I am not sure Michael has made the correct choice here–minority representation provisions are part of the electoral system, after all–but I am also not sure this is incorrect. The system really is challenging to classify and quantify. I note in particular his decision to count its assembly size–and therefore, its district magnitude, given there are no district divisions unless we count the ethnic reservation/guarantee as separate “districts”–as 100 before 2014 but as the full 120 since then. Here, for reference, are the indices he reports in the main part of the document:
The unusual nature of the system is what results in the effective number of seat-winning parties (NS) sometimes being higher than the effective number of vote-earning parties (NV), something that is otherwise rare, and certainly should not happen in a single-district nationwide proportional system. As I noted in the earlier discussion, in 2021 it was even the case that a single party list won a majority of votes, but did not win a majority of the full 120 seats. Because I assume all legislators are equal, and that a government needs a majority of the 120, and not just the 100, I think it is incorrect to treat assembly size as not including the 20 ethnic representatives. Gallagher’s data from 2014 do include them, and I think that should be the case for the earlier years as well.
The question of how to calculate the indices is indeed a vexing one. Gallagher very helpfully explains his choices and what would change if we use a different assumption about what “counts.” This allows the researcher using his valuable resource the ability easily to make his or her own decision. But this researcher still is not sure which decision to make with respect to this system!
I am not comfortable with the idea of counting these various ethnic guarantees as additional “districts” even though I see the case for it (which Henry made in a comment to the previous planting). That lack of comfort is not solely because these “districts” overlay the main one. That is, after all, the case of the Maori districts in New Zealand (each of which encompasses the territory of several general electorates). For that matter, it is also the case with any two-tier system. Rather, the conceptual difficulty is that a given party list may win seats in either component of the system–the general 100 or the set-aside for their ethnic group–if they qualify for additional seats beyond their ethnic group’s reservation/guarantee.
However we conceptualize the system, I believe all these parties should be taken into account in calculating the effective number of parties (votes and seats). The question of whether we count them for deviation from proportionality is less clear to me.
I think I need to count this as a non-simple system (by the criteria used on Votes from Seats), giving us a unique case of what could be called a single nationwide district PR system that is nonetheless complex. For countries whose electoral system has just a few ethnic set-asides (like Colombia or Croatia), I tend to ignore the reserved seats when thinking of whether they are “simple” districted or national-district systems. But when such seats are a sixth of the total, they are clearly a complicating feature, as the unusual outcomes reveal.
Given my sudden fascination with small assemblies, I was poking around in election results from St Kitts and Nevis, a Caribbean sovereign state with a population of just over 52,000. With 11 elected members, its assembly certainly counts as small. The 2000 election is really something. Look at the national result:
The second largest party got no seats, while two parties with less than 10% each won a seat or two. This is a first-past-the-post system. The problem the PAM had was it came in second in all eight seats it contested, i.e., every district on the island of St. Christopher (none were close). The advantage the CCM and NRP had is they run only on the island of Nevis, which has three district. Here are the district results.
Note that there is some pretty serious malapportionment here, as well. Nevis constituencies have many fewer voters than St. Christopher constituencies. In fact, the three Nevis districts together have only about 1.2 times the population of the most populous St. Christopher district.
So what should we have according to the Seat Product Model? The seat product is 11 (magnitude of 1, times assembly size of 11), so the effective number of seat-winning parties should be 1.49. In this election it was actually 1.75. That’s actually not a terrible miss! But in most elections it has been considerably higher than that–as high as 3.90 in 2015. So just for fun, a quick look at that one:
(Last column is seats won, but the heading did not copy over.)
This time, the PAM benefitted greatly! It is in a clear second place in votes, yet won a plurality of seats. Not a majority, however. According to Wikipedia, there were alliances. But even at the alliance level, there was a plurality reversal: “The outgoing coalition (SKNLP and NRP) secured 50.08% of votes but got only 4 seats, the winning coalition (PAM, PLP and CCM) won 7 seats with only 49.92% of votes.” Oh, cool: Another case of pre-electoral alliances! The effective number of alliances was just 1.86.
We might not expect regionalism in such a small country, with a small assembly. But the party preferences of the two islands obviously are genuinely different (and the PLP is “regional” in that it contested only two districts on St. Christopher); yet the parties aggregate into alliances for purposes of national politics.
The malapportionment is still noteworthy–look at the small population of Nevis 10. However, one of the other two districts is now the most populous in the country, quite unlike in 2000.
Final point: Its population may be small, but according to the cube root law St Kitts and Nevis should have an assembly more than three times what it actually has: 37. If they were proportional to registered voters, Nevis would be allotted nine of those 37 seats. It currently has 3 of the 11, so 27%, so quite close to its population share, unlike in 2000 when it was overrepresented. Making the seats allocated by island more easily fit population balance in itself would be a good argument for increasing assembly size, but an even better argument would be making anomalous results like the two elections shown here less likely–even if they insist on sticking with FPTP.
What do we consider the political system of Guyana to be? On the one hand, there is an official who is both head of state and head of government, who is determined by nationwide plurality vote. On the other hand, the constitution, in Article 106, paragraph 6, states:
The Cabinet including the President shall resign if the Government is defeated by the vote of a majority of all the elected members of the National Assembly on a vote of confidence.
Thus the president is clearly subject to majority confidence, like a parliamentary head of government–President David Granger and his cabinet fell due to a vote in December, 2018. Superficially, this implies a form of elected prime-ministerial government (like Israel 1996–2001), in that an elected head of government, and the cabinet, must maintain confidence in order to stay in office. Thus we appear to have separate origin and fused survival. Moreover, the president has no veto power other than suspensory (article 170, para. 4-5), and no other constitutional legislative powers that can be used against the majority of parliament.
It is, however, questionable whether we should conceptualize the executive’s origin as separate. The president is elected as the designated candidate on the list of the party that wins a plurality. On this point, the constitution, at Art. 177, says, in part, that a list of candidates for parliament,
shall designate not more than one of those candidates as a Presidential candidate. An elector voting at such an election in favour of a list shall be deemed to be also voting in favour of the Presidential candidate named in the list.
There is thus no separate election for president. On the one hand, this could be classified as just another case of fused-ballot presidential election, like the Dominican Republic and Honduras have had at times in the past. (I do not generally consider these systems non-presidential just because voters can’t ticket-split between president and congress, although a case could be made for considering them in a distinct class.) On the other hand, defining the president as the head of a winning party list, rather than as a separate candidacy, could be said to be no more separate origin than we have in Botswana and South Africa (cases I consider unequivocally parliamentary). What is unclear to me is what happens in Guyana if the plurality list in the parliamentary election is opposed by a multiparty post-electoral majority in parliament. Is the head of the plurality list still president? It seems so. Yet Art. 106 implies such a leader would not remain in office.
It is thus unclear how this case should be classified, and I think I have tended to ignore it in the past. Now that I am planning no longer to ignore it, I need to decide if it is “parliamentary” or “hybrid.” There might be a case to be made that this is just a parliamentary system where the leader’s election only appears direct and separate. Or it could be that it is a hybrid of separate election but parliamentary-style fused survival through the no-confidence mechanism in Art. 106.
I should note that there is a constitutional office of Prime Minister, so unlike in Botswana or South Africa it might be odd to say that the “President” is really a prime minister on account of being dependent on parliamentary-majority confidence. However, the PM is clearly a subordinate appointee of the president (and also serves as Vice President, and the President may appoint others to be Vice Presidents as well). So I would not let this quirk determine which executive-type box I put the case in.
As for the country’s electoral system, it appears to be a straightforward case of two-tier PR. There are both regional multi-seat districts and a nationwide PR tier, and it seems there is full compensatory allocation. (See constitutional article 160 or the election results at Psephos.) This would make it one of the few two-tier PR systems outside of Europe (leaving aside the question of whether MMP–found in New Zealand, Lesotho, and Bolivia–is a sub-type of two-tier PR or not). Thus the case is valuable for my goal of maximum coverage of both simple and two-tier PR around the world. (For instance, my recent queries about small dependent territories and free-list systems, and ongoing efforts to make sense of remainder-pooling systems.)
But does Guyana have a parliamentary system, some sort of parliamentarized hybrid presidential system, or an elected prime-ministerial system?
In the previous planting asking whether free-list PR violated my own definition of a “simple system, I mentioned the criterion of avoiding violation of the rank-size principle in allocation of seats to votes within district (see footnote 2). I later happened up a major example of violation of the rank-size principle: Kosovo in 2021!
It is a single district of 120 seats, but per Wikipedia:
The Assembly had [under the Constitutional Framework] 120 members elected for a three-year term: 100 members elected by proportional representation, and 20 members representing national minorities (10 Serbian, 4 Roma, Ashkali and Egyptian, 3 Bosniak, 2 Turkish and 1 Gorani). Under the new Constitution of 2008, the guaranteed seats for Serbs and other minorities remains the same, but in addition they may gain extra seats according to their share of the vote.
The result of this is that there are parties with as much as 2.5% of the votes but no seats (there is also a 5% legal threshold for non-ethnic parties), and parties with as little as 0.14% who have seats when somewhat larger ethnic parties do not. For instance, the United Roma Party of Kosovo has a seat with 1,208 votes while the Innovative Turkish Party, which I presume is an “ethnic” party, with 1,243 votes, has none. That would be because the two set-aside Turkish seats were won by the Turkish Democratic Party of Kosovo, which had almost 6,500 votes (0.75%).
Perhaps it is not a “single district” and we should think of each ethnic group’s set-aside representation as a distinct district in addition to the general constituency. But that is certainly not how I generally understand “district.” In any case, there is nothing “simple” about the provision or its impact on outcomes, particularly regarding the rank-size criterion.
In addition, these provisions result in the odd case of a party with a majority of the vote not getting a majority of the seats, which is certainly unusual for a proportional representation system!
This seems like a trick question. Of course, free-list has all sorts of complex features. In such a system, the typical rules are that any voter may vote for as many candidates as he or she wishes, even across different lists (panachage). A vote for any candidate on a list counts as a vote for that list for purposes of determining proportional seat allocation across lists, as well as for the candidate in competition among other candidates on that list.
However, this system handles votes and seats for lists just like any other list-PR system: It is designed to allocate seats to lists first, and only then to candidates. It thus is “simple” on the inter-party dimension, unlike SNTV or MNTV or STV (where candidate votes do not count towards aggregate party vote totals and seats are allocated based only on candidate votes).
My general definition of a “simple” electoral system is one that is a single-tier, single-round, party-vote system. The free-list could be said to violate that last part of the definition, in that “party vote” maybe should mean a single party vote per voter. My instinct is to keep free list in, because it remains “simple” in terms of how it processes the votes across lists. But I could be convinced otherwise, given that effectively every voter can vote for more than one list–a “dividual vote” in Gallagher’s terms.1
In Votes from Seats, Taagepera and I kept at least three free-list systems in our dataset: Honduras (since 2005), Luxembourg, and Switzerland. The issue came back to my mind because of my consideration of including some smaller countries and non-independent territories in a dataset for some further analysis of key questions. One of the smaller countries that could be added to the data is Liechtenstein, which I believe uses a free-list PR system. My gut says “yes, include” but now I wonder if we already violated our own criteria2 in having those free-list systems in the prior analysis. To be clear, none of our results would be changed if we had dropped them.3 It is just a matter of consistency of criteria.
Questions like this always nag comparative analysis, or science more generally. What things are part of the set being analyzed? It is not always clear-cut.
Note that there is no question regarding standard open-list PR: Even if there are multiple candidate preference votes cast per voter, as in Peru, only a single list vote is registered per voter.
In fact, on p. 31 of Votes from Seats, we say “Only categorical ballots and a single round of voting are simple, by our definition.” A free-list ballot is dividual and thus not categorical. However, the reason we give for limiting the coverage to categorical ballots is that “other ballot formats… may violate a basic criterion for simplicity in the translation of votes into seats: the rank-size principle” (emphasis in original). For example, the party with the most aggregate votes in a district may not have the most seats allocated in the district (or at least tied for most with the second-most voted party). This violation of the rank-size principle can occur with SNTV, STV, and MNTV, but as noted above it can’t occur in free-list PR (per my understanding, anyway). I note that in a later work, Party Personnel, my coauthors and I seem to adopt a stricter definition. On p. 53 of that book, we say that simple means “a voter votes once, and this vote counts for the entire party list of candidates.” Yet the conceptual point there is somewhat different, in that we are referring to “simple vote” not simple electoral system, and we remove open-list PR from the standard of simple vote because they permit differentiation of candidates within a list in the same district. But as for the vote counting for the entire list, free list still meets that part of the criterion. (A reminder that “voting system” is not a synonym for “electoral system”!)
Although I did not think of this possible issue with free lists at the time, I definitely ran robustness-check regressions with Switzerland dropped. I did so mainly because of its multiparty alliance feature, which also is a complex feature for reasons discussed in the book (mainly with reference to Finland and Chile). Doing so did not affect the results, so we left the case in. There are not enough elections from the other free-list cases, nor are they observably different on our outcomes of interest, that they could affect results. (Switzerland is observably different–far more fragmented than expected for its seat product, and that seems to be mostly due to alliances, even above the impact of its ethnic fragmentation–see p. 269 of Votes from Seats. But the inclusion or exclusion fo the case is immaterial for the overall results.)
I am going to do a little crowd-sourcing here. What do people think is a reasonable way to define “autonomous enough” to include a territory in a set of small assemblies worthy of comparative analysis alongside independent nations with small assemblies?
That is, there are various countries with very small assemblies that are recognized as independent states, such as St. Kitts and Nevis (assembly of 11 seats) or Antigua & Barbuda (17). Like the two just mentioned, most of the small-assembly independent states that are also democracies with small assemblies are in one world region (Caribbean) and use one type of electoral system (FPTP).
Now suppose one wanted to branch out and include small territories that were either not in the Caribbean or used PR. Suppose further that one did not want to include obviously fully dependent territories that just happen to hold elections for an internal legislative council. Where would one draw the line?
For instance, are the Faroe Islands and Greenland “autonomous enough” to include? What about Aruba and Curaçao? These use PR systems, and the first two are not Caribbean. Or the Cook Islands, with is FPTP but non-Caribbean?
One would need a reasonable standard for autonomy. I sort of feel the places I just named might qualify, but I do not know why I feel that way. And I do not want the can of worms opened whereby I’d be asked–legitimately–why did you exclude Turks and Caicos (for example)? (Other than, well, I already had enough FPTP Caribbean cases.)
The smallest currently included independent country in my related datasets seems to be St. Kitts & Nevis (pop 54k). One of the territories I mentioned is much smaller than that (Cook Islands only 15k), but others are of the same order as St. Kitts (like Faroe Islands and Greenland, 53-55k). I probably have a floor somewhere on population–which might well exclude Cook Islands–but my current query is for a reasonable standard on what is sufficiently self-governing to be comparable to small independent states for purposes of analyzing their assemblies and electoral systems.
It had been a very mild chilling season to start, but suddenly the chill mostly has caught up with last year. In all my years monitoring winter chill for my deciduous orchards–in San Diego County and now since mid-winter 2012-13 in Yolo County, pictured above–I have experienced very few 24+ hour periods like the current one. Below is a capture from my temperature station from Saturday evening. The high for the day was 44F. The low was 33F, but the temperature was below about 36 for only around five hours. And since then it has been even more remarkable: all night long and until a little after eight on Sunday morning the temperature has been a steady 40. As I type this, a little after 10:30 a.m., it is only 42.
This range is prime chilling. An hour between about 38 and 45 is a full “chill unit.” Hours below about 38 but above freezing count for somewhat less than a full chill unit. Above 45 it also tapers, with some chill models saying you need to subtract hours above 65 or so from your running count (I have some reservations about that, based only on my own monitoring, but it matters little in my current climate–at least for now). Stone fruits and other deciduous fruiting trees have a chilling requirement, varying by fruit variety. Many varieties I grow here do their best with over 500 hours (or “units”), and a few would like 600. The hours/units need to be consecutive, but extended warm spells in the winter can accelerate the process of breaking dormancy. If that happens before the variety’s chilling requirement is met, fruit set will be reduced or nonexistent.
At the moment of my writing, we have had 24 chill units in the past 24 hours, and probably 20 in the preceding 24 hours. According to the UCANR station nearest me, the season total stands at around 234 chill units. At this point last year, it was 264. Last winter was a very good one. As of early December, I was a little concerned about the current winter chill season, as it had been so mild. The UCANR station, for example, showed only 122 chill units as of 9 December, compared to 211 on the same date the previous year–and 3 vs. 39 back on Nov. 17! But starting on the 10th of December, we have been enjoying overnight lows anywhere from 30 (which means some hours of no chill) to mid-40s (the prime range) with only one early morning low above that. And our daytime highs during this spell have not broken 60 and generally have been in the low 50s, till the unusual 44 yesterday. A couple good weeks really can make up for a slow start!
I am pleased to announce the publication of a new article, “The Party Personnel Datasets: Advancing Comparative Research in Party Behavior and Legislative Organization Across Electoral Systems” in Legislative Studies Quarterly (open access), coauthored with Matthew E. Bergman (first author), Cory L. Struthers, Robert J. Pekkanen, and Ellis Krauss.
The article introduces the datasets used in the recently published book, Party Personnel Strategies(Oxford, 2021). The data include more countries and many more variables than were covered in the research reported in the book. The datasets themselves are available at the Dataverse.
Here is the article abstract:
This paper introduces eight country-level datasets with >50,000 observations that can be used to analyze novel comparative questions concerning party personnel strategies—how parties recruit candidates and allocate members across party, legislative, and cabinet positions. We make these datasets public to inspire comparative research, especially from an electoral systems perspective; electoral systems shape constituency representation and influence how parties recruit candidates and organize members in legislative and government bodies. In this paper, we first briefly review the relevant literature on electoral nomination and post-election appointment and then describe our motivations for constructing multi-country datasets that can be used to further comparative research. To illustrate the possibilities in these new datasets, we show how recruitment and placement of parliamentarians with particular personal characteristics correlates with their placement onto specific committees and cabinet posts. A conclusion identifies other areas of research that might benefit from using the party personnel datasets.
On 21 November, Chile held its first round presidential contest and elections for both chambers of congress. These elections come in the context of the ongoing process of a constitutional assembly, and thus are critical inasmuch as they elect the authorities who will be responsible for implementing the new constitution (assuming the assembly agrees on a text that is then approved by referendum). The outcome confirms the considerable fragmentation already apparent in the elections for the assembly itself earlier this year.
The presidential election is sending two candidates to the runoff that together won just over half the votes. In the lead coming out of the first round is José Antonio Kast, on 27.8%, followed by Gabriel Boric on 25.8%. The third place candidate was well back, on 12.80%, with another on 12.79%, the fifth place finisher on 11.6%, and two more rounding out the field. That is some considerable fragmentation.
It is a striking collapse of the center, as Kast is well to the right and Boric well to the left. It is pretty much the nightmare scenario for two-round majority election. While the runoff will require the winner to tack to the center to win, the occupant of the chief executive’s office will be quite extreme, whoever wins the runoff. He will then have to construct alliances in a fragmented congress, with whatever powers are granted in a new constitution.
The congressional outcome is so complex that I am not going to attempt to break it down in much detail. You can see the results for Deputies and Senators on the SERVEL website, or with helpful color coding by party and alliance on the Wikipedia page. In the Chamber of Deputies, the largest single party appears to be National Renewal (RN) with just 25 of the 155 seats. By alliance, the largest is Chile Podemos Más (of which RN is a part), with 53. This is a center-right combine associated with outgoing President Sebastián Piñera. (This alliance also has the most seats in the constitutional assembly elected in May, but that is just 37 of 155.) The alliance supporting Kast, Chritian Social Front, has a mere 15 Deputies in the newly elected Chamber. It won 11.2% of the vote, or about 40% of the vote its presidential candidate obtained–lots of ticket-splitting there. The alliance supporting Boric, Apruebo Dignidad, did a little better, with 37 seats (it has 28 in the constitutional assembly). It won 20.9% of the votes, which is 81% of its presidential candidate’s vote. The biggest party comprising this alliance is the Communist Party, which won 12 seats.
Needless to say, further alliance-building–both in advance of the presidential runoff and in the congress for whoever is elected–will be necessary. It also is going to be very interesting to see what changes might be introduced in the new proposed constitution to the executive structure and executive-legislative power balance. Negretto (2021) observes that constitutional assemblies that have no majority force tend to produce constitutions with more constraints on the executive than the previous constitution (referring to processes occurring within ongoing democracies). Given that the current Chilean constitution has one of the strongest presidencies anywhere, there is a lot of room for new constraints. How far will they go? I am not sure if a semi-presidential (let alone parliamentary) system is even on the table, but it probably should be. They should also consider moving either to a unicameral congress, or convert the senate into a more explicitly regional body with substantially diminished powers.
I recently learned of an electoral system design proposed by some activists in Canada. They call it “local PR“; I am not fond of the name, given that it plays into the argument that proportional representation threatens local representation, which I do not believe is a claim supported by the evidence–if it is MMP or, with pure PR, if district magnitude is not too large and/or there are preference votes. However, it may be very good branding, given that misconception of PR is so widely held.
I wonder what readers think of this idea. Basically, it is a form of PR with nominating districts, a model that has been discussed on the pages (leaves?) of this virtual orchard before–including by JD on Éric Grenier’s previous proposal for Canada, and in discussions of Romania, Slovenia and Denmark. However, in an important twist from those models–as I understand them–this proposal ensures every nominating districts has one of its local candidates elected, while still being proportional over the wider allocation districts (which combine existing single-seat districts). In this sense, the “nominating districts” are not just subdistricts in which candidates run–although they are definitely that–but also are single-seat electoral districts in the sense that each one has one and only one of its candidates elected within it. (Typical nominating-district PR can have either more than one candidate from a sub-district elected or can have some sub-districts with no local candidate elected (or both).) JD calls these systems “districted-ordered lists” which is also a fine moniker.
The specific proposal is to use ranked ballots, so it is a variant on STV. I am inclined to like the general goal behind the model, as it is highly compatible with my Emergency Electoral Reform for the US House. (In that, I push open-list PR, but I also point out my proposal could be done with STV.)
Probably the most important page for understanding what is being proposed is the one on “counting votes” (which is actually just as much about allocating seats). Two key paragraphs are:
The counting process under Local PR is done in rounds where each round elects one candidate. It maximizes the value of every ballot while keeping every candidate in the running as long as possible.
In each round, a riding is won by the first candidate to acquire the number of votes needed to win a seat [a Droop quota–ed.]. This is called reaching quota. If no candidate in the region reaches quota based on first ranked preferences (the “1”s), the ballots of the candidate with the fewest votes are redistributed to candidates who are next-ranked on these ballots. This is repeated until one of the remaining candidates reaches quota. Once a candidate reaches quota, he or she is elected and other candidates from the same riding are eliminated, concluding the round.
Subsequent rounds are started with all of the original candidates except those who have been eliminated from ridings with an elected candidate. Ballots for the eliminated candidates are redistributed to next-ranked candidates. The round continues until another candidate reaches quota. Rounds continue until one locally-nominated candidate has been elected in each riding.
There are important further details on that page that are worth your time if you are interested in exploring the idea.
I can see plenty of advantages, and also disadvantages (see JD’s post on the Grenier proposal for general criticisms of the wider family). Such is the nature of electoral system designs. It is always about tradeoffs. I am curious what regulars around here (as well as any always-welcome newcomers) think of it.
No reason here to doubt that the logical model, NS = s1–4/3, applies equally well to two-tier systems as it does to simple, single-tier systems. This was a question I raised in the earlier planting on the revision of the extended Seat Product Model (incorporating two-tier systems without an empirical constant).
Thus any deviations of regression output from the precise predictions of the models–as reported in that earlier post–are not caused by some systematic difference in this relationship for two-tier systems. Such deviations are just noise. For instance, the regression intercept on these 472 elections is significantly greater than zero. Yet a nonzero intercept is impossible. It can’t be that the effective number of parties is any different from 1.0 (the log of which is 0) if the largest party has 100% of the seats.* More to the point for the question I had, the regression shows no significant difference in slope (or intercept for that matter) between single-tier and two-tier systems. They behave the same in this sense, meaning that when the compensation tier increases the effective number of parties and reduces the seat share of the largest, it does so while preserving NS = s1–4/3, on average. And, by the way, for those who care about such things, the R2=0.899.
Bottom line: there is no statistically significant difference between single-tier and two-tier electoral systems in how the effective number of parties is related to the size of the largest.
* If I suppress the constant (while also eliminating the binary for “simple”) the coefficient is –1.341, or almost precisely the logically required –4/3. When run with the constant, it is –1.235, but the 95% confidence interval includes –1.333.
In the previous planting, I presented a revised version of the extended Seat Product Model. I noted that in the process of attempting to improve on the logical model, I discovered some inconsistencies in the treatment of remainder pooling systems in the dataset used in Votes from Seats. Here I describe the problem and how I corrected it. The changes here may still require further refinement, but at least they make the treatment of the cases internally consistent.
This first began to bother me even before Votes from Seats had been published. Figure 17.2 in the book shows how well (or not) the extended seat product model accounts for the effective number of seat-winning parties (NS) over time in several two-tier PR systems (plus Japan, included despite not fitting the category for reasons explained in the book). It plots every election in the dataset for this set of countries, with the observed value of NS shown with the solid grey line in each country plot. The expectation from the extended Seat Product Model (Equation 15.2) is marked by the dashed line. This equation is:
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 countries that changed from simple to complex, the plots also show the expectation in the era of the simple system with the solid dark line. The troublesome case here is Austria, but why? That is my “Austrian Question.” It led me down quite a rabbit hole, but I think I have it figured out, more or less.
It always seemed unlikely that the design of the Austrian electoral system was such that expectedNS could have reached well over 6 in the latter part of the time series! But that is what our data showed, supposedly. When you get an absurd result, generally you should impeach the data, not the model.1
The problem turned out to be that for several remainder-pooling systems, including Austria, some seats were effectively counted twice in the derivation of the extended seat product. We drew most of our data from Bormann and Golder’sDemocratic Electoral Systems Around the World. However, the manner in which we did so handled remainder-pooling systems poorly. With one important exception that I will note below, the error was not in the original data, but in our application of it.
In a remainder-pooling system there is no fixed upper tier. Most two-tier compensatory systems have a fixed number of seats which are allocated nationally (or regionally) to “correct” for distortions in votes-to-seats allocation produced by the lower district magnitude of the basic tier. An example would be the system of Denmark, with 139 basic-tier seats and 40 compensatory seats. Others have a fixed minimum, such as the MMP systems of Germany and New Zealand (where the upper tier can expand if needed due to “overhang” seats, but it has a fixed starting size). In a remainder-pooling system, on the other hand, the “upper tier” can be as large or as small as needed to generate compensation. In theory, all seats could be allocated in the basic tier, and it would end up no different from a simple system. Typically these systems work by stipulating that parties earn seats based on full quotas (usually Hare quota, sometimes Hagenbach-Bischoff) in the districts. Any seats not filled are then “pooled” in a supra-district tier where they are allocated based on pooled votes, rather than being filled within districts. The upper tier is thus whatever number of remainder seats there are from all of the districts, which can vary from election to election depending on how votes are distributed among the parties and across the basic-tier districts.
A particular challenge in the analysis of these systems is that all seats may be attached to districts, and national reporting agencies vary in whether they indicate that a given seat is actually based on supra-district allocation. Thus a district might have, say, five seats, and in the determination of quotas, two parties may have obtained a total of three seats through quotas in the district. The other two seats go to the remainder pool. Maybe, once all the national seat allocation is complete, one of those two remainder seats goes to the largest party (bringing it up to three) and one goes to a third party that was short of a quota in the initial allocation. The complication is that while all five seats are assigned to candidates who were on party lists in the district, only three were assigned based solely on votes cast in the district. The other two were assigned according to the compensation mechanism, drawing upon the pooled votes from across multiple districts. Where is the upper tier? It is sort of a phantom, and if we count the two seats in our hypothetical example as part of the upper tier, and we also count them as part of the district (basic tier), we have double counted them!
Here is where the Austrian case comes in. If we look at the 1990 election, we see an assembly size of 183, with 9 basic-tier districts, averaging 20.3 seats apiece. Bormann and Golder report that 25 seats were allocated as “upperseats”. In our Equation 15.2, the input parameters were MSB=20.3*(183–25)=3207 (rounding off) and t=(25/183)=0.137. That is, the basic-tier seat product is mean district magnitude multiplied by the size of the basic tier (which is total assembly size minus upper seats). But hold on! Those 25 upper-tier seats are taken out of the 20.3 seats per (average) district. Yet our original calculation takes them only out of the “S” part, but not out of the “M” part. They should not be counted in both tiers! Those 25 seats came from the 9 districts, so 25/9=2.8 remainder seats per district, on average. This gives us an adjusted basic-tier M=20.3–2.8=17.5. Now we have MSB=17.5*(183–25)=17.5*158=2765, and t=0.137. This changes the “expected” NS (based on Equation 15.2) from 4.35 to 4.25. Not a huge difference, but one that more accurately reflects how the system actually works.
Where things really went haywire was with the electoral reform that took place before the 1994 election. The Bormann and Golder dataset correctly notes that the number of basic-tier districts was increased to 43. With S=183 unchanged, this is a mean district magnitude of M=183/43=4.26, a figure which matches the description in Electoral System Change in Europe, maintained by Jean-Benoit Pilet and Alan Renwick. However, for some reason, the Bormann and Golder gives first-tier mean district magnitude for the post-1992 system as 17.2. The indicated values of “upper seats” range from 78 to 111 in the elections of 1994–2008. When we apply the same procedures of the preceding paragraph to elections in these years, we get a reduction in MSB from the 2669 we used in the book to a more accurate 196.7. That is quite a change! It comes from the reduction in district magnitude to 4.26, which in turn greatly pushes up the number of seats allocated in upper tiers.2 When we stop double counting the remainder seats, we actually have an adjusted basic-tier magnitude of less than 2, and an upper tier ratio, t=0.5. This changes that rather absurd “expected NS” depicted in Figure 17.2 as 6.3 for recent elections to a more reasonable 3.83. And, in fact actually observed NS in recent years has tended to be in the 3.4–4.2 range.
Here is the corrected version of the figure. (I left Japan off this one.) In addition to using the corrected data, as just explained, it also uses the revision of the extended Seat Product Model:
NS = (1–t)–2/3(MSB)1/6.
Austria is no longer shown as system that should be “expected” to have an effective number of parties around six! It still has an observed NS in most years that is smaller than expected, but that’s another story. We are not the first to observe that Austria used to have an unusually consolidated party system for its electoral system.3 In fact, in recent years it seems that the revamped design of the system and the increasingly fragmented party system have finally come into closer agreement–provided we use the revised SPM (as explained in the previous planting) and the corrected electoral-system data, and not the inconsistent data we were using before.
And, here for the first time, is a graph of largest party seat share in these systems, compared to expectations. This seemed worth including because, as noted in the previous planting, the s1 model for two-tier works a little better than the one for NS. Moreover, it was on s1 that the revised logic was based.
Note that the data plots show a light horizontal line at s1=0.5, given the importance of that level of party seat share for so much of parliamentary politics.
1. Assuming the model is on solid grounds, which was very much not the case of the original version of application to two-tier PR. I hope it is now, with the revision!
2. Plural because the 9 provincial districts still exist but are now an intermediate compensation tier, and there is a single national final compensation tier. This additional complication should not affect our estimation of the system’s impact on party-system outputs. (It principally affects which candidates from which of a given party’s lists earn the various compensation seats.)
3. This is not unique to Austria. Several European party systems used to have effective number of parties smaller than expected for their electoral system. In recent decades, many have become more fragmented, although the fragmenting trend is not significant, when compared to the SPM baseline). The trend implies that, in many cases, their electoral systems are shaping their party systems more as expected now than in the early post-war decades. In the past, the full electoral system effect may have been tamped down by the stronger role of the major party organizations in society. This is a very big question that it far beyond the scope of my current tasks.
In order to attempt a further validation of the procedure, I calculated the number of quota seats expected in each district based on my district-level dataset, derived originally from CLEA. I can then sum this up across districts in a given election, and subtract the result from the total assembly size to arrive at an indicator of what the upper-tier size should have been in that election. When I do this, I usually come close to the value for “upperseats”in Bormann & Golder, although not always precisely. I do not know what explains the deviations, but in all but one election they are so small that I would not fret. For the two elections used as examples from Austria above, I get 24 remainder-pooled seats in 1990 (vs. B&G 25) and 111 in 2008 (identical to B&G). Ideally, we would be able to estimate what upper-tier seats should be, on average, for a given design of a remainder-pooling system. Then we could estimate the parameters needed for the extended SPM even if data sources do not separate out the seats allocated on district votes from those allocated via supra-district pooling. This would introduce some unknown error, given that the actual number of remainder-pooled seats can vary depending on election results, for constant institutions. For instance, for the current Austrian system, it has ranged from 81 to 111 between 1995 and 2008. Perhaps there is some mathematical relationship that connects this average (92) to fixed parameters of the electoral system, and that works across remainder-pooling electoral systems. If there is, it has not revealed itself to me yet.
The extended version of the Seat Product Model (SPM), devised to be applicable to two-tier PR systems as well as simple electoral systems, states:
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. In the case of a simple (single-tier) system, this reduces to the basic SPM: NS =(MS)1/6, given that for simple systems, by definition, t=0 and SB=S, the total size of the elected assembly.
Ever since this formula first appeared in my 2016 Electoral Studiesarticle with Huey Li (and later as Equation 15.2 in Shugart and Taagepera, 2017, Votes from Seats) I have been bothered by that “2.5.” The SPM for simple systems is a logical model, meaning its parameters are derived without recourse to the data. That is, the SPM is not an empirical regression fit, but a deductive model of how the effective number of seat-winning parties (and other electoral-system outputs) should be connected to two key inputs of the electoral system, if certain starting assumptions hold. When we turn to statistical analysis, if the logic is on the right track, we will be able to confirm both the final model’s prediction and the various steps that go into it. For simple systems, such confirmation was already done in Taagepera’s 2007 book, Predicting Party Sizes; Li and Shugart (2016) and Shugart and Taagepera (2017) tested the model and its logical antecedents on a much larger dataset and then engaged in the process of extending the model and its regression test in various ways, including to cover more complex systems. Yet the derivation of the “2.5” was not grounded in logic, but in an empirical average effect, as explained in a convoluted footnote on p. 263 of Votes from Seats (and in an online appendix to the Li-Shugart piece).
If one is committed to logical models, one should aim to rid oneself of empirically determined constants of this sort (although, to be fair, such constants do exist in some otherwise logical formulas in physics and other sciences). Well, a recent Eureka! moment led me to the discovery of a logical basis, which results in a somewhat revised formula. This revised version of the extended Seat Product Model is:
NS = (1–t)–2/3(MSB)1/6.
The variables included are the same, but the “2.5” is gone! This revision produces results that are almost identical to the original version, but stand on a firmer logical foundation, as I shall elaborate below.
Consider a few examples for hypothetical electoral systems.
NS (Eq. 15.2)
It may not work especially well with very high MSB, or with t>>.5. But neither does equation 15.2 (the original version); in fact, in the book we say it is valid only for t≤0.5. While not ideal from a modelling perspective, it is not too important in the real world of electoral systems: cases we would recognize as two-tier PR rarely have an upper compensation tier consisting of much more than 60% of total S; relatedly, SB much greater than around 300 is not likely to be very common. My examples of MSB =2,500 are motivated by the notion of SB=300 and a decently proportional basic-tier M=8.3.
Testing on our dataset via OLS works out well, for both versions of the formula. Our largest-sample regression test of Equation 15.2, in Table 15.1 of Votes from Seats, regression 3, yields:
log NS = –0.066 + 0.166log MSB + 0.399t .
Logically, we expect a constant of zero and a coefficient of 0.167 on the log of MSB; the coefficient on t is expected to be 0.398=log2.5 (but as noted, the latter is not logically based but rather expected only from knowledge of relationships in the data for two-tier systems). In other words, it works to almost point predictions for what we expected before running the regression! Now, let’s consider the revised formula. Using the same data as in the test of Equation 15.2 in the book, OLS yields:
log NS = –0.059 + 0.165log MSB – 0.654 log(1–t) .
Again we expect a constant at zero and 0.167 on log MSB . Per the revised logic presented here, the coefficient on log(1–t) should be –0.667. This result is not too bad!1
OK, how did I get to this point? Glad you asked. It was staring me in the face all along, but I could not see it.
I started the logical (re-)modeling with seat share of the largest party, s1, as it was easier to conceptualize how it would work. First of all, we know that for simple systems we have s1= (MS)–1/8; this is another of the logical models comprising the SPM and it is confirmed statistically. So this must also be the starting point for the extension to two-tier systems (although none of my published works to date reports any such extended model for s1). Knowing nothing else about the components of a two-tier system, we have a range of possible impact of the upper-tier compensation on the basic-tier largest party size (s1B). It can have no effect, in which case it is 1*s1B. In other words, in this minimal-effect scenario the party with the largest share of seats can emerge with the same share of overall seats after compensation as it already had from basic-tier allocation. At the maximum impact, all compensation seats go to parties other than the largest, in which case the effect is (1–t)*s1B. A fundamental law of compensation systems is that s1 ≤ s1B. (and NS ≥ NSB); by definition, they can’t enhance the position of the largest party relative to its basic-tier performance.2
Let’s see from some hypothetical examples. Suppose there are 100 seats, 50 of which are in the basic tier. The largest party gets 20 of those 50 seats, for s1B = 0.4. If compensation also nets it 20 of the 50 compensation seats, it emerges with 40 of 100 seats, for s1=0.4 = 1*s1B. If, on the other hand, it gets none of the upper-tier seats, it ends up with 20 of 100 seats, for s1=0.2 = (1–t)*s1B. For a smaller t example… Suppose there are 100 seats, 80 of which are in the basic tier, and the largest gets 32 seats, so again s1B = 0.4. If compensation nets it 8 of the 20 compensation seats (t=0.2), it emerges with 40 of 100 seats, for s1=0.4 = 1*s1B. If, on the other hand, it gets none of the upper-tier seats, it ends up with 32 of 100 seats, for s1=0.32 = (1–0.2)*s1B = 0.8*0.4=0.32.
In the absence of other information, we can assume the upper tier effect is the geometric average of these logical extremes (i.e, the square root of the product of 1 and 1–t), so:
and then because of the established relationship of NS = s1–4/3, which was also posited and confirmed by Taagepera (2007) and further confirmed by Shugart and Taagepera (2017), we must also have:
NS = (1–t)–2/3(MSB)1/6.
Testing of the s1 formula on the original data used for testing Equation 15.2 is less impressive than what was reported above for NS, but statistically still works. The coefficient on log(1–t) is actually 0.344 instead of 0.5, but its 95% confidence interval is 0.098–0.591. It is possible that the better fit to the expectation of NS than that of s1 is telling us that these systems have a different relationship of NS to s1, which I could imagine being so. This remains to be explored further. In the meantime, however, an issue with the data used in the original tests has come to light. This might seem like bad news, but in fact it is not.
The data we used in the article and book contain some inconsistencies for a few two-tier systems, specifically those that use “remainder pooling” for the compensation mechanism. The good news is that when these inconsistencies are corrected, the models remain robust! In fact, with the corrections, the s1 model turns out much better than with the original data. Given that s1 is the quantity on which the logic of the revised equation was based, it is good to know that when testing with the correct data, it is s1 that fits revised expectations best! On the other hand, the NS model ends up being a little more off.3 Again, this must be due to the compensation mechanism of at least some of these systems affecting the relationship of s1 to NS in some way. This is not terribly surprising. The fact that–by definition–only under-represented parties can obtain compensation seats could alter this relationship by boosting some parties and not others. However, this remains to be explored.
A further extension of the extended SPM would be to allow the exponent on (1–t) to vary with the size of the basic tier. Logically, the first term of the right-hand side of the equation should be closer to (1–t)0=1 if the basic tier already delivers a high degree of proportionality, and closer to (1–t)1=1–t when the upper tier has to “work” harder to correct deviations arising from basic-tier allocation. In fact, this is clearly the case, as two real-world examples will show. In South Africa, where the basic tier consists of 200 seats and a mean district magnitude of 22.2, there can’t possibly be much disproportionality to correct. Indeed, the largest party–the hegemonic ANC– had 69% of the basic tier seats in 2009. Once the compensation tier (with t=0.5) went to work, the ANC emerged with 65.9%. This is much less change from basic tier to final overall s1 than expected from the equation. (Never mind that this observed s1 is “too high” for such a proportional system in the first place! I am simply focusing on what the compensation tier does with what it has to work with.) The ratio of overall s1 to the basic-tier s1B in this case is 0.956, which is approximately (1–t)0.066, or very close to the minimum impact possible. On the other hand, there is Albania 2001. The largest party emerged from the basic tier (100 seats, all M=1)4 with 69% of the seats–just like in the South Africa example, but in this case that was significant overrepresentation. Once the upper tier (with t=0.258) got to work, this was cut down to 52.1%. The ratio of overall s1 to the basic-tier s1B here is 0.755, which is approximately (1–t)0.95, or very close to the maximum impact possible given the size of the upper tier relative to the total assembly.
These two examples show that the actual exponent on (1–t) really can vary over the theoretical range (0–1); the 0.5 proposed in the formula above is just an average (“in the absence of any other information”). Ideally, we would incorporate the expected s1 or NS from the basic tier into the derivation of the exponent for the impact of the upper tier. Doing so would allow the formula to recognize that how much impact the upper tier has depends on two things: (1) how large it is, relative to the total assembly (as explained by 1–t), and (2) how much distortion exists in the basic tier to be corrected (as represented by the basic-tier seat product, MSB).
However, incorporating this “other information” is not so straightforward. At least I have not found a way to do it. Nonetheless, the two examples provide further validation of the logic of the connection of the impact through 1–t. This, coupled with regression validation of the posited average effect in the dataset, as reported above, suggests that there really is a theoretical basis to the impact of upper-tier compensation on the basic-tier’s seat product, and that it rests on firmer logical grounds than the “2.5” in the originally proposed formula.
This a step forward for the scientific understanding of two-tier proportional representation!
In the next installment of the series, I will explain what went wrong with the original data on certain two-tier systems and how correcting it improves model fit (as it should!).
1. The reported results here ignore the coefficients on the log of the effective number of ethnic groups and the latter’s interaction with the the log of the seat product. These are of no theoretical interest and are, in any case, statistically insignificant. (As explained at length in both Li & Shugart and Shugart & Taagepera, the interaction of district magnitude and ethnic fragmentation posited in widely cited earlier works almost completely vanishes once the electoral-system effect is specified properly–via the seat product and not simply magnitude.)
2. Perhaps in bizarre circumstances they can; but leave these aside.
3. This is what we get with the corrected data, First, for seat share of the largest party:
log s1 = 0.047 – 0.126log MSB + 0.433 log(1–t) .
(Recall from above that we expect a constant of zero, a coefficient of –0.125 on log MSB and 0.5 on log(1–t).)
For effective number of seat-winning parties:
log NS = –0.111 + 0.186log MSB – 0.792 log(1–t).
Both of those coefficients are somewhat removed from the logical expectations (0.167 and –0.667, respectively). However, the expectations are easily within the 95% confidence intervals. The constant term, expected to be zero, is part of the problem. While insignificant, its value of –0.111 could affect the others. Logically, it must be zero (if MSB=1 and t=0, there is an anchor point at which NS =1; anything else is absurd). If we suppress the constant, we get:
log NS = 0.152log MSB – 0.713 log(1–t).
These are acceptably close (and statistically indistinguishable from expected values, but then so were those in the version with constant). Nonetheless, as noted above, the deviation of this result from the near-precise fit of most tests of the SPM probably tells us something about the relationship between s1 and NS in these two-tier systems. Just what remains to be seen.
The article also has interesting angles in Party Personnel and federalism. The politician profiled is André Lamontagne, currently the Quebec Minister of Agriculture for the government of the Coalition Avenir Québec. In his pre-political career Lamontagne was, among other things, a supermarket owner. He is referred to in the article as “a rare minister interested in how food is processed and sold, rather than just how it’s grown.”
He is currently deeply involved in federal–provincial–territorial (FPT) bargaining over a better deal for food suppliers, touched off by fees imposed by Walmart that trade association Food Health and Consumer Products of Canada called “diabolical“. Other big companies in the food retail business sought to join suppliers to initiate policy changes that would lead to a code of conduct for how much grocery chains could charge suppliers for “for a range of perks or infractions, including product promotions and penalizing late or incomplete shipments.”
Implementing such a thing, however, was a bit harder, even as political pressure mounted. Conservative agriculture critic Lianne Rood repeatedly asked about the subject in question period, but the government determined a code was out of federal jurisdiction, since regulating terms of sale is a provincial issue.
…The thought of 10 different regulations stretched across a national food supply chain wasn’t appealing, so [federal] agriculture minister [Marie-Claude] Bibeau suggested the federal government could help coordinate a more coherent response across the country.
To do that, the feds needed a provincial ally to help champion the issue through the FPT.
Minister Lamontagne says, “For me, it was very easy to understand what was happening,” given his background. So he became that provincial ally. His involvement in this issue thus offers a mini-case study in how parties might harness the prior experience of their politicians to advance a given policy reform, as well as a good case of the role of federalism in the political economy of food.
Increasing numbers of local councils in New Zealand are switching to the single transferable vote (STV) system. An article by Tim Newman, Nelson Reporter (via Stuff), indicates that in “2022 Nelson will be one of 15 councils using the STV system, and one of four adopting it for the first time.”
The Nelson version of STV (which the article indicates is approved but still subject to an appeal process) will be somewhat more complex than I would think necessary.
Under the new model two general wards have been set up, Central and Stoke-Tāhunanui , with four councillors to be elected per ward. For each ward, the population per councillor will be approximately 6400.
Running parallel to the general wards will be the Whakatū Māori Ward, which covers the whole city and will only be eligible for those on the Māori Roll.
One councillor will be elected from this ward, which has a population per councillor of about 3300.
In addition to the wards, there will also three “at-large” councillors representing the whole city. The mayor will also be voted at large.
So if I am understanding this correctly, it will be doubly parallel. For electing the 12 council members there are both districts (wards) and a citywide component in addition to the Maori special district. And all by STV, except maybe the single Maori member (it is not clear if this is by STV (AV) or not). One would think they could simply use STV–either citywide or in districts–with a rule ensuring a minimal number of those elected are Maori. Or, slightly more complex than that, but less than what is now likely to be adopted, two sets of districts–general and Maori–but not three.
The current system seems to be MNTV, but the article is a little confusing on this point. It says:
In previous elections, voting in Nelson has been conducted “at large”, meaning that voters could vote for any of the 12 council candidates standing for election, along with mayoral candidates.
I am taking that to mean the voter had 12 votes and the top 12 were elected, but I wish it was clearer. The adoption of STV is a positive development, even if it has been done with more complex districting than seems necessary.