systems roughly equivalent in their impact on the party system–i.e., on the 60% of variance mentioned above, not the country-specific 40%–as the simple districted PR system of Poland (S=460, M=11) but not as permissive as Brazil (S=513, M=19) or pre-1956 Netherlands (M=S=100). Note that each of these systems has a much higher magnitude than the basic-tier M of Germany (1) or larger assembly than Denmark (S=179; M=13.5). Yet their impact on the nationwide party system should be fairly similar.

Now, suppose you are more interested in “effective district magnitude” than in the seat product. I mean, you should be interested in the seat product, because it tells you more about a system’s impact on the party system than does magnitude alone! But there may be value in knowing the input parameters separately. You can find S easily enough, even for a complex system. But what about (effective) M? This is easy, too! Just take the effective seat product and divide it by the assembly size.

Thus we have an effective M for Germany in 2009 of 7.9 and for Denmark in 2007 of 36.9. These values give us an idea of how, for their given assembly sizes, their compensatory PR systems make district magnitude “effectively”–i.e., in terms of impact on the inter-party dimension–much larger than the basic-tier districts actually are. If we think low M is desirable for generating local representation–a key aspect of the intra-party dimension–we might conclude that Germany gets the advantages M=1 in local representation while also getting the advantages of the proportionality of 8-seat districts. (Best of both worlds?) By comparison, simple districted PR systems with average M around 8 seats include Switzerland and Costa Rica. (The Swiss system is complex in various ways, but not in its districting.) Eight is also the minimum magnitude in Brazil. Denmark gets whatever local representation advantages might come from an actual mean M of 13.5, yet the proportionality, for its assembly size, as if those districts elected, on average, 37 members. Actual districts of about this magnitude occur only in a relatively few districts within simple systems. For instance, the district for Madrid in Spain has M in the mid-30s, but that system’s overall average is only 6.7 (i.e., somewhat smaller than Germany’s effective M).

Now, what about mixed-member majoritarian (MMM) systems. Unlike MMP, these are not designed with a compensatory upper tier. In Votes from Seats, Taagepera and I basically conclude that we are unable to generalize about them. Each MMM system is sui generis. Maybe we gave up too soon! I will describe a procedure for estimating an effective seat product and effective magnitude for MMM systems, in which the basic tier normally has M=1, and there is a list-PR component that is allocated in “parallel” rather than to compensate for deviations from proportionality arising out of the basic tier.

The most straightforward means of estimating the effective seat product is to treat the system as a halfway house between MMP and FPTP. That is, they have some commonality with MMP, in having both M=1 and a list-PR component (not actually a “tier” as Gallagher and Mitchell (2005) explain). But they also have commonality with FPTP, where all seats are M=1 plurality, in that they reward a party that is able to win many of the basic seats in a way that MMP does not. If we take the geometric average of the effective seat product derived as if it were MMP and the effective seat product as if it were FPTP, we might have a reasonable estimate for MMM.

In doing this, I played with both an “effective FPTP seat product” from the basic tier alone and an effective FPTP seat product based on assuming the actual assembly size. The latter works better (in the sense of “predicting,” on average for a set of MMM systems, what their actual NS is), and I think it makes more logical sense. After all, the system should be more permissive than if were a FPTP system in which all those list-PR component seats did not exist. So we are taking the geometric average of (1) a hypothetical system in which the entire assembly is divided into a number of single-seat electoral districts (Eeff) that is Eeff = EB+tS, where EB is the actual number of single-seat districts in the basic tier and S and t are as defined before, and (2) a hypothetical system that is MMP instead of MMM but otherwise identical.

When we do this, we get the following based on a couple sample MMM systems. In Japan, the effective seat product becomes approximately 1,070, roughly equivalent to moderate-M simple districted PR systems in the Dominican Republic or pre-1965 Norway. For South Korea, we would have an effective seat product of 458, or very roughly the same as the US House, and also close to the districted PR system of Costa Rica.

Here is how those are derived, using the example of Japan. We have S=480, with 300 single-seat districts and 180 list-PR seats. Thus t=0.375. If it were two-tier PR (specifically, MMP), the extended seat product would expect NS=3.65, from which we would derive an effective seat product, (MS)eff=3.666 =2,400. But it is MMM. So let’s calculate an effective FPTP seat product. Eeff = EB+tS=300+180=480 (from which we would expect NS=2.80). We just take the geometric mean of these two seat-product estimates: (2400*480)1/2=1,070. This leads to an expected NS=3.19, letting us see just how much the non-compensatory feature reduces expected party-system fragmentation relative to MMP as well as how much more permissive it is than if it were FPTP.

How does this work out in practice? Well, for Japan it is accurate for the 2000 election (NS=3.17), but several other elections have had NS much lower. That is perhaps due to election-specific factors (producing huge swings in 2005 and 2009, for example). As I alluded to above already, over the wider set of MMM systems, this method is pretty good on average. For 40 elections in 17 countries, a ratio of actual NS to that predicted from this method is 1.0075 (median 0.925). The worst-predicted is Italy (1994-2001), but that is mainly because the blocs that formed to cope with MMM contained many parties (plus Italy’s system had a partial-compensation feature). If I drop Italy, I get a mean of 1.0024 (but a median of only 0.894) on 37 elections.

If we want an effective magnitude for MMM, we can again use the simple formula, Meff=(MS)eff/S. For Japan, this would give us Meff=2.25; for Korea Meff=1.5. Intuitively, these make sense. In terms of districting, these systems are more similar to FPTP than they are to MMP, or even to districted PR. That is, they put a strong premium on the plurality party, while also giving the runner-up party a considerable incentive to attend to district interests in the hopes of swinging the actual district seat their way next time (because the system puts a high premium on M=1 wins, unlike MMP). This is, by the way, a theme of the forthcoming Party Personnel book of which I am a coauthor.

(A quirk here is that Thailand’s system of 2001 and 2005 gets an effective magnitude of 0.92! This is strange, given that magnitude–the real kind–obviously has a lower limit of 1.0, but it is perhaps tolerable inasmuch as it signals that Thailand’s MMM was really strongly majoritarian, given only 100 list seats out of 500, which means most list seats would also be won by any party that performed very well in the M=1 seats, which is indeed very much what happened in 2005. The concept of an “effective” magnitude less than 1.0 implies a degree of majoritarianism that one might get from multi-seat plurality of the MNTV or list-plurality kind.)

In this planting, I have shown that it is possible to develop an “effective seat product” for two-tier PR systems that allows such systems to be scaled along with simple, single-tier systems. The exercise allows us to say what sort of simple system an actual two-tier system most resembles in its institutional impact on inter-party variables, like the effective number of seat-winning parties, size of the largest party, and disproportionality (using formulas of the Seat Product Model). From the effective seat product, we can also determine an “effective magnitude” by simply dividing the calculated effective seat product by actual assembly size. This derivation lets us understand how the upper tier makes the individual district effectively more proportional while retaining an actual (basic-tier) magnitude that facilitates a more localized representation. Further, I have shown that MMM systems can be treated as intermediary between a hypothetical MMP (with the same basic-tier and upper-tier structure) and a hypothetical FPTP in which the entire assembly consists of single-seat districts. Again, this procedure can be extended to derive an effective magnitude. For actual MMP systems in Germany and also New Zealand, we end up with an effective magnitude in the 6–8 range. For actual MMM systems, we typically get an effective magnitude in the 1.5–3 range.

I will post files that have these summary statistics for a wide range of systems in case they may be of use to researchers or other interested readers. These are separate files for MMM, MMP, and two-tier PR (i.e, those that also use PR in their basic tiers), along with a codebook. (Links go to Dropbox (account not required); the first three files are .CSV and the codebook is .RTF.)

Added note: In the spreadsheets, the values of basic-tier seat product (MB) and tier ratio (t) are not election-specific, but are system averages. We used a definition of “system” that is based on how Lijphart (1994) defines criteria for a “change” in system. This is important only because it means the values may not exactly match what you would calculate from the raw values at a given election, if there have been small tweaks to magnitude or other variables during an otherwise steady-state “system”. These should make for only very minor differences and only for some countries.

Does the electoral system affect polling errors, and what about presidentialism?

I will attempt to answer the questions in the title through an examination of the dataset that accompanies Jennings and Wlezien (2018), Election polling errors across time and space. The main purpose of the article is to investigate the question as to whether polls have become less reliable over time. One of their key findings can be summarized from the following brief excerpt:

We find that, contrary to much conventional wisdom, the recent performance of polls has not been outside the ordinary; if anything, polling errors are getting smaller on average, not bigger.

A secondary task of Jennings and Wlezien is to ask whether the institutional context matters for polling accuracy. This sort of question is just what this virtual orchard exists for, and I was not satisfied with the treatment of electoral systems in the article. Fortunately, their dataset is available and is in Stata format, so I went about both replicating what they did (which I was able to do without any issues) and then merging in other data I have and making various new codings and analyses.

My hunch was that, if we operationalize the electoral system as more than “proportional or not”, we would find that more “permissive” electoral systems–those that favor higher party-system fragmentation and proportionality–would tend to have larger polling errors. I reasoned that when there are more parties in the system (as is usually the case under more permissive systems), voters have more choices that might be broadly acceptable to them, and hence late shifts from party to party might be more likely to be missed by the polls. This is contrary to what the authors expect and find, which is that mean absolute error tends to be lower in proportional representation (PR) systems than under “SMD” (single-member districts, which as I always feel I must add, is not an electoral system type, but simply a district magnitude). See their Table 2, which shows a mean absolute error in the last week before electoral day of 1.62 under PR and 2.28 under “SMD”.

The authors also expect and show that presidential elections have systematically higher error than legislative elections (2.70 vs. 1.83, according to the same table). They also have a nifty Figure 1 that shows that presidential election polling is both more volatile over the timeline of a given election campaign in its mean absolute error and exhibits higher error than legislative election polling at almost any point from 200 days before the election to the last pre-election polls. Importantly, even presidential election polls become more accurate near the end, but they still retain higher error than legislative elections even immediately before the election.

This finding on presidential elections is consistent with my own theoretical priors. Because presidential contests are between individuals who have a “personal vote” and who are not necessarily reliable agents of the party organization, but are selected because their parties think they can win a nationwide contest (Samuels and Shugart, 2010), the contest for president should be harder to poll than for legislative elections, all else equal. That is, winning presidential candidates attract floating voters–that is pretty much the entire goal of finding the right presidential candidate–and these might be more likely to be missed, even late in the campaign.

To test my own hunches on the impact of institutions on polling errors, I ran a regression (OLS) similar to what is reported in the authors’ Table 3: “Regressions of absolute vote-poll error using polls from the week before Election Day.” This regression shows, among other results, a strong significant effect of presidential elections (i.e., more polling error), and a negative and significant effect of PR. It also shows that the strongest effect among included variables is party size: those parties that get more than 20% of the vote tend to have larger absolute polling errors, all else equal. (I include this variable as a control in my regression as well.)

The main item of dissatisfaction for me was the dichotomy, PR vs. SMD. (Even if we call it PR vs. plurality/majority, I’d still be dissatisfied). My general rule is do not dichotomize electoral systems! Systems are more or less permissive, and are best characterized by their seat product, which is defined as mean district magnitude times assembly size. Thus I wanted to explore what the result would be if I used the seat product to define the electoral system.

I also had a further hunch, which was that presidential elections would be especially challenging to poll in institutional settings in which the electoral system for the assembly is highly permissive. In these cases, either small parties enter the presidential contest to “show the flag” even though they may have little chance to win–and hence voters may be more likely to defect at the end–or they form pre-election joint candidacies with other parties. In the latter case, some voters may hedge about whether they will vote for a candidate of an allied party when their preferred party has no candidate. Either situation should tend to make polling more difficult, inflating error even late in the campaign. To test this requires interacting the seat product with the binary variable for election type (presidential or legislative). My regression has 642 observations; theirs has 763. The difference is due to a few complex systems having unclear seat product plus a dropping of some elections that I explain below. Their findings hold on my smaller sample with almost the precise same coefficients, and so I do not think the different sample sizes matter for the conclusions.

When I do this, and graph the result (using Stata ‘margins’ command), I get the following.

I am both right and wrong! On the electoral system effect, the seat product does not matter at all for error in legislative elections. That is, we do not see either the finding Jennings and Wlezien report of lower error under PR (compared to “SMD”), nor my expectation that error would increase as the seat product increases–EXCEPT: It seems I was right in my expectation that error in presidential contests increases with the seat product of the (legislative) electoral system.

The graph shows the estimated output and 95% confidence intervals for presidential elections (black lines and data points) and for legislative (gray). We see that the error is higher, on average, for presidential systems for all seat products greater than a logged value of about 2.75, and increasingly so as the seat product rises. Note that a logged value of 2.75 is an unlogged seat product of 562. Countries in this range include France, India, the Dominican Republic, and Peru. (Note that some of these are “PR” and some “SMD”; that is the point, in that district magnitude and formula are not the only features that determine how permissive an entire national electoral system is–see Shugart and Taagepera, 2017.)

I have checked the result in various ways, both with alternative codings of the electoral system variable, and with sub-sets, as well as by selectively dropping specific countries that comprise many data points. For instance, I thought maybe Brazil (seat product of 9,669, or a logged value just short of 4) was driving the effect, or maybe the USA (435; logged =2.64) was. No. It is robust to these and other exclusions.

For alternatives on the coding of electoral system, the effect is similar if I revert to the dichotomy, and it also works if I just use the log of mean district magnitude (thereby ignoring assembly size).

For executive format types, running the regression on sub-samples also is robust. If I run only the presidential elections in pure presidential systems (73 obs.), I still get a strong positive and significant effect of the seat product on polling error. If I run only on pure parliamentary systems (410 obs.), I get no impact of the seat product. If I restrict the sample only to semi-presidential systems (159 obs.), the interactive effect holds (and all coefficients stay roughly the same) just as when all systems are included. So it seems there is a real effect here of the seat product–standing in for electoral system permissiveness–on the accuracy of polling near the end of presidential election campaigns.

I want to briefly describe a few other data choices I made. First of all, legislative elections in pure presidential systems are dropped. The Jennings and Wlezien regression sample actually has no such elections other than US midterm elections, and I do not think we can generalize from that experience to legislative vs. presidential elections in other presidential systems. (Most are concurrent anyway, as is every presidential election in the US and thus the other half of the total number of congressional elections.)

However, I did check within systems where we have both presidential and legislative polls available. All countries in the Jennings-Wlezien regression sample that are represented by both types of election are semi-presidential, aside from the US. In the US, Poland, and Portugal, the pattern holds: mean error is greater in presidential elections than in assembly elections in the same country. But the difference is significant only in Portugal. In Croatia the effect goes the other way, but to a trivial degree and there are only three legislative elections included. (If I pool all these countries, the difference across election types is statistically significant, but the magnitude of the difference is small: 2.22 for legislative and 2.78 for presidential.)

The astute reader will have noticed that the x-axis of the graph is labelled, effective seat product. This is because I need a way to include two-tier systems and the seat product’s strict definition (average magnitude X assembly size) only works for single-tier systems. There is a way to estimate the seat product equivalent for a two-tier system as if it were simple. I promise to explain that some time soon, but here is not the place for it. (UPDATE: Now planted.)

I also checked one other thing that I wanted to report before concluding. I wondered if there would be a different effect if a given election had an effective number of parties (seat-winning) greater than expected from its seat product. The intuition is that polling would be tend to off more if the party (or presidential) contest were more fragmented than expected for the given electoral system. The answer is that it does not alter the basic pattern, whereby it makes no difference to legislative elections (in parliamentary or semi-presidential systems). For presidential elections, there is a tendency for significantly higher error the more the fragmentation of the legislative election is greater than expected for the seat product. The graph below shows a plot of this election; as you can probably tell from the data plot, the fit of this regression is poorer than the one reported earlier. Still, there may be something here that is worth investigating further.

MMP in NZ: An example of “best of both worlds” in action

In Shugart and Wattenberg (2001) we ask if mixed-member systems offer a “best of both worlds.” That is, do they allow simultaneously for the benefits of local representation and individual-member accountability that are the (supposed) advantages of single-seat plurality (FPTP) and the representation of smaller national parties that might struggle to win districts but would be represented under proportional representation (PR).

There was a question mark in the book’s subtitle. Over time, I have come to believe that indeed the proportional type (MMP) does have a strong tendency to offer the best of both worlds. The reason is that members elected in districts have incentives to behave as local representatives at the time that there is close approximation between party vote and seat shares (assuming compensation is carried out nationwide or in large regions). The majoritarian type (MMM, as in Japan and Taiwan) probably does not; it is much closer in its overall incentive structure to FPTP, even though it does indeed permit smaller national parties to win seats.

For MMP, the “best of both worlds” argument assumes that parties nominate dually–meaning many elected members will have run in a district and had a (realistically electable) list position simultaneously. If they do, then even the list-elected members will have a local base, and should have incentives to act as the local “face” of the party, including possibly by offering constituent services. Both prior anecdotes I have shared from New Zealand (e.g., “shadow MPs” who win from the list and maintain a local office) and my forthcoming coauthored book, Party Personnel, offer further evidence that MMP does indeed work in this way.

Now comes a terrific anecdote from New Zealand’s 2020 election. In this election, Labour won a majority of seats (64/120) with 49.1% of the nationwide party list vote. In the nominal tier of single-seat districts (electorates) it won 43 of the 72 available seats. Its win included some districts that are normally strongholds of the center-right National Party (which won 35 seats overall and just 26 districts).

Commenting on some of the Labour wins in mostly rural districts, Federated Farmers president Andrew Hoggard said:

in some “flipped” electorates Labour list MPs had worked hard to raise their profile and get involved with the community and this had paid off when they campaigned for the electorate.

This is an ideal description of how the “best of both worlds” argument works: list-elected members have incentives to attend to local needs of the district in which they ran for the nominal seat (but “lost”) in hopes of capturing the local plurality in the next election.

Of course, there were other factors at work as well. I will offer another planting about one of those factors separately. There is also some uncertainty at this stage just exactly the degree to which rural voters flipped, as the wins may have come in significant part from very large swings in the town areas within districts that also include large rural areas. Regardless, MMP offers the key advantage of giving most elected members, if dually nominated, a tie to a local constituency while ensuring close approximation of overall seat totals to party-list votes.

Academics and journalists

This is such an interesting comment about academics and journalists by Andrew Gelman, in response to question as to whether he and Nate Silver might do a joint podcast or other discussion about election forecasting (Gelman says he’s asked and Silver has not responded):
____
The more general question, maybe, is how journalists and academics can interact. A traditional model is that the academic does the research and the journalist writes about it. Or the academic does the work and the journalists writes about it with a critical eye, Felix Salmon style. A different model is that the journalist and the researcher are the same person: that’s what Nate [Silver] is doing. Maybe a better way to put this is that the “journalist” and “academic” roles have been erased and replaced by the analyst, who does both. Bill James was a pioneer in this. Finally, there’s the model in which the academics and journalists collaborate, which is what Merlin and I are doing with Elliott [Morris]. At this point, you might ask, why do Merlin and I need Elliott at all: why would a forecast by two political scientists be improved by a journalist? The immediate answer is that the Economist forecast is Elliott’s baby: he came to us to ask for help. The longer answer is that 3 people are better than 2, and the distinction between academic and journalist is not always so clear. I do a lot of writing, Elliott does a lot of programming, and we both have thought a lot about politics. I’ve found that collaboration almost always makes things better, as long as the collaborators can get along.
Anyway, Nate seems pretty set in his go-it-alone, don’t involve academic researchers approach, and I really like to collaborate, so maybe that’s one reason we’re having difficulty communicating.
Also, unrelatedly, Nate is a public figure and so he suffers from what I’ve called the David Brooks or Paul Krugman problem: he gets so much low-quality criticism from randos on the internet, that he’s developed a way of pattern of ignoring or firing back at criticism, rather than engaging with it directly. It can be hard to have a conversation, public or private, with someone who’s gotten into the habit of considering outside criticism as a nuisance rather than a source of valuable input.

Dividing the Rulers: How Majority Cycling Saves Democracy

The following is a guest planting by Dr. Yuhui Li. I suggested Dr. Li draft something for this blog about his recently published book. (Note: I was the Ph.D. committee chair for Huey at UC Davis.)

You can buy the book by clicking here, and taking advantage of a discount! You can get 30% off by entering the code, UMCYCLING (for a limited time).


I’m grateful that Matthew offers to post this introduction of my book Dividing the Rulers: How Majority Cycling Saves Democracy. I hope it may interest some fellow political scientists.

The initial thought about the project originated from a debate I had years ago on Chinese social media regarding the choice of political systems. It appeared to me that many people were skeptical about the idea of democracy out of the fear that the majority, at least in theory, could be as tyrannical as individual dictators. But years later, when I learned about the social choice theories as a PhD student, I noticed an almost opposite criticism of democracy from academia, namely the instability of social choice. Both arguments sound convincing, but also at odds with each other: It’s hard to imagine a decision-making body that is both cyclical and tyrannical. In the process of solving the puzzle, I came across Nicholas Miller (1983) and Anthony McGann (2006) and realized that the two arguments can be reconciled. Cycling and the tyranny of the majority can both exist, but they can be negatively correlated with each other. As cycling is clearly the lesser of the two evils, it may be exactly the reason that democracies tend to be less tyrannical than alternative systems.

So building on Miller and McGann, I started to develop a theory and design an experiment to untangle the process of how cycling can actually be a good thing and help the temporary losers of an electoral game. I argue that in a voting body, the key factor that prevents cycling is the cost incurred on those who defect from the winning coalition. If a country’s legislative body has a low “defection cost”, cycling is more likely, and the distributive outcome more equal.

I have to admit, unfortunately, that my modeling skills are not enough to formalize a game with continuous options and highly unstable equilibria, but I did present a rather convincing strategic process showing that in a three-player committee, if the defection cost is higher than 50% of the distributable benefits in a given round, cycling cannot happen. I then conducted an experiment by grouping respondents into three-player committees to verify that process. The experiment results turned out to be more variant than I had expected, but largely confirmed the hypothesis that a high defection cost can deter cycling and result in a more “tyrannical” outcome, with less frequent power alternation. I show that while cycling introduces uncertainty into the policy outcome, it is exactly that short-run uncertainty that creates the long-run equality by reshuffling winners and losers.

In the second half of the book, I connect such a phenomenon to the design of electoral institutions. I argue that low defection costs explain the favorable distributive outcome in countries in which the parliament does not have a majority party and the executive is subordinate to that parliament. This way, not only is the winning coalition more inclusive, but more importantly, it is vulnerable to defection and gives the losing side a better bargaining position.

While it is a common belief in the literature that the outcome of electoral system design cannot be predicted with high accuracy, I construct a comprehensive dataset on countries’ largest party vote shares and show that a no-majority party system can be guaranteed in almost any country as long as the electoral system is sufficiently proportional. I explain such a phenomenon by developing a demand and supply theory of political parties, explaining why, with very few exceptions such as South Africa’s ANC, a majority party’s politicians and voters both have strong incentives to split as long as the electoral system allows small parties to survive. And therefore the aforementioned theory that cycling leads to equality is not merely a thought exercise, but an attainable outcome given appropriate institutional design.

There are two features of this book that I think are worth noting. First, it goes beyond positive empirical study of political institutions and offers a clear normative objective for institutional design, which is to ensure an unstable winning coalition to guard against a tyrannical government, whether it represents a majority or not. And second, the book is accessible for readers with minimal political science training, as I strive to convince as many people as possible by using intuitive methods and providing explanations to advanced concepts.