The output indicators for Italy 2022: Yes, MMM in a smaller assembly really mattered

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.

2018 Party2018 Bloc2022 Party2022 Bloc
D2 (%)3.985.027.3011.74

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.


  1. 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.
  2. 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 2022

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.



  1. 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.
  2. 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.

The effects (or their lack) of fused presidential–assembly ballots

A question that has arisen* is whether fused ballots–a single vote electing president and assembly, i.e., with no opportunity for ticket-splitting–suppress the number of parties, particularly when the president is elected by plurality and assembly by PR.

A challenge in addressing this question is that fused ballots are rather rare. Moreover, they may be adopted/abolished by ruling parties/coalitions based on expectations of advantage. In other words, the direction of causality between party-system outputs and rules is more ambiguous than usual. With such caveats reiterated, here is what I find.

This is for pure presidential systems, only because I am not aware of cases of semi-presidential systems that fuse presidential and assembly votes. (In parliamentary systems, the option does not arise, or in a sense the vote is always fused. I did not include the brief case in Israel of separate and direct election of an executive who was still responsible to the parliamentary majority.)

My outcome of interest is the ratio of expected effective number of seat-winning parties (NS) or seat share of the largest party (s1) to the expectation, given the seat product of the assembly (first chamber) electoral system.

For NS, the ratio in non-fused cases is 1.13, for fused it is 0.927. This looks like good news for the hypothesis that fused ballots restrict party systems more than the separate vote does. However, the difference is not close to significant (p=0.12).

For s1, the ratio in non-fused is 1.012, and in fused it is 1.047. Obviously that’s not significant. (Also, the seat product model is pretty good–even for presidential systems!)

Note that for NS, the mean assembly party system in a presidential democracy tends to be more fragmented than expected from its electoral system. Probably not what most people expect. Perhaps this is driven by the unusually fragmented case of Brazil. If I take it out, the ratios in non-fused are 1.083 for Ns and 1.031 for s1. So not much impact.

Perhaps one should drop Uruguay from the set of fused cases. Not because ballots are not clearly fused, but because the electoral system is so different. Before 1999, parties could present multiple presidential candidates (and pool votes at party level for determining which party would win), and since then the fused ballot is only for the first round of a two-round presidential election. However, if we do this, we have only four cases left, so it is kind of meaningless. For the record, we would then have about a p=0.1 signifiant result in the expected direction. But I would put no stock in a result comparing four elections (in two countries) in one group to over 150 in the other group!

This is the list of cases with fused ballots that I am using. If I missed some, please let me know. (Angola, the case that prompted me to investigate this, is not in the dataset, nor are other countries that are not generally classified as democratic.)

      country   year  
Dominican Rep   1978  
     Honduras   1993  
     Honduras   1997  
     Honduras   2001  
      Uruguay   1989  
      Uruguay   1994  
      Uruguay   1999  
      Uruguay   2004  
      Uruguay   2009  
      Uruguay   2014  
      Uruguay   2019  

To this list could be added Bolivia. However, I did not include it because elections for president were not direct before 2005 (congress chose from top three if the popular vote did not yield a majority) and since 1997 the fusion has been only between the presidential vote and the party list vote of an MMP system.

(* A version of this text was originally posted as a comment in a thread on Angola, but it seemed to warrant a place in the center row of the virtual orchard.)

Chile’s constitutional referendum

It seems Chile’s voters are quite decisively rejecting the proposed new constitution. Turnout was high.

Such a result would be quite an indictment of the entire process. Others may know better than I would, but I would imagine it is unusual in a democracy for a constitutional-replacement project to result in failure at its final stage. The constituent assembly evidently did a poor job at looking down the game tree and discerning what the public would accept.

In an earlier thread, there has been a discussion ongoing about the constitution, and a link to the draft (both Spanish and English).

Fifty Shades of Republic | Part 3: constitutional amendment rules

This post is part of Fifty Shades of Republic, a series of overviews of US political institutions at the state level

While the Federal Constitution is arguably the world’s oldest national constitution, the states were the ones that began the practice of having ‘written’ constitutions – entrenched laws with a higher status than regular laws, establishing the main features of the system of government. Since I’ve been doing some work on constitution amendment rules (of both national and US state constitutions) for my dissertation, I thought I’d do this topic next (it is also closely related to the topic of a podcast I am currently preparing for Leviathan’s Couch).

The amendment procedure has far-reaching effects. John Burgess, one of the 19th century pioneers of political science, argued it to be the most important part of a constitution. Constitutional amendment procedures entrench written constitutions, making them harder (or, at least, different) for politicians to change than regular laws. Entrenchment is meant as a means to provide the system of government with stability and to protect basic rights from change by temporary majorities. However, it also often leads to the constitutional entrenchment of various policy measures that do not pertain to the state’s basic institutions, either as a result of opportunistic coalitions seeking to protect legislation from future change or because restrictive provisions in the constitution make the incorporation of contradictory provisions into the constitutional text the easiest way of passing certain policies. Lastly, entrenchment is also an important driver of the power of the judiciary (to whom enforcement of the constitutional hierarchy is delegated).

Most US states have two or more of the following tracks to initiating a constitutional amendment: by the legislature, by a voter initiative, or by constitutional convention. The final stage is almost always ratification by voters in a referendum.

Map 1: legislative and voter initiative tracks to amendment – click for full size


Supermajorities – 28 states today require a supermajority for passage in the state legislature. 22 only require regular majorities (simple or absolute) before going to referendum.

Of those only requiring approval by one legislature:

  • 10 states (turquoise) require a majority in both houses
  • 9 states (blue) require 3/5 in both houses
  • 16 states (dark blue) require 2/3 in both houses.

Of those requiring intervening elections:

  • 11 states (pink) require a majority in both houses before and after the elections
  • 3 states (red) require a 2/3 supermajority at one stage but not both. In Tennessee, the votes after the election must be by 2/3 in both houses; in Vermont, the amendment must be supported by 2/3 before the election, although only in the state Senate. South Carolina (dark red) requires 2/3 in both houses, after which the amendment is put to the voters at the following election. The referendum, however, is not final; it the amendment is approved, the newly-elected legislature must ratify it by majority vote in both houses.
  • Delaware (green) requires 2/3 in both houses both before AND after the intervening election, with no referendum requirement.

Intervening elections – 15 states require approval by two legislatures separated by intervening elections (shown on the map in various shades of red). A few of those states allow this requirement to be bypassed by supermajority support in the legislature (shown by a blue asterisk, with the shade of blue corresponding to the required supermajority (in states without intervening election requirement – see below) – only exception being Connecticut, where ¾ is needed to bypass the intervening election requirement). Since main idea behind this institution is often said to have been to allow voters input on constitutional amendments through the election process, many states that had this feature in earlier constitutions removed it when introducing ratification of amendments by referendum, but many have kept it nonetheless.

Initiative – Currently, 17 states allow voters to propose amendments to referendum by petition (indicated by a capital letter I on the map). The exact signature requirements vary widely from state to state. This provision originated in the Progressive era, although a few states introduced it later.


Referendum – the referendum requirement became a near-universal feature by the time of the Civil War. In states that did not have it to begin with, it often replaced requirements for intervening elections and/or assembly supermajorities. Referendums today require a majority to ratify in almost all states; the denominator is sometimes simply the number of valid votes on the respective amendment question, but in some states it is the more demanding number of people voting at the election, so that ballots left blank count as a ‘no’. In a few states a supermajority is required for some or all amendments, e.g. in Colorado, 55%, in New Hampshire, 2/3.

Legislative vote – today, Delaware (in green) is the only state not to require voter approval for constitutional amendments – the second round of 2/3 vote in the legislature makes an amendment part of the constitution. As noted above, South Carolina does require voter approval, but an amendment approved by voters is still subject to a final (majority) vote by both houses.

Map 2: constitutional convention track to amendment (or replacement) – click for full size

Legislative convention call – In 6 states, the legislature can directly order the election of a constitutional convention (without needing voter approval) by either majority (light green) or supermajority (green) in both houses.

Legislative convention proposal – In 30 states, a convention call by the legislature must be ratified by voters. In some states the proposal can be made is by a majority (light purple), in others by supermajority (purple) in both houses. In Pennsylvania, there is precedent for this, even though the state constitution does not provide for it.

Ambiguous, referendum required – In 3 states, the constitution requires the summoning of a constitutional conventions to be approved by voters, but is silent on whether the legislature can propose this (pale blue).

Automatic ballot question – In 14 states, a convention proposal must be placed before voters at least once every certain number of years. This is indicated on the map by the specific number of years in each case.

Initiative – In 17 states, voters can initiate the summoning of a convention, either by the constitution’s explicit provision or by virtue of the possibility of proposing one using the procedure for initiating amendments. This is indicated by a capital letter I on the map.

No provision – in 11 states, the constitution does not provide for the calling of a constitutional convention (grey) nor does the state have any established practice. De facto, each of these state legislature could summon a convention by means of the regular amendment procedure.

Constitutions are usually silent on the conditions for conventions’ proposals to be made or ratified, with the exception of requiring a referendum as on ‘regular’ amendments. A few noteworthy exceptional provisions include Illinois’ requirement for 60% voter approval for any kind of convention proposal to be successful, New Hampshire’s requirement for amendments to be proposed by 3/5 vote of the convention, and Minnesota’s requirement for 60% voter approval to ratify any amendment proposed by a convention.

International comparisons

While explicit constitutional recognition of a convention route is somewhat unusual, state constitutions’ regular amendment procedures in state constitutions are very comparable to those of many national constitutions around the world. Here are a few essentially exact parallels:

  • Minnesota, Rhode Island – Ireland (majority + referendum)
  • Texas, Maine – Japan, Romania (2/3 + referendum)
  • Oregon, Arkansas – Switzerland (majority + referendum, initiative option)
  • New York, Virginia – Denmark (majority + election + majority + referendum)

However, there are some clear differences, as well. Around the world, amendment procedures that do not require direct voter approval are far more common than among US states. In fact, most democracies today do not require a referendum at all. Meanwhile, many other democracies have a referendum as just one potential method of ratification – an alternative to a legislative supermajority (so not an absolute requirement), or required for some changes but not all.

Meanwhile, it’s internationally rare for referendums to be combined with an intervening election requirement (especially when further combined with supermajorities). I just gave the example of Denmark, but I think it’s the only one, at least for the main amendment procedure; Spain has a procedure for 2/3 legislative vote before and after an election, followed by a referendum, but this procedure is reserved for amendments to the chapters on fundamental rights and the Crown.

Angola 2022: What (effective) seat product and impact on the outcome?

Earlier this week, in trying to understand the Angolan electoral system, I was unsure whether the allocation of the national list seats was compensatory, or in parallel to the provincial district results. In the comments, Miguel was kind enough to quote the relevant sections of the electoral law, confirming that allocation is parallel.

The results show the ruling MPLA won 51% of the vote and the main opposition UNITA 44%. I will take these as given, and not speculate on whether they are the “real” vote totals or a product of “electoral alchemy.” Rather, I am interested in whether the translation of these votes into seats suggests the MPLA chose a system that would benefit it considerably, or not.

The MPLA has won 124 of the 220 seats. That is 56.3% of the seats, for an advantage ratio (%seats/%votes) of 1.10. How does this compare with an “average” electoral system? I checked my dataset, restricting it to “simple” systems, even though Angola’s is not simple, and to those that are not FPTP or other M=1. The average across 377 such elections is… 1.12.

In other words, if the MPLA was trying to give itself a considerable seat advantage from this electoral system design, it kind of failed.

There is certainly one aspect of the electoral system design that looks like “rigging” via the rules: The provincial tier is highly malapportioned. The 18 provinces vary widely in population, yet each elects five members. See the images with preliminary vote totals in another comment from Miguel or see the CNE site, which also includes seats now. Given the use of D’Hondt at this level and the ample margins in rural provinces, the MPLA won 4-1 in several districts (and 5-0 in one)1 and 3-2 in all others aside from the three where UNITA was ahead. (UNITA won 4-1 in Cabinda.)

What undermines the MPLA’s own advantage considerably is the nationwide list component, which constitutes just under three fifths of all the seats (and uses Hare quota and largest remainders). If the MPLA had really wanted to create a system to advantage itself, it could have done so by making this tier smaller, or by various other designs.

I do note that UNITA is somewhat underrepresented. Its 90 seats is 40.9%. Given 44% of the votes, its advantage ratio is 0.928. Across a subset of electoral systems fitting the criteria I referred to above, this is quite low. In fact, the average for second parties is 1.075. (Subset because my dataset does not currently have second party shares for all elections; there are 147 elections here.)

In this sense, the electoral system’s design did indeed punish the main opposition. So if this was the MPLA goal, mission accomplished. The malapportionment must be a main cause of this, combined with the parallel (non-compensatory) allocation of the national seats. It should be noted as well, however, that with only two big parties, if one is overrepresented even a little bit (as the MPLA was), the second will probably be more underrepresented than would be the case in a multiparty system more typical of PR electoral systems.

Interestingly, much of the disadvantage to UNITA went to the advantage of smaller parties instead of to MPLA. There were three other parties, each of which won 2 seats. Two seats is 0.91% of the assembly; these parties had from 1.14% to 1.02% of the votes apiece. These small parties won only in the national district, where the only threshold was that a party could not win a seat by remainder unless it had already won a seat.2 Given that the national district is 130 seats, it could easily have supported even more parties than the five that won at least 2 seats. The largest party to win no seats had 0.75%. A simple quota for this district would be 0.769%, so this party was below the weak threshold anyway.

The effective numbers of parties were 2.20 by votes and 2.06 by seats–note not much difference there.3 The deviation from proportionality (Gallagher’s “least squares index”) was 4.44%. The latter figure, using again my set of simple non-FPTP systems, is not much different from average (4.87%). So all in all, despite the unusual electoral system, it is not a terribly remarkable result in terms of election indices.

As far as the effective seat product is concerned, for a parallel system I have found the satisfactory method is to take the geometric mean of what we would get if the basic tier were the entire system and what we would get if the system were compensatory. The seat product of the basic tier of this system is straightforward: district magnitude of 5, times tier size of 90 gives us 450. The formula for compensatory based on these parameters (an update and slight modification of a method I have shown here before) would yield an effective seat product of 3844. But because it is actually parallel, we take the geometric average of these values, which is 1315.

An effective seat product of 1315 is in the general range of the simple seat product Norway had (1297) before it adopted a small compensatory tier after 1985, or Peru’s in 1980 or 1985 (1296), and also not much smaller than Switzerland’s (1540).4

The disproportionality we should expect from an effective seat product of of 1315 would be around three percent; the actual 4.4% is thus not too much higher. The seat share of the largest party in this election is about 1.4 times expectation5 from such a seat product and the effective number of seat-winning parties is about 0.62 the expectation. Obviously, this is due to MPLA political dominance. Or perhaps due to unfair vote reporting. That I can’t say. What I can say is that, despite a fairly unusual combination of extreme malapportionment in one tier and a greater than 50% parallel national tier, the impact this electoral system had on the seat allocation and disproportionality was not anything too out of the ordinary.

Finally, an interesting question but one I will not attempt to answer is whether, had UNITA won a narrow plurality of the nationwide vote, could the MPLA have retained a plurality or even majority of the assembly seats? Given the malapportionment and parallel allocation, I will say maybe. However, once again, I will point out that if they had wanted to ensure they could “win by losing,” the design they came up with was perhaps a little too “fair” to really be in their best (presumed to be anti-democratic) interest. On the other hand, if they are open to a gradual transition to democracy, and perhaps losing a fair election in five or ten years’ time, the system isn’t too bad. It plays to the MPLA’s regional strength yet does not overrepresent it greatly, and it creates space for the opposition, both UNITA and other parties, to operate.



  1. MPLA won 4-1 in Cuanza Sul, Moxico, Namibe, Huíla, and Cuando Cubango. It won 5-0 in Cunene (where the votes split 82.9%–14.4%). It is really striking that most of these strong MPLA districts are in the south, where UNITA was most present in the civil war. Meanwhile, the UNITA pluralities are Luanda (the capital and largest by far), Cabinda (the non-contiguous oil-rich enclave in the far north which has had a separatist movement) and Zaire (also in the northwest).
  2. It is not clear to me if this means a party could have won a provincial seat and thus been eligible for a remainder seat in the national district, or it had to have won a quota of nationwide votes. In any case, as all provincial seats were won by MPLA or UNITA, this detail would not have affected the results of this election.
  3. If I knew nothing other than that the effective number of vote-earning parties in some election was 2.2, I would expect the effective number of seat-winning parties to be around 1.72, based on logically derived, and empirically supported, formulas in Votes from Seats.
  4. By comparison, if we used the “as if compensatory” estimate of 3844, we would be in roughly the range of single-tier systems like Finland (3076 in 2019) or another former Portuguese colony, East Timor (4225). Indonesia is also in this seat-product neighborhood (4134), as was the French PR system of 1986 (3174).
  5. A ratio of actual to expected of 1.38 is near the 90th percentile for over a thousand elections, simple and complex, in the dataset (and would be about the same if I looked at just the simple non-FPTP subset).

Angola 2022

Angola is holding a general election today. According to news reports (e.g., BBC) the long-ruling MPLA faces a serious challenge this time from UNITA. I share the skepticism of many observers that the MPLA would actually accept defeat. But I am going to leave that aside, and do what F&V is known for: trying to understand the electoral rules and constitutional structure, in the event the election produces an acceptably fair outcome.

One news story I saw indicated that the voters have only one vote, and that the leader of the party with the most votes becomes president. A Wikipedia article corroborates that, and more importantly, so does the constitution itself, very explicitly (Art. 109). However, the Wikipedia article states that direct election of the president was abolished by the 2010 constitution. That would be an inaccurate portrayal of the provision: If a plurality-winning party’s leader becomes president, even in the absence of clearing 50% of the vote, and need not bargain with other parties to attain the position, that is direct election. More properly it should be thought of as a fused ballot, not indirect election. Similar fused presidential–assembly ballots, with plurality election, have been used in the past in Honduras and the Dominican Republic, for example.

As for the assembly election, the Wikipedia article referenced above says,

The 220 members are elected in two ways; 90 are elected from 18 five-seat constituencies and 130 from a single nationwide constituency. Both constituency types use a closed list proportional representation system : the D’Hondt method in the provincial constituencies and the simple quota largest remainder method in the nationwide constituency. [Links in original; I have not verified them for accuracy.]

It does not say whether this national component is compensatory or parallel. This could be important, as the basic tier evidently consists of equal-magnitude districts based on provinces that are quite unequal in population. I know nothing about the political geography of Angola, other than that when it was still a rebel movement, UNITA tended to be stronger in the south.

On the other hand, whether the system is parallel or compensatory and the degree of malapportionment may not matter greatly given that the national component is 59% of the total assembly. Parallel PR systems are rare, but have existed in various places at times (including Guatemala and Niger). Compensatory two-tier PR is fairly common, of course (e.g., Denmark or South Africa). There is a link in the Wiki page to what seemed would be the election law at the Aceproject. Unfortunately, it is not the full text, just introductory material regarding the law’s taking effect. The constitution itself sets out the two tiers, but not other key electoral rules, other than stating it must be proportional representation (Art. 143-4).

As to the executive format, it appears from my reading of the constitution to be pure presidential. There is no mention of a prime minister, the term is fixed, and the president has legislative powers, including a veto requiring two thirds of the assembly to override and the authority (Art. 124) to “issue provisional Presidential legislative decrees whenever, for reasons of urgency and need, this measure proves necessary in order to defend the public interest” (126). The cabinet (Council of Ministers) is defined as a mere “auxiliary body serving the President of the Republic” (134).

Here’s hoping the exercise in learning about Angolan political institutions matters, whatever the free choice of Angolan citizens.

Proposals for Israeli political reform–again

One thing I like about following Israeli politics is that there is no lack of willingness to propose institutional reforms to deal with (real or perceived) problems of governance. They are not always good ideas (see the term limit proposal proposed by a party in the outgoing coalition), but it is good that there is a willingness to debate ideas for political reform.

A news update from the TOI today mentions a couple that are in play during the current election campaign. The National Unity Party, led by Benny Gantz and Gideon Saar, is proposing to (1) require more than an absolute majority for the Knesset to dissolve1 itself, and (2) not make the failure to pass a budget a cause for automatic dissolution.

The second of these is an excellent idea, and I have thought for some time this should be changed. The problem with the current provision was on display in 2020 when then-PM Benjamin Netanyahu prevented the alternation of the premiership to which he had agreed from going ahead by withholding votes for the budget, thereby forcing an early election and breakup of the “unity” government. That the planned alternation would have been to Gantz is surely why the latter now wants to change this provision. Regardless of motive and experience of the proposer, the idea is sound. While it may seem straightforward that the inability to pass a budget is evidence of a lack of parliamentary confidence, it need not be so. I believe there are other parliamentary systems that can run on an automatic “continuing resolution” (borrowing a term from US politics), at least for a set period of time, if no new budget has been agreed. It is sensible as a way to prevent coalition partners from forcing an early election “passively” as opposed to actively attaining a majority for dissolution or government replacement.

As for the supermajority–specifically 70 members (58.3%)–to dissolve, the idea goes well with the proposal on the budget, and more importantly with the existing constructive vote of no confidence. Under the latter rule, in place since around 2015, the Knesset majority is not able to vote to dismiss the government unless there are 61 votes for a specific alternative. The new provisions proposed by National Unity would cement the notion that the government remains until the Knesset votes in an alternative (or the regular term ends).

Provisions for a parliament to dissolve itself are not the norm. Israel is an unusual case in this respect as far as I know.2 It is probably permitted elsewhere (see the Early Parliamentary General Election Act passed in the UK in 2019) if not specifically prohibited, but I am not sure I could name another case where a common path to an early election is the parliamentary majority passing a law to set a new election. Regarding having a super-majority vote to set an election, it is reminiscent of the debates leading up to the Fixed Term Parliament Act passed by the Conservative–Liberal Democrat coalition in the UK in 2011.3

The TOI update also notes another proposal, this one from the Yisrael Beiteinu party (Avigdor Liberman). It would require at least 90 members of the Knesset to bring down a government within two years of its formation. That’s a 75% majority requirement! The TOI says the first proposal of National Unity mentioned above is “similar” to this one from YB. But it is not similar! A super-majority for dissolution of the Knesset is consistent with the parliamentary form of government. A super-majority for dismissal of a cabinet is contrary to the very core of the parliamentary principle. I do not know where else such provisions can be found, other than Papua New Guinea4–not normally a shining model of effective governance that others seek to emulate.

The constructive vote of no confidence already introduces some potential for separation of powers (more to the point, of separation of purpose) in that a government potentially can face majority opposition yet remain in office. Yet it preserves the core of the parliamentary principle by ensuring that if a majority of the voters’ elected representatives prefers a different coalition be in power, it can proceed immediately to enforce its preference. Shielding a government from such majority preference, and allowing it to govern for up to two years unless a very substantial super-majority votes it out, is a recipe not for stability but for deadlock.

Gantz’s two reform ideas are promising. Liberman’s is very bad.



  1. As I have probably said before, technically the Knesset is never dissolved. It continues to hold legislative authority, albeit normally remains out of session, between the calling of an early (or regular) election and the installation of the new Knesset after the election. Lacking a good alternative term, I will go on calling it “dissolution.”
  2. Papua New Guinea has such a provision, I learned as I was drafting this. See Article 105.1.c: an absolute majority of parliament may vote to dissolve.
  3. The Johnson government repealed it with the passage of The Dissolution and Calling of Parliament Act 2022.
  4. See the PNG constitution, Article 145.4: “A motion of no confidence in the Prime Minister or in the Ministry may not be moved during the period of eighteen months commencing on the date of the appointment of the Prime Minister.” PNG also has a constructive provision that applies for most, but not all, of the term (145.2.a: “A motion of no confidence in the Prime Minister or the Ministry… moved during the first four years of the life of Parliament shall not be allowed unless it nominates the next Prime Minister”.)

At-Large Legislative Contests in the 2020 Puerto Rico General Election

While most seats in both houses of the Legislative Assembly of Puerto Rico are chosen by plurality (single-seat districts in the House, two-seat districts in the Senate), there are 11 seats in each body – out of a total of 27 in the Senate and 51 in the House of Representatives – that are filled on an at-large basis, by Single Non-Transferable Vote (SNTV). The 2020 election in the U.S. Commonwealth was notable not only for the fact that candidates from five parties secured at-large representation (along with a sitting independent senator), but also for the unexpectedly poor showing of the largest opposition party, the pro-Commonwealth Popular Democratic Party (PPD) in the at-large legislative races.

To be certain, the outcome of the election was nothing short of a political earthquake, with both the ruling, pro-statehood New Progressive Party (PNP) and PPD polling their worst results ever: 33.24% and 31.75% of the valid votes for governor, for a combined share of 64.99%. Meanwhile, the island’s perennial third party, the left-wing Puerto Rican Independence Party (PIP) shot up from 2.13% in 2016 to 13.58%, but the new Citizens’ Victory Movement (MVC) – ideologically diverse but broadly left-liberal – outdid PIP with 13.95%. Another new party, the Christian-conservative Project Dignity (PD) won 6.80%.

Despite their respective setbacks, the two major parties continued to monopolize between themselves all legislative district seats (MVC narrowly lost a House race in San Juan to PNP), with PPD securing a majority of these in both houses despite polling fewer votes than PNP, due to latter’s concentration of votes in the San Juan metropolitan area. So why did PPD fail to do as well in the at-large legislative races? The answer lies in the workings of the at-large representation system in Puerto Rico, known in Spanish as representación por acumulación.

Specifically, since politics in Puerto Rico evolved into a two-party system in 1968, following 28 years of PPD dominance, the two major parties have nominated six at-large candidates each for both the Senate and the House of Representatives in every election (from 1952 to 1968 PPD nominated seven at-large candidates to each legislative body). In order to guarantee each candidate has an equal chance of being elected, parties vary the order in which candidates are listed on the ballot in each of the island’s electoral districts – precintos in Spanish – 110 in total since 2012 (to be increased to 114 in 2024); parties assign candidates a set of electoral districts known as a legislative bloc – bloque legislativo in Spanish – in which they are placed at the top of their respective party lists, and as such automatically receive straight votes cast for their party, which have constituted the majority of ballots in every election; party ticket votes with votes cast for other at-large candidates from the same party are considered split votes. (See sample ballot.)

From 1972 to 2012, PNP and PPD elected four to six at-large candidates each in both the Senate and the House. Nonetheless, over the years an increasing number of voters cast either split ballots or bypassed party tickets altogether and voted for candidates only – in Spanish voto por candidatura – and PIP, which nominated single at-large candidates for each body from 1984 onward, was able to tap into that vote to secure seats for its at-large candidates in nearly every election during that period (the party won no at-large seats in 2008 and only a Senate at-large mandate in 2012). Even so, as recently as the 2012 election 81.27% of valid legislative ballots were straight votes, and the overall impact of split/candidacy votes was comparatively limited.

However, in 2016 split/candidacy voting soared from 18.73% to 35.62% of the legislative ballot valid vote, and the main beneficiary was José Vargas-Vidot, who became Puerto Rico’s first-ever independent candidate to win a legislative seat, securing a Senate at-large mandate and topping the poll as well. In fact, his vote total was made up entirely of split/candidacy ballots, since no provision is made to cast a straight vote for an independent candidate, and his victory reduced PPD to three at-large Senate seats (with PIP winning one and PNP the remaining six).

Although PNP returned to power in the 2016 election, the party polled its worst result up to that point in the gubernatorial election, and PPD its second-worst, with the major parties’ combined share of valid votes declining from 95.56% in 2012 to 80.67%. Meanwhile, independent candidate Alexandra Lúgaro won a respectable 11.13% of the vote, and went on to found MVC in 2019. By then, the marked decline of PPD in 2016, along with the emergence of Lúgaro’s new party and the success of the Vargas Vidot independent candidacy called into question the wisdom of nominating six at-large candidates in 2020, when five might have a better chance of securing election. To that end, a proposal was made to the party leadership, which however was rejected after a former but still highly influential party leader spoke against it, insisting that “too much was in play,” that nominating five at-large candidates instead of six could be perceived as an admission of weakness, and prevent the party from winning an overall majority in either or both houses of the Legislative Assembly.

(In the interests of full disclosure, I should note I collaborated in the proposal calling for the nomination of five PPD at-large candidates, and was present at the party leadership meeting in which it was discussed and turned down.)

As it was, MVC anticipated it would fare at least as well as Lúgaro did in her independent gubernatorial run in 2016, and nominated two at-large candidates for both legislative bodies, using Lúgaro’s 2016 vote as the basis for the corresponding legislative blocs. Meanwhile, PNP and PPD ran their usual six-candidate slates for both the Senate and the House, PIP and PD nominated single candidates for both houses, and Sen. Vargas-Vidot ran for re-election. However, although every MVC, PIP and PD at-large candidate as well as Sen. Vargas-Vidot was successful in the 2020 election, PNP only won four at-large seats in the Senate and five in the House, while PPD won just two at-large seats in both houses, as detailed in the following table (full results are available on my Elections in Puerto Rico website):

House Senate
Party % Seats % Seats
PNP 33.84 5 33.37 4
PPD 36.03 2 31.27 2
PIP 10.56 1 11.29 1
MVC 12.83 2 10.99 2
PD 6.73 1 7.33 1
Ind. 5.76 1

In both the Senate and House at-large races, the combined percentages obtained by all six PPD candidates – 31.27% in the Senate and 36.03% in the House suggested that while securing six of eleven seats might not have been a realistic goal, the party should have done better than winning just two seats (18.18%) in each case. However, an additional complication was that PPD candidates fared quite unevenly, although it should be noted these disparities weren’t due to the makeup of the PPD legislative blocs; instead, the large number of split/candidacy votes – which increased to 40.15% of all valid legislative ballots in 2020 – made the legislative bloc arrangements far less meaningful, as many voters backed candidates who weren’t assigned the top spot in their electoral districts. The uneven performance of PPD at-large candidates on account of split/candidacy votes was particularly evident in the House of Representatives, as shown in the following table:

Candidate Straight Split/Cand. Total
Héctor Ferrer 48,750 93,100 141,850
Jesús Manuel Ortiz-González 52,591 19,359 71,950
Enid Monge 52,031 6,474 58,505
Keyliz Méndez-Torres 48,416 8,827 57,243
Yaramary Torres 48,348 6,774 55,122
Gabriel López-Arrieta 45,817 4,838 50,655

In fact, Ferrer polled 73,213 votes outside his assigned legislative bloc – a figure which by itself exceeded the vote totals of the remaining five PPD House at-large candidates.

Among PPD Senate at-large candidates, the split/candidacy vote total disparities weren’t as marked, but even then the two winning candidates had the largest totals on that column:

Candidate Straight Split/Cand. Total
Juan Zaragoza-Gómez 52,591 21,218 73,809
José Luis Dalmau-Santiago 52,031 19,865 71,896
Aníbal José (Jossie) Torres 45,817 15,385 61,202
Brenda López-De-Arrarás 48,348 11,613 59,961
Ada Álvarez-Conde 48,750 8,470 57,220
Luis Vega-Ramos 48,416 6,234 54,650

Another factor at play is that many voters don’t understand the workings of SNTV, and for one reason or another cast their votes under the incorrect assumption they can vote for up to six candidates in each legislative body – as if it were a Multiple Non-Transferable Vote (MNTV) election – instead of only one. Ballot design might be at play, as at-large races are the only instance in which the number of nominations doesn’t go hand in hand with the maximum number of votes a voter may cast, but the fact is that both PNP and PPD actually use MNTV in their internal party primaries to choose at-large nominees, and many voters – sometimes including even seasoned political analysts – mistakenly assume that system is also in place for general elections, ballot instructions to the contrary notwithstanding.

The introduction in 2016 of vote counting machines providing detailed overvote and undervote statistics highlighted the confusion surrounding the way in which at-large legislators are chosen. Specifically, although overvoting in at-large legislative races, while somewhat reduced in 2020 (due to the efforts of how-to-vote campaigns from civic groups), is still significantly higher than in district races chosen by plurality voting, where it remains negligible (even though the vote counting machines are supposed to warn the voter about overvoting and undervoting). Besides overvoting, some PNP or PPD voters back third-party or independent at-large candidates under the assumption they are giving just one of six votes to such candidates, with the remaining five votes they think they have (but really don’t) going to the rest of their preferred party slate, when in fact they are giving their sole vote to a candidate outside their party.

Another issue in at-large legislative races is the so-called invasion of electoral districts, in which major party at-large candidates actively campaign for votes in electoral districts that don’t belong to their assigned legislative bloc, fully aware they are taking away votes from fellow party candidates. Suffice it to say this is a very sensitive matter, and there’s no information to confirm whether or not it took place in 2020.

It should also be noted that the 2020 general election in Puerto Rico was carried out under a new electoral law imposed unilaterally by PNP just months before the election, over the objections of opposition parties. One of the more controversial provisions of the law granted the ruling party near-absolute control of the Elections Commission, which had been run on a power-sharing basis among registered parties since a major reform in 1983 (following the disastrous 1980 election, in which the Elections Commission had been under PNP’s full control as well). While there were few issues with in-person polling, either election day or advanced, the tally of the bulk of advance/absentee votes in special polling station 77, mainly domicile and mail-in votes, accounting for about one-eight of all ballots, proved to be extremely problematic from the beginning, not least because its ten-fold expansion under the new electoral law overwhelmed the agency. To this day the exact number of voters requesting advance ballots in 2020 remains unknown, the results of polling station 77 are riddled with discrepancies – often quite significant – in every electoral district, and some believe the cited issues might have adversely affected PPD in the at-large contests. However, PNP leaders insist there is nothing wrong with the electoral law, and to date have resisted attempts to reform it ahead of the 2024 general election.

At any rate, the decision by PPD leaders to nominate six at-large candidates in 2020 for both houses proved to be a monumental blunder, which had the effect of exposing the very weakness that party leaders desperately wanted to conceal; in practical terms it resulted in a Senate in which no party had overall control of a legislative body for the first time since 1940; PPD won a plurality of Senate seats and an overall majority of one in the House.

But would PPD have been better off by nominating five at-large candidates instead of six? According to a Senate-only, post-election simulation I ran with five candidates, the answer is affirmative: at least four candidates, and possibly all five would have been elected. Even so, it’s by no means certain PPD will nominate in 2024 five at-large candidates instead of six, not least because many party leaders remain in denial about the major changes in voting trends that took place in 2016 and 2020, insisting they are nothing more than a transient phenomenon. That said, it’s worth remembering that in Spain it took several years for PP and (to a lesser degree) PSOE leaders to finally come to terms with a similar shift away from two-party dominance after 2015.

Finally, from time to time some PNP and PPD leaders have called for the elimination of at-large legislative seats, thus resulting in a Legislative Assembly elected in its entirety by plurality in districts. However, such calls appear to be motivated by a desire to get rid of independent and third-party legislators; that such a move could backfire in future elections in which either PNP or PPD, or both might no longer be major parties appears not to have been considered at all. And while leaders of both parties might scoff at such prospects in the here and now, they cannot be ruled out altogether in the long run, all the more so since as a result of their steady decline the two major parties appear to be increasingly dependent on the support of old voters, much like CDU/CSU and SPD in Germany’s 2021 Bundestag election. In fact, in the 2020 general election PNP and PPD won between themselves 87.71% of the advance/absentee vote in the gubernatorial race, 85% of which came from voters aged 60 or older; but among the younger election day voters they polled just 60.68% between themselves. All the same, doing away with the at-large legislative seats would require amending the Constitution of Puerto Rico, and for the time being it does not appear such an amendment – which would have to be approved by voters in a binding referendum – will be forthcoming.

Election indicators in Taiwan, SNTV era

I noticed that the always handy Election Indices file maintained by Michael Gallagher on his Electoral Systems page did not include Taiwan’s SNTV era of competitive elections (1992-2004). I needed the indicators for something I am working on. It just so happened that I had the candidate-level data for those years (thanks to Nathan Batto sharing them some years ago for another project). So I set out to calculate some key indices. In the off chance anyone needs them, here they are.

In the table below, “D2” is Gallagher’s “least squares” index of disproportionality (as a share, rather than percentage), “Nv” is the effective number of vote-earning parties, and “Ns” is the effective number of seat-winning parties.


I calculated these by considering every independent candidate–and there are many of them, although not many won seats–as a separate “party.” This is the only really proper way to do these indices–especially for a purely nominal system like SNTV–if one has the data at candidate level, and in the absence of any information as to groups of these candidates being de-facto parties.

Values for Ns and Nv for these elections can be found in Bormann and Golder (as “enpp1” and “enep1”, respectively). However, my Nv values are somewhat higher because the index values in Bormann and Golder’s dataset would have been estimated from aggregated votes of “others” (including “independents”). That is, they do not take all others/independents to be one party (as is sometimes erroneously done by others), but without the candidate-level data, any such estimate could fall short of the method I am using, based on complete data on every candidate’s votes and formal party affiliation, if any. My calculations for Ns match theirs for enpp1 almost exactly, as they should, given that relatively few independents won seats (43 over the 5 elections).

Hungary 2022 – how biased an electoral map?

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.

Did Thailand’s parliament just vote to switch to MMP?

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.

France 2022: Assessing the honeymoon election and towards a model of the impact of election timing on the president’s party’s seats

Was the French 2022 honeymoon election one that defies the usual impact of such election timing? Not to offer a spoiler, but the answer is yes and no.

Back around the time of the presidential runoff, I restated what I often say about elections for assembly held shortly after a presidential election: they are not an opportunity for the voters to “check” the president they have just chosen; presidential and semi-presidential systems just do not work that way. Well, usually. It seems hard to escape the notion that voters did just that–by holding Emmanuel Macron’s allies in Ensemble to less than a majority of seats, and by delivering bigger than expected seat totals to the Mélenchon-led united left (Nupes) and even to Le Pen’s National Rally (RN).

There will not be cohabitation, which was what I really meant in the French context when saying that honeymoon elections were not an opportunity to check the president. The results have not offered up any conceivable assembly majority that would impose its own choice for premier on Macron. I was also generally careful to say that I thought Macron’s allies would win a majority of seats, or close to it. They are relatively close, but considerably farther away that I expected, on about 42%. So, how does this outcome compare to honeymoon elections generally?

I have prepared an updated version of a graph I have shared before. An earlier version appears in Votes from Seats, as Figure 12.2. The x-axis is elapsed time, E, defined as the share of the period between presidential elections at which the assembly election occurs. The y-axis is the presidential seat ratio, RP, calculated by dividing the vote share of the party (or pre-electoral alliance) supporting the president by the president’s own vote share in the first or sole round. The diagonal line is a regression best fit on the nonconcurrent elections (those with E>0), and is RP=1.2–0.7E.

I added the France 2022 data point and label a little larger than the others, to call attention to it. The most notable thing is that this is the only case of a really extreme honeymoon–defined loosely as those with E<.05 but E>0–to have a value of RP<1.00. So in that sense, it is a poor performance. There are other honeymoons for which E≤0.1 that are below RP=1.00, including Chile 1965 and Poland 2001. In the Chilean case, the result obtains simply because the right did not present its own presidential candidate, but ran separately in the congressional election. Although this post is focused on honeymoon and other nonconcurrent elections, I also added labels to the two cases of concurrent elections (E=0) that have unusually low presidential vote ratios. Note that on average, RP in concurrent elections tends to be a bit below 1.00, as a combination of strategic voting and small-party abstention from the presidential contest leads assembly voting to be more fragmented than presidential voting, hence lowering RP. However, in very early term elections, the president’s party/alliance almost always gains. So France 2022 is unusual, but not a massive outlier. In fact, in terms of distance from the regression line, it is about equivalent to France 1997 or El Salvador 2006 (labelled).

We see that the 2022 election also features the lowest RP of any of France’s six honeymoon elections to date. The 2002 election (Chirac) produced an especially huge boost, whereas the 2017 election, when Macron had just been elected the first time, is almost on the regression line. (The regression does not include elections after 2015 because the dataset was collected around then; I added these more recent ones to the graph directly.) I also want to call attention to Volodomyr Zelenskyy’s 2019 honeymoon result in Ukraine for Servants of the People, as it is also among the most extreme honeymoon vote surges recorded anywhere as expected, perhaps aided by how uninstitutionalized that country’s party system has been. (If I wanted to be provocative, I’d say that factor also has been present in France, given frequent realignments on the right, the emergence of Macron, etc.)

(As an aside, I was somewhat surprised that an outlier, the one case of E>0.6 to have RP>1 is the French late-midterm election of 1986. This is remembered as the election that produced the first cohabitation of the French Fifth Republic. But the vote share of the Socialists was still considerably higher than Mitterrand’s own vote share in the presidential first round of 1981, when the Communists had presented their own candidate.1)

So much for the votes. I was wondering what happens if we look at seats? Strangely I had never done this before (at least with this dataset). This graph has as its y-axis the seat share of the president’s party (or alliance) divided by the president’s own first or sole-round votes, which I will call RPs. The x-axis is the same. In addition to plotting a best fit line, the diagonal, I also added the 95% confidence intervals from the regression estimates to this graph. There is also a lowess (local regression) plotted as the very thin grey line. Note how flat it is for a long portion of the term, a fact related to a point I will come to at the end (and also suggesting a more complex than linear fit may be more accurate, but I want to keep it simple for now).

The regression line here is very close to RPs=1.5–E, which is a wonderfully elegant formula! It says that at a midterm election, a president’s party’s seat share would be, all else equal, the same as his or her own vote share half a term earlier. At a truly extreme honeymoon election–imagine one held the day after the president was elected, but with the result known–the seat share would be about 1.5 times the president’s vote share. At an extreme counter-honeymoon it would drop to around 0.5. So where did Macron’s Ensemble come out in the election just concluded? His RPs=1.52! So the party actually did about what the average trend says to expect. It was his 2017 surge that was higher than we perhaps should have expected (although, again, not as high as Chirac’s in 2002).

The result in the second figure is obviously holding constant the electoral system, so it should be taken with a grain of salt, given the importance of variation in electoral systems in shaping the size of the largest party (which is usually the president’s party, at least until we get to midterms and beyond).

What I find particularly elegant about the equation is its suggestion that midterm elections are no-effect elections, in terms of seat share for the president’s party. This was presumably what major party leaders were going for in the Dominican Republic when they shifted to the world’s only ever case (to my knowledge) of an all-midterm cycle. Both president and congress were elected to four-year terms, each at the halfway point of the other. (Actual outcomes during were not always no-effect, though on average they were close2; they have since changed back to their former concurrent elections.) This may seem a surprise to readers who know the American system and its infamous midterm decline, but actually the midterm-election median in the US is 0.969. In an almost pure two-party system, anything below 1.00 might look bad, and be both politically consequential and also somewhat over-interpreted. But 0.969 is not really that much below 1.00! Okay I am cheating just a little by reporting the median. The mean is 0.943; it is brought down by a few major “shellackings” like 2010 (0.891), although 1990 was worse (0.719, in this case because G.H.W. Bush had won such a big landslide of his own).3

In concurrent elections, the regression suggests also that on average, RPs is around 1.00. For the US, the median is 0.979, and the mean is 1.009. Note how it is higher than the midterm average, but perhaps not as much as one might expect.4

At this point, both these equations are just empirical regression best fits, not logical models. There is logic behind the general effects of electoral cycles on a presidential party’s performance, but not a logical basis for the specific parameters observed. I would very much like to have such a logical basis, but I have not hit upon it. Yet.

(Considerably nerdier and some rather half-baked stuff the rest of the way.) Such a logical model may be closer now that there is a simple and elegant empirical connection between presidential votes and seats. Seat shares are more directly connected to parameters of the electoral system than votes shares are–even vote shares for assembly parties, but vote shares for presidential candidates are a good deal more remote from the assembly electoral system. Nonetheless, in Votes from Seats we do derive a predictive formula for the effective number of presidential candidates, based on the assembly’s seat product. A regression reported in the book confirms its plausibility, but with rather low R2. From that formula one could get an expected relationship for the leading presidential candidate’s vote total, vp. It would be vp = 2–3/8[(MS)1/4 +1]–1/4. We already have, for the seat share of the largest party, s1=(MS)–1/8. It so happens that these return the same value at around MS=175. Expectations of vp<s1 or s1<vp would then depend on whether MS (mean district magnitude times assembly size) is higher or lower than 175; for most presidential systems it is a good deal higher (the median in this sample of elections, including semi-presidential, is 480). Tying this observation to the one about midterm elections (E=0.5) yielding actual (not predicted) sp=vp and accepting for simplification that the president’s party seat share (sp) is also the largest party seat share, at least in elections that are not after the midterm, might be a path towards a model. But that may take a while yet. Below I will copy a table of what the formulas for vp and s1 yield at various values of seat product, MS, for simple systems. These values of s1 are without regard to elapsed time when the assembly election takes place.

Table of expected values of presidential vote shares (pv) and largest assembly party seat share (s1)

Note how we would expect president’s parties to have a seat share greater than the president’s own vote share at low MS due to system disproportionality, but higher as MS increases beyond 175, presumably because of strategic behavior being different around the majoritarian presidential election and the more permissive assembly electoral system. The smallest MS observed in this dataset for a (semi-)presidential system is 124 (Sierra Leone, 2002, 2007). The largest is 202,500 (Ukraine, 2006, 2007). For nonconcurrent elections, the minimum MS is 240 (Chile, 1997, 2001).


  1. Also, Mitterand himself had finished second in the first round, with 25.9% of the votes (the incumbent, Giscard, had 28.3%). The Communist candidate had 15.4%. In the 1986 election, Socialists won 31% of the votes, for RP=1.2. (I am not counting the Communists as part of Mitterrand’s alliance by then, as he had fired the Communist ministers that were in his initial cabinet.)
  2. The values for RPs in these Dominican elections were: 0.587 in 1998, 0.975 in 2002, 0.945 in 2006, and 1.067 in 2010. So other than that first run, if the no-effect was what they wanted, they basically got it.
  3. [Added, 21 June.] I somehow forgot that my first publication on this topic, in the APSR in 1995, also used seats as its outcome of interest–but it was change in seat percentage for the president’s party from the prior assembly election (with president’s vote share as a control). Looking back on that pub, I see that my regression there would agree with my updated analysis here in suggesting that midterm elections, all else constant, are no-effect elections. The regression line clearly passes very near the change=0, E=0.5 point in the article’s Figure 1. And, yes, in that article I commented on this as a “particularly striking feature” (p. 332).
  4. The way I set up the regression, its constant term would be the RPs when E=0, a concurrent election. This constant is actually 0.95, but its 95% confidence interval includes 1.00 (it is 0.844–1.057). The coefficient on the nonconcurrent dummy is 0.552, from which I get the approximation, 1.5, in the equation in the second figure (summing this coefficient and the constant). The coefficient on E is –1.072. R2=0.215.

France 2022 fourth round (legislative runoffs)

Sunday is the final round of the four-round French election–two rounds for president, two for National Assembly. Thus the legislative runoffs are now upon us. Although we have the unusual case of a honeymoon election in which the leader of an opposition alliance is proclaiming he is running for prime minister, probably the only real question in the results is whether the just-reelected President Macron gets a assembly majority or not. (See earlier planting for discussion of such points.)

In advance of the runoffs, I been poking around in the statements (profession de foi) that candidates make available. It’s a great resource for anyone wanting study patterns in the way the candidates and parties/alliances communicate. I am not about to look at this systematically, but I note a few stark differences in presentation. (Most of the following is based on a comment by me at the earlier post, but with some elaboration.)

Every candidate for an assembly seat runs with a substitute, who would replace the the originally elected member were the latter to vacate the seat for any reason (including becoming a cabinet minister). Thus, in effect, France has two-person (closed) lists for each single-seat district. The replacement is typically, although not always, featured on the statement (and, from photos I have seen, in campaign signs). But there is considerable variation in how they are presented.

Also, as typifies highly presidentialized parties (or, given that this includes major opposition parties, too, leader-ized?) as France has, almost every candidate is featured next to the presidential candidate in whose alliance the assembly candidate was running.

For example, in Bouches-du-Rhône no. 4, the candidate from Nupes features the principal and the substitute prominently, side by side. The national leader, in this case “candidate for premier” Mélenchon, is shown towards the bottom of the first page. This is the reverse of what seems to be the norm for candidates of Ensemble or RN, where the candidate is pictured (photo-shopped, more to the point) next to the leader, with the substitute in a smaller photo on a later page.

For instance, see the Ensemble candidate in the same district.

See this one for a candidate of RN (Bouches-du-Rhône no. 1). Unlike most that I have seen for candidates in other parties, this does not talk about the candidate or the district at all. It just tells what the RN party program is. It also does not mention the substitute. Instead, a picture of the main candidate with Le Pen and also (strangely) a picture of the party president, Jordan Barella. The main message comes through clearly in all caps at the top: “La seule opposition à Macron” (the only opposition to Macron).

Here is another RN candidate statement that is marginally less party-centric than that one. In Hérault no. 7, it is a little more specific to the local context, not in the sense of any mention of district issues, but in calling out the “extreme left” opponent in the district who must be stopped. The Nupes candidate in the same district has a statement that looks like the other Nupes one I mentioned before (and with minor variation, all those from Nupes that I have seen). It has the substitute depicted side-by-side with the principle and featured more prominently than the national leader, while still making room for a photo of Mélenchon at the bottom of the first page. It also has at the very top, “Face au RN, pas d’abstention”–a call not to abstain, given the contest is against the RN. Otherwise, it is mostly oriented around the national program of the alliance.

In general, the Ensemble statements seem to say the most about the candidates themselves, with information on their career on the second page, often along with some words about the district’s needs. Maybe this is to be expected for the alliance that has already won the presidency, and now wants to show how the majority Macron is seeking would be in tune with local voters’ needs. The other two main forces, RN and Nupes, on the other hand, need to emphasize how they seek to counter the president’s national policy priorities. The candidates in Nupes and RN most certainly are not cultivating a personal vote or a local vote on their statements–or rather on the subset of statements I saw.

I actually did find one from Ensemble that did not show a photo of Macron at all, although it does say “presidential majority” at the bottom of the front page. Instead, it shows the principal candidate and the substitute standing side-by-side in a park. This district is one of the three-way runoffs, Dordogne no. 3 (first round: NUPES 24%, Ensemble 23%, RN 22%), and the second page of the statement has a large block of text denouncing the “extremes” represented by the other two runoff candidates’ national programs. It still saved plenty of locally targeted information about priorities.

We can probably draw some conclusions from these patterns–if they are indeed patterns–about the priorities of the parties and alliances, in terms of local vs. national emphasis, as well as how important the leader is to the vote-seeking strategy. I looked at dozens, and while I can’t claim they were representative of the wider set of districts, it seems they just might be.