In the pre-election planting I pointed out how much more disproportional Italy’s electoral system would be, given the substantial reduction in assembly size. The current allocation rules and balance between single-seat districts and list-PR seats remained unchanged since 2018, but the assembly size was cut from 630 to 400. (Here I will be referring only to the Chamber of Deputies.) The system is mixed-member majoritarian (MMM).
Assuming I calculated things correctly–and I think I did, but the party vs. bloc calculations can be a little confusing, so caveats apply–here is how the change mattered.
I will report effective number of seat-winning parties (NS), effective number of vote-earning parties (NV), and deviation from proportionality (D2, the Gallagher index also known as the Least Squares Index). I will report both by individual party and by pre-electoral bloc. I believe that for an electoral system like this, the bloc figures are more meaningful, but here you have both and can decide which one works for your analytic purposes.
The change is pretty dramatic. Taking that last line first–disproportionality–we see an increase at the bloc level from around five percent to nearly twelve percent. The 2018 bloc-level figure is a level just below what we might see in a moderately proportional system like Estonia (5.3% in 2019) or Spain (5.37% in 2016) or Luxembourg (5.20% in 2013). The 2022 bloc-level figure is closer to what we might find with a majoritarian system, such as Canada (11.3% in 1988) or the UK (11.8% in 2019) or to take a “brotherly” MMM example, Japan (11.5% in 2000). Thus the increase is quite consistent with how I characterized the system in the previous post, as having changed from an effective seat product just over 900 (consistent with moderate PR) to one of 650 (the same as the value for the UK) solely due to assembly-size reduction.
The effective number of seat-winning blocs is certainly in the ballpark of expectations under a majoritarian system, with 2.90 in 2018 and a drop to 2.40 in 2022 when the assembly size reduction makes it even more majoritarian. The reduction in 2022 occurs in spite of a slightly increased fragmentation of the vote, even at the bloc level (from 3.36 to 3.44). That is, of course, why the disproportionality is so high in 2022.
The bottom line result is that the center-right bloc obtained 59.3% of the seats on 43.8% of votes–a classic majoritarian outcome. In 2018, for comparison, it had 42.1% of the seats on 37.0% of the votes. Its votes grew by 6.8 percentage points, but its seats by 17.2. Some of that is due to the bigger gap between the top two two blocs this time around, which in turn was a product of the center-left’s less complete alliance formation, but a lot of it is the lower number of single-seat districts resulting from the cut in the Chamber size.
Based on the seat product model, by which we expect NS=(MS)1/6, and using the numbers reported earlier for effective seat product, we should expect the 2018 system to yield NS=3.12 and the 2022 system to yield 2.94 (based on effective seat products of 920 and 650, respectively). These are “politics blind” expectations, based solely on the systems’ fundamental design features–district magnitude of the basic tier and the sizes of the tiers that comprise the assembly. We can see that in both elections the actual outcome by blocs was a little less fragmented than these expected values, but not to any extraordinary degree. The calculation of effective seat product for these complex systems gets their impact on the assembly party system about right.
As I mentioned, I do think these indicators are more meaningful when calculated on party level for a system like this. The parties within a bloc coordinate nominations in the single-seat districts, and the contest over who will form the post-election government takes place between blocs. Thus the blocs are the meaningful units. On the other hand, nothing commits the parties within a bloc to continuing to work together, and they agree that the votes for list will determine which one gets the prime ministerial post if the bloc wins a majority. The parties thus remain relevant and competitive actors, too. The outcome at party level was a little less “blocky” overall this time, with more parties gaining significant vote and seat shares despite being outside a bloc.1 But even at the party level, what is likely to matter most–at least in the short run–is that the largest party within the largest bloc has a majority of its bloc’s seats (119 of 237 for the Brothers), despite only 26% of the overall vote for parties.2
All in all, the the key take-home outcome is that the MMM system strongly rewarded the parties that had coalesced to form the biggest bloc, and the largest party within that bloc. That is just as we would expect MMM to do, particularly with such a reduction in assembly size.
Five Star was in this category both elections. In 2018 it won 32.7% of votes and 36% of seats. This time it dropped to 15.4% of votes and 13% of seats. In addition, Action–Italia Viva in this election had 7.8% of votes and 5.3% of seats. More to the point, the three biggest blocs (counting Five Star as one of the “blocs”) had 92.5% of the votes in 2018 but just 85.4% in 2022.
Quite different from 2018 when the League had just 47% of its bloc’s seats–which were in any case not a majority of the Chamber. The League’s party vote in 2018 was 17.4%.
Italy votes in general elections today. The Brothers of Italy is expected to be the largest party, in a pre-electoral alliance with the League and Forza Italia that may end up with a substantial majority of seats in both houses.
The electoral system is similar to that used in 2018 in that it is mixed-member majoritarian despite having just over 60% of seats elected in the party-list proportional component of the system. In an important sense, however, this year’s version is even more majoritarian–the size of both chambers has been reduced substantially. Other things equal–as they are–a smaller assembly is less proportional (or “permissive” to small parties). And when you combine a relatively majoritarian system with a smaller assembly, you get a more majoritarian system overall. The new Chamber of Deputies, at 400 seats, is closer to the cube root law expectation for a country the size of Italy, but nonetheless the impact would be to favor more substantially than before the largest party or pre-electoral alliance, relative to the 2018 system which had a Chamber size of 630. The size of the Senate has been reduced correspondingly from 315 to 200 seats.
How is the system mixed-member majoritarian (MMM) and not mixed-member proportional (MMP)? This question has been asked before. The answer is straightforward: the seats a party wins in the list component are simply added on to those that it wins in the nominal component (single-seat districts decided by plurality). There is no compensation mechanism, not even a partial one like in the 1994–2001 version Italy used.1 There is a single vote, but whether voters can split their votes between nominal and list components has no bearing on the classification, which depends entirely on whether the list seats are allocated so as to compensate for deviations from proportionality arising from the district results (as under MMP) or not (as with “parallel” allocation under MMM).
The results from 2018, aggregated by pre-election alliances that coordinate nominations in the single-seat districts, certainly made this clear. The center-right alliance combined for 37% of the votes. This alliance won 42% of the seats, which is not terribly disproportional. However, we have to remember that more than three fifths of the seats are elected by PR. The nature of the system can be seen by looking at the detailed breakdown. The alliance won 111 nominal seats (out of 232, for 47.8%). Thus they were over-represented in this component of the system, as expected from single-seat plurality. If the list component were compensatory, as under MMP, the share of list seats won by this alliance should have been lower than its share of the vote. Yet it won 39.1% of them (111 of 386). It should have ended up with somewhere around 233 seats were these seats compensatory, but instead won 265 (including 3 seats for Italians overseas).
If we take the largest opposition force, the dynamic is even clearer. This was Five Star, which ran on its own, not as a part of any pre-electoral alliance. It won 32.7% of the vote, and 93 of the 232 nominal seats. That is 40%, so it is also slightly overrepresented in this component. To this it added 133 list seats, which is 34.5%, ending up with 227 seats total (including 1 abroad), or 36.0%. That the system was MMM becomes clearer still if we consider the second largest opposition alliance, the center-left. It had 22.9% of the vote, and won 28 nominal seats. This is only 12.1% of these seats–sever underrepresentation, as expected for a third party under single-seat plurality. Its list seat total was 88, which is 22.8% of the list component. Yes, 22.8%, so it got near-perfect proportional representation. However, it got this proportional result only in the list seats themselves. Overall, due to the punishment in the nominal seats, it was underrepresented, ending up with 122 seats (including 6 from Italians abroad), which is 19.4%. It was not severely underrepresented in the final result because–again–the list component is so large. However, were the system MMP they should have had approximately 110 list seats instead of just 88, in order to make their overall seats proportional to list votes. And, as already covered, the other alliances and parties would have had their list seats cut somewhat due to a compensation mechanism, if it were MMP. Thus the system is MMM, albeit with a large list component. I should also add that when I say “list votes” I mean votes aggregated from the nominal contests, given there is only a single fused ballot and not separate list and nominal votes (as there are in the MMM systems of Japan and Lithuania, or in the MMP systems of Germany and New Zealand).
Because polling for today’s election shows the Brothers of Italy in the lead and the combined center-right alliance clearing 40% of the vote while the second place center-left alliance looks to be under 30%, the system likely would provide a substantially larger boost to the center-right this time around than last, even if the rules were unchanged. However, assembly size is a core defining characteristic of an electoral system. If the rules for how seats are allocated are unchanged, and the balance in an MMM system between nominal and list seats is also unchanged, the key variable in how majoritarian it will be overall is assembly size. As already noted, both houses are half as large in the 2022 system as they were in 2018. This change promises a further boost to the winning alliance. There are only 147 single-seat contests in the Chamber of Deputies this time (around as many as in the Australian House of Representatives) and only 74 in the Italian Senate (about as many as in Liberia’s first chamber), it will be even more “work” for the list-PR component allocation to offset, despite its size relative to the nominal, given it is non-compensatory.
In terms of effective seat product, my estimations have it at 920 in the 2018 election. The goal behind the effective seat product is to allow us a rough approximation of what simple electoral system a given complex system is most similar to, in terms of its impact on the party system. Simple, single-tier systems with seat products in the 900–1000 ballpark include Luxembourg (900) and Greenland (961). The former has an assembly about ten percent the size of Italy’s in 2018, yet in terms of impact of the party system, the design of Italy’s system made it more like the simple PR system for the 60-seat assembly of Luxembourg than like other assemblies with 600+ seats and PR allocation (e.g., Germany’s effective seat product is currently around 1800 and Italy’s under its old PR system prior to the early 1990s was around 9800). As for Greenland, they get an effective seat product of 961 from an assembly of only 31 seats by allocating in a single territory-wide district. In other words, while Italy 2018 was a system of MMM, the large assembly and large share of seats allocated in the list component make the Chamber system of 2018 similar to a small-assembly PR system. But what about 2022?
The calculation of the effective seat product for the new Chamber of Deputies system would be around 650. In other words, roughly the same effect on a party system as Britain’s FPTP system, despite the election of over three fifths of deputies in a PR component. This is a fairly substantial reduction. It is based on the “as if” calculation of (1) an MMP system with same parameters as Italy’s new system, which would be an effective seat product of around 2860, and (2) a FPTP system of the actual size of Italy’s nominal component (147). For MMM, we take the geometric average of these two values, which is (rounded) about 650. This is very slightly less restrictive than the MMM system that was in use from 1994 to 2011 (for which the effective seat product could be said to have been around 660). Applying the same procedure to the Senate electoral system of 2022 would yield an effective seat product of around 370, implying roughly the same impact on the party system as the FPTP system of the Canadian House of Commons has.
In conclusion, Italy now has the most restrictive and thus plurality-favoring electoral system it has had in the post-WWII era.2 Despite still having a fragmented multiparty system in which parties enter pre-electoral alliances, it has an electoral system that is more like FPTP in the UK (in the case of the Chamber) or Canada (in the case of Italy’s Senate) than like a PR or MMP system. If the largest alliance clears 40% of the votes, as expected, it should obtain a substantial bonus in seats, due to the relatively majoritarian design of the system.
That system was also MMM. It was often mis-classified in various sources as MMP. The misunderstanding was somewhat more justifiable than for the current one, because of the partial compensation mechanism, which was based on adjusting party-list votes according to nominal seat performance (rather than allocating list seats with regard to nominal seats won as is done under MMP). Even with the partial-compensation mechanism, that former system also should be classified as MMM.
All of Italy’s post-war electoral systems have been complex in one way or another. Above I mentioned that the system in use as of the early 1990s had an effective seat product around 9800. That was a remainder-pooling PR system and Italy has not used a PR system since then. The mixed-member system put in place in 1994 had an effective seat product around 660. The bonus-adjusted system from 2006 through 2013 comes out to around 1325 (but this is a more challenging system to estimate because of its unusual features). In all cases, these numbers refer only to the Chamber. Also, the calculation of effective seat product for the 1994–2001 system does not take the partial compensation mechanism into account. Perhaps it should, which would increase the effective seat product of that former system to some (small) degree. However, it is not clear how one would carry out such an adjustment, given the unusual nature of the mechanism. I do not think it is necessary or worthwhile to attempt.
Hungary’s 2022 election resulted in an overwhelming victory for the incumbent Fidesz party, led by Prime Minister Viktor Orban, against a broad opposition coalition, led by Peter Marki-Zay, comprised of liberals, social democrats and the nationalist Jobbik party. Orban’s twelve-year-long government has been the focus of international attention over its nationalist policies and weakening of democratic institutions.
One of the earliest initiatives of Orban’s government was a set of amendments to the electoral law in 2011. While Hungary retained a mixed-member system, the three-tier system introduced in 1989 was replaced with a two-tier system. The size of the legislature was cut drastically, from 386 to 199. This involved a redrawing of the single-seat districts, as the number of these districts fell from 176 to 106: the two-round system previously used for these seats was replaced by first-past-the-post.
The process of drawing new electoral boundaries and introducing a new electoral system represents an excellent opportunity for a governing political party to entrench its own advantages. Fidesz had a completely free hand in that process, owing to its two-thirds constitutional majority. So, what does the electoral system look like?
Based on the 2022 results, there is a clear negative relationship between Fidesz vote share and registration numbers. Interestingly, this is driven by very high registration in the electoral districts of suburban Pest county, which is the cluster on the right of the plot: Budapest, the opposition’s stronghold, has roughly average enrolment.
But what does this mean in terms of actual election results? In order to examine this, I simulated a set of uniform swings1 between Fidesz and the Alliance for Hungary. The below plot shows seat totals in the single-seat districts at different vote shares for both the opposition alliance and Fidesz (vote shares for the other parties were kept constant).
The vertical line shows where the two parties tie – approximately 44% of the vote each, or a swing of 7.8% towards the opposition. At this level, Fidesz would win 56 single-seat districts to 50 in total for the opposition. In order to win a majority of the single-seat districts, the Alliance would need approximately 46% of the vote to 43% for Fidesz.
Of course, the list seats need to be taken into account. The below plot shows the number of total seats each party would have won with the same vote shares as in the prior plot. The vote share for the other parties is held constant, and I assume that the nationalist My Homeland party would have held onto its 5% of the vote and 6 seats, and that the German minority would have elected its single member under the special procedure for ethnic minority parties.
The effect of the list seats is fairly minor. A tied vote would give the Alliance 91 seats to 100 for Fidesz, the slimmest of absolute majorities. Fidesz loses this majority at a fractionally lower share of the vote. However, for the opposition to win a plurality, they need about the same 46-43 vote share as they need for a majority of the single-seat districts, and to win the 100 seats required for an absolute majority they need 47% of the vote to 42% for Fidesz.
How serious is this effect? How does it compare to other jurisdictions? One method which has received some use in the (inevitably US-centric) gerrymandering literature is the ‘efficiency gap’, which calculates the difference between the number of wasted votes for the two major parties, as a proportion of all votes. I calculate the efficiency gap at this election to be 5.2%, again ignoring votes for minor parties. According to the paper laying out the efficiency gap measure, this gives Hungary a map roughly as biased towards Fidesz as the maps in Minnesota or South Carolina were towards the Republican Party, or the map of California was towards the Democratic Party. Hungarian bias, however, does not seem to be as strong as that in North Carolina or Florida.
Hungary’s 2012 electoral map, then, provides Fidesz with a modest but meaningful electoral advantage, only slightly ameliorated by the list tier. Nonetheless, the opposition at this election achieved a vote share well short of what would be needed to win a majority. Unlike in Poland, the role of the electoral system in the installation of this government has been seemingly fairly minimal.
1 Note that ‘swing’ is here defined as percentage points subtracted from Fidesz’s (or the opposition alliance’s) vote and added to the opposition alliance’s (or Fidesz’s) vote share. I believe this is the Australian definition, as opposed to a British one that (I think) averages the two figures.
Via the Nation from Thailand, it seems that a joint sitting of parliament has voted to adopt mixed-member proportional representation (MMP) instead of a mixed-member majoritarian (MMM) system. The headline reads, “Parliament votes for party-list MP calculation method to be divided by 500.”
The meeting, which comprised senators and members of the House of Representatives, chose whether to divide the party-list MP calculation by 500 or by 100. The first choice won with 354 votes in favour, 162 votes against, 37 abstentions and four no votes.
The meeting rejected the use of 100 to calculate party-list seats, which is the current method, by 392 votes to 160, with 23 abstentions and two no votes.
This is a somewhat awkward way of stating the choice between MMP or MMM, but it works. Let’s take a couple of examples to demonstrate. Suppose there are 36 million valid votes, and there is a party with 6 million votes, or one sixth. If the division is by 500, then a simple quota for a seat is 72,000 votes. This party has 83 full quotas (6M/72k=83, discarding the fraction, 1/3). If instead the division is by 100, then a simple quota is 360,000 votes. Our hypothetical party with six million votes now has 16 quotas.
The first scenario logically implies MMP. The party might have won, let’s say, 30 nominal seats (single-seat district contests in which the plurality wins the seat). It is entitled to 83 seats. So it gets 53 list seats, to bring its nominal total of 30 up to its full share of 83 quotas out of 500. It is thus proportionally represented.
The second scenario logically implies MMM. Again, let’s say it has 30 single-seat wins. Its 16 quotas mean 16 list seats, which it will add to its 30, for a total of 46 seats. This is a little short of ten percent (9.2%, to be precise). It is under-rerepsented.
Note that in the first scenario, it has one sixth of the total 500 seats. In the second it has one sixth of the 100 list seats. This is precisely how MMP vs. MMM works.
Now let’s take a somewhat larger party, with nine million votes. If the division is by 500, it has 125 full quotas. The hypothetical vote total has been chosen to roughly reflect the For Thais Party (PPT) in 2019, which actually won 7.8 million votes. That made it second largest party in votes, but it won the most nominal seats, 136. So let’s give it in our hypothetical that number as well.1 It is over-represented already! It is entitled to 125, based on full quotas with the denominator of 500. In other words, it has 11 overhangs. It will keep these, but it will get no list seats. Even though the system is MMP, the other parties that need compensation from the list seats will remain somewhat under-represented as a result.
If instead the division is by 100, this party has 25 full quotas. It thus wins a quarter of the 100 list seats, and adds these to its 136 nominal seats, for a total of 161. This is 32.2% of the total, under the hypothetical MMM system. It is over-represented, given it had 25% of the vote. It was also over-represented under MMP, as we saw in the outcome with division by 500. However, in that case, its seat percentage is 136/500=27.2%, which is much closer to its vote percentage than the MMM example.2
The Nation article concludes with this puzzling note:
However, Thammasat University public law specialist Prinya Thaewanarumitkul expressed concern on Facebook on Wednesday that the new formula would result in the number of list MPs exceeding the number allowed by the constitution.
No, it would not. Or, rather, it would not have to do so. The public law specialist seems to be assuming the overhangs would be compensated, by adding further list seats. But MMP does not necessarily do this, and if the list seats are restricted to 100, it will not generate more than 100 list seats for the simple reason that it can’t. The “extra” implied seats do not exist, and we simply reduce the total compensation potential when there are overhangs in the nominal tier. You keep 100 list seats, but the parties that have not already won at least their full quotas worth in the nominal tier get fewer of the list seats. This can be accomplished by recalculating the quota. In the scenario here, assuming those 11 overhangs for the party with nine million votes are the only overhangs the election produced, the quotas would be recalculated with a denominator of 500-11=489. Now parties get a list seats for each 73,619 votes they have earned (instead of 72,000). Our party with the six million votes is now entitled to 81 total (again, discarding fractions) rather than 83. And other parties–not considered in these illustrations–get similar reductions in what would have been their entitled final shares had there been no overhangs generated by parties that got over-represented due to success in the nominal tier.
In conclusion, it seems Thailand has chosen to shift to MMP. However, it will not be a highly proportional version of MMP, given that 20% of total seats in a compensation tier is on the small side. It is still MMP, and need not permit expansion of the list tier in order to so qualify.
I should also not that this was the second reading of the bill, not final passage.
1. In the 2019 election, there were 350 nominal seats and 150 list, but rather than weight the seats to totals out of 400 nominal seats, I will just go with the raw numbers of seats PPT won in 2019.
2. In all these scenarios, for simplicity, I have ignored remainder seats, which result from the fractions that are ignored after seats are assigned via full quotas.
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.
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 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 expectedNS), 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:
(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.
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.
Heinz Brandenburg on Twitter walks readers through a very useful explainer on how the current Germany version of MMP deals with overhangs through a multi-layered compensation mechanism, and why it could mean the new Bundestag will top out at more than 800 seats!
It is best to read it in its native Twitter, but following is the text of most of it (courtesy of the ThreadReader app) . The starting point, not quoted here, is a poll of current party standing in the state of Bavaria.
[the remainder of this text is not mine, but Brandenburg’s; numbers correspond to tweets in the thread]
Last time around, the CSU won 38.8% of the vote but all of the constituencies in Bavaria (they even swept all of Munich). That results in so-called overhang and compensatory seats. How are these calculated?
1/ Well, there are 93 regular seats allocated to Bavaria, 46 of which are constituencies. CSU winning them all meant 46 seats, but they only had 38.8% of the list vote or about 42% of the vote once you discount votes for parties that did not get into the Bundestag.
2/ 42% of the vote would mean their proportional share of seats was 39, not 46. So they got 7 Ueberhangmandate (overhang seats), i.e. 7 more seats than their proportional share.
3/ Since 2013, these seats have to be compensated for. So other parties get additional seats, to the extent that the 46 seats the CSU won amount to 42% of the total number of seats in Bavaria. So Bavaria actually had 108 seats in the Bundestag, not 93.
4/ But that is not the end of it. Bavaria’s 93 seats are proportional to its population size. If the state’s seat share increases to 108, then the 15 other states also need a larger share. And it wasn’t only Bavaria.
5/ Baden-Wuerttemberg got 96 instead of 76 because of the CDU winning all constituencies, Brandenburg 25 instead of 20 because CDU won all but one constituency, Hamburg 16 instead of 12 because SPD won all but one constituency, and so on.
6/ What happens then is that to keep the 16 states’ share of seats in the Bundestag proportional, not only overhang seats within states need to be compensated, but overhang and compensatory seats within states have to be compensated across states.
7/ So North Rhine-Westphalia (NRW), the biggest German state, did not produce any overhang seats, because SPD and CDU are more evenly balanced there. But it got 14 compensatory seats, to make up for additional seats given to other states.
8/ It is not a perfect compensation across states. Bavaria and Baden-Wuerttemberg have 15 and 20 seats, respectively, more than their normal share in the 2017 Bundestag. NRW only 14, despite being the larger state.
9/ Berlin, Niedersachsen and NRW were the only states where no overhang seats were dished out in 2017, largely a reflection of dominance of the CDU in a fragmenting party landscape.
10/ CDU won all seats in five states, almost all seats in over a dozen states, despite having their worst election result in history, with 33%.
Could be very different this time around, with them down to 20% and the SPD at 25%. More states could get away without overhang seats.
11/ But one single state can make a big difference, and if the result in Bavaria is anywhere close to the recent polls (CSU 28%) it could be a dramatic effect.
12/ Even at 28%, the CSU would like win almost all constituencies. These are the four most marginal seats. Muenchen-Nord and Nuernberg-Nord are most likely to fall to the SPD. But the others are not certain.
So the CSU could still end up with 42-44 seats, on just 28% of the vote, or 31% if we remove votes for parties that do not get into the Bundestag.
14/ By my calculations, that would mean Bavaria’s seat share increases to 129 seats from their current 108 (and their nominal allocation of 93).
Once other states are compensated, that would get us to possibly 840 seats.
15/ A few changes have been made, which I have taken into account – the first three overhang seats will not be compensated, which would keep Bavaria’s share at 129 rather than 135 under 2017 rules.
16/ And overhangs can also be compensated against a party’s list seats in other states. But I don’t think that applies to the CSU. They won’t take CDU seats away in other states to compensate for CSU over-representations.
17/ So one such lop-sided result, under increasing fragmentation – where suddenly 28% of the vote share allow a party to win almost all constituencies – can have incredible effects on the size of the Bundestag.
18/ The nominal size of the Bundestag is 598. This one result in Bavaria could increase the size of parliament by 40%.
The parliament of Thailand has again adopted electoral system changes. However, the WaPo is confused (and confusing) about what has been done. On the one hand, it says it is a “system of mixed-member proportional representation” (MMP).
On the other hand, it also says the new system is “a throwback to the system implemented under a 1997 constitution that sought to disadvantage smaller parties.”
Only one of those statements can be true.
The 1997 system was definitely mixed-member majoritarian (MMM), sometimes called a “parallel” system, and was indeed highly disadvantageous to small parties, by design. So much so, that its effective magnitude is probably best considered somewhat less than one. That is, despite a component of seats that are themselves allocated proportionally, its effect on the party system would be more like that of a multi-seat plurality system than like FPTP, let alone MMP.
It may be that the current system is indeed already MMP, based on what was enacted in 2016. So I am not saying that the statement about the new system being a “throwback” must be the true one, rather than the one about it being MMP.
The only clear statement in the WaPo article about a change from the status quo is that it will “give voters two separate ballots instead of the single one used in the 2019 election.” This is not a variable that divides MMP from MMM, but rather one that can take either value (one vote or two) within either type.
Thailand has changed its electoral system so many times that I can’t keep track. But it would not seem too much to ask of journalists reporting on electoral system changes to have a basic grasp of the topic so as to avoid making contradictory statements like the ones quoted above.
The following was a comment by Manuel on a post about the 2018 election. It certainly deserves a more prominent planting hole, so I am copying it here. Please note the following is authored by Manuel Alvarez-Rivera of the always valuable Election Resources on the Internet, not by me.
Note Manuel’s very interesting observation that this time the system functioned as pure mixed-member majoritarian (MMM), i.e., with “parallel” allocation of the single-seat district and list components, rather than with any compensatory allocation.
Preliminary results of the June 6, 2021 Chamber of Deputies election in Mexico indicate that no gaming of the 8% disparity cap took place this year, largely because the ruling “Juntos Hacemos Historia” (JHH; Together We Make History) coalition won fewer single-member mandates than in 2018.
With 99.6% of the tally sheets processed, Mexico’s Preliminary Election Results Program (PREP) reports the distribution of Chamber of Deputies single-member seats stands as follows:
PAN – 33 PRI – 11 PRD – 0 PVEM – 1 PT – 0 MC – 7 MORENA – 64 PES – 0 RSP – 0 FXM – 0 PAN-PRI-PRD – 65 PVEM-PT-MORENA – 119
The PAN-PRI-PRD “Va por México” (VPM) opposition coalition ran candidates in 219 of 300 Chamber districts, while JHH (PVEM-PT-MORENA) contested 183. On the basis of the coalition agreements published on the National Electoral Institute (INE) website, the party distribution of single-member seats would be as follows, with party single-member seat and vote shares in parentheses:
The absence of PVEM-PT-MORENA and PAN-PRI-PRD coalition candidates in many districts made little difference in the overall election outcome. Had both coalitions ran in all 300 districts, the MORENA-led coalition would have had a net loss of just four seats, gained by the PAN-led coalition.
Meanwhile, the official allocation of PR list seats won’t be known until as late as the third week of August, but on the basis of preliminary figures it would be as follows:
PAN – 41 PRI – 40 PRD – 8 PVEM – 12 PT – 7 MC – 16 MORENA – 76 PES – 0 RSP – 0 FXM – 0
Consequently, the overall composition of the Chamber of Deputies would be as follows (seat shares in parentheses):
Since no party hit the 8% disparity cap, Mexico’s Chamber of Deputies electoral system operated in a purely parallel manner in this year’s election. Moreover, the JHH coalition parties won between themselves 47.76% of the “effective national vote” cast for parties entitled to take part in the allocation of PR seats. As such, the parties’ joint share of 55.8% of the Chamber seats happened to be just 8.04% above their effective national vote aggregate percentage. Had PR list seats been distributed among coalitions (as opposed to individual parties), the application of the 8% disparity cap would have reduced their overall seat total by only a single mandate.
Finally, the over-representation of the PVEM-PT-MORENA coalition in the Chamber of Deputies – where it retained a reduced but comfortable majority – stems largely from its continued dominance in twelve states in southern Mexico, where it won 85 of 99 single-member seats (85.9%) with 49.1% of the vote, while the PAN-PRI-PRD coalition trailed well behind with 32.9% of the vote and 14 seats (14.1%). In the rest of the country the election was closely fought, and while the VPM coalition parties won the popular vote, 43.5% to 39.2% for the JHH coalition partners, the latter still won slightly more district seats (99) than the former (95). Meanwhile, MC won all its seven district seats in Jalisco state, where it topped the poll with 31.5%, in a close three-way race with the PAN-PRI-PRD and PVEM-PT-MORENA coalitions, which polled 31.3% and 28.6%, respectively.
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.
Quebec was to have a referendum on a proposed new mixed-member electoral system concurrent with the next provincial election in 2022. However, that plan is now “on hold” as the bill will not be passed in time.
As noted in an earlier comment thread, initially by Dave Hutcheson, former First Minister of Scotland, Alex Salmond, has formed a new party called Alba. It plans to run only list candidates. This has raised some questions about whether this is a “gaming” of the MMP system to enhance the majority of pro-independence parties, bypassing the compensation mechanism. For instance, a pro-independence voter could vote for the Scottish National Party candidate in their single-seat district and the Alba list.
I don’t believe this is true “gaming” in the sense of the dummy lists we have seen in MMP systems in Albania and Lesotho in the past (or even the recent Korean election), but “gaming” does not have a precise definition.
I recommend reading Dave’s comment (linked above) and then the following comment in the same thread by JD Mussel as well as the Politico story he links to. There will also be another new party entering on the pro-union side, All 4 Unity, headed by good old George Galloway (about whom I have written before, most recently under the title, “Galloway is back”; well, he’s back again!). It is similarly motivated to Salmond’s entry: to enhance the total seats for his side of the divide through encouraging tactical split voting.
Then, to get a sense of just how Alba’s entry could affect the result, Leonardo Carella has a very interesting and valuable Twitter thread, viewable in one page thanks to Thread Reader, with simulations under various scenarios.
As I said, I have my doubts this party entry is as problematic as some see it, but it is a debatable point. So, what do readers think?
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.
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!
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.
[Update, late April, 2022: I have continued to refine this method, and the specific values mentioned below no longer hold (due a revision of the estimation of the exponent in the model for two-tier systems), although the basic framework remains the same. User beware! This also means that the datasets linked at the end of this post are not accurate. I will upload corrected ones at some point.]
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:
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 effectiveM).
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.) [As noted at the top of this article, these files should no longer be used. At some point I will upload corrections. Sorry for the inconvenience.]
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.
Earlier, I noted that in the New Zealand 2020 election, the Labour Party flipped several seats in mostly rural single-seat districts that are normally strongholds of the National Party.
Commenting on those swings, North Canterbury Federated Farmers president Cameron Henderson said:
There were definitely “strategic farmers” voting Labour in an effort to avoid a Labour-Greens government.
He added a caveat, that most of the vote swings in these seats came from urban voters within predominantly rural electorates. Nonetheless, his confidence that there were strategic farmers is a nice anecdote regarding what some political scientists have regarded as strategic voting motivated not by who can win locally but by which parties may form government.
As I noted in my election preview in late July, there were only two likely outcomes of this election: A Labour–Green coalition or a Labour single-party majority. There were no occasions over the last several months when a National-led government was likely based on any publicly available evidence. For most farmers, a government in which the center-left Labour Party has a parliamentary majority is a much more palatable outcome than one in which that party needs the Greens for its majority.