The Fruits and Votes readership survey

I’d like to thank everyone who filled in the survey of the Fruits and Votes readership. We got a total of eighty responses, which, given the amount of views this blog receives on a regular basis, seems like enough to draw inferences from.


The United States, with roughly 4-5% of world population, represents 33% of this blog’s viewership. Australia and New Zealand, with just 0.4% of world population, represent nearly 20% of readership. It’s Asia (60% of world population, 2.5% of responses), as well as Africa (no responses whatsoever) where Fruits and Votes is disproportionally less viewed.


For reasons that should be relatively obvious to fellow readers, those under 18 are under-represented, with those over 30 being over-represented (given the Western-centric tilt of the readership, this presumably makes some sense).

85% of you come here for the votes: the remaining 15% are here for fruits and votes, while no one wants fruit only.

The most popular region, with 54% of readers enjoying posts from it (this is approval voting), is Canada, Australia and New Zealand-only 24% of readers enjoy posts from South Asia. 99% of readers enjoy reading about electoral systems (a practically Soviet figure!), while executive formats and federalism secured the approval of 55of readers.


We asked what sort of electoral system you most liked for a country with unicameral parliaments and parliaments. A third of you went for MMP, while about a quarter opted for STV: the most popular system overall was some form of list PR, which received the support of nearly 40% of you, although division over list types split the pro-list vote. No one opted for first-past-the-post, and only four readers opted for any form of non-PR system.


Interestingly enough, by far the most popular electoral system for an elected President is probably the rarest-a majority of you opted for preferential voting, used only in Ireland and (sort of) Sri Lanka. The more popular two-round system came in a strong second, while the other options (FPTP+variations of the two-round system) made little impact. Note that the one entry for “presidents should not be politically powerful” was written in before I closed that option.


Honduras 2017

Honduras has presidential and congressional elections today. I know essentially  nothing about the elections except: (1) There is widespread fear they will not be fair, and (2) The congress is elected by free-list PR.

It is for the latter reason that I share the following image, which I found on Twitter, posted by Pablo Secchi.

The ballot is similar to that in neighboring El Salvador, which also uses a free list. The voter may cast up to M votes, where M is the district magnitude (number of seats elected from the district). The votes may be cast without regard for party, but each candidate vote is also a vote for the list on which the candidate was nominated. Thus it is a party-list PR system, but one in which voters are free to spread their support across multiple parties. It also means that voters are weighted differently, according to whether they cast all their votes or not.

It appears that voters can simply cast a list vote. I believe that doing so is equivalent to casting votes for as many candidates as are nominated on that list (presumably always M).

Chile 2017: Meet your new seat product

As discussed previously, Chile has changed its electoral system for assembly elections (and for senate). The seat product (mean district magnitude times assembly size) was increased substantially. Now that the 2017 Chilean election results are in, did the result come close to the Seat Product Model (SPM) predictions?

The old seat product was 240 (2 x 120). The new seat product is 852.5 (5.5 x 155). This should yield a substantially more fragmented assembly, according to the SPM (see Votes from Seats for details).

I will use the effective number of parties (seats and votes) based on alliances. The reason for this choice is that it is a list PR system, and the electoral system works on the lists, taking their votes in each district and determining each list’s seats. Lists are open, and typically presented by pre-election alliances, and the candidates on a list typically come from different parties. But the question of which parties win the seats is entirely a matter of the intra-list distribution of preference votes (the lists are open), and not an effect of the electoral system’s operation on the entities that it actually processes through seat-allocations formula–the lists. However, I will include the calculation by sub-alliance parties, too, for comparison purposes.

The predicted values with the new system, for effective number of seat-winning lists (NS) and effective number of vote-earning lists (NV), given a seat product of 825.5, are:

NS=3.08 (SPM, new system)

NV=3.45 (SPM, new system).

The actual result, by alliance lists, was:



So the Chamber of Deputies is almost exactly as fragmented as the SPM predicts! In the very first election under the new system! The voting result is somewhat more fragmented than expected, but not wide of the mark (about 14%). It is not too surprising that the votes are more off the prediction than the seats; voters have no experience with the new system to draw on. However, the electoral system resulted in an assembly party system (or more accurately, alliance system) fully consisted with its expected “mechanical” effect. The SPM for NS is derived from the constraints of the number of seats in the average district and the total number of seats, whereas the SPM for NV makes a potentially hazardous assumption about how many “pertinent” losers will win substantial votes. We can hardly ask for better adjustment to new rules than what we get in the NS result! (And really, that Nresult is not too shabby, either.)

Now, if we go by sub-alliance parties, the system seems utterly fragmented. We get NS=7.59 and NV=10.60. These results really are meaningless, however, from the standpoint of assessing how the electoral system constrains outcomes. These numbers should be used only if we are specifically interested in the behavior of parties within alliances, but not for more typical inter-party (inter-list) electoral-system analysis. It is a list system, so in systems where lists and “parties” are not the same thing, it is important to use the former.

To put this in context, we should compare the results under the former system. First of all, what was expected from the former system?

NS=2.49 (SPM, old system)

NV=2.90 (SPM, old system).

Here is the table of results, for which I include Np, the effective number of presidential candidates, as well as NV and Ns on both alliance lists and sub-alliance parties.

By alliance By sub-list party
year NS NV NP NS (sub) NV (sub)
1993 1.95 2.24 2.47 4.86 6.55
1997 2.06 2.54 2.47 5.02 6.95
2001 2.03 2.33 2.19 5.94 6.57
2005 2.02 2.36 3.01 5.59 6.58
2009 2.17 2.56 3.07 5.65 7.32
mean 2.05 2.41 2.64 5.41 6.79

We see that the old party (alliance) system was really much more de-fragmented than it should have been, given the electoral system. The party and alliance leaders, and the voters, seem to have enjoyed their newfound relative lack of mechanical constraints in 2017!

Can the SPM also predict NP? In Votes from Seats, we claim that it can. We offer a model that extends form NV  to NP; given that we also claim to be able to predict NV from the seat product (and show that this is possible on a wide range of elections), then we can also connect NP to the seat product. We offer this prediction of NP from the seat product as a counterweight to standard “coattails” arguments that assume presidential candidacies shape assembly fragmentation. Our argument is the reverse: assembly voting, and the electoral system that indirectly constraints it, shapes presidential fragmentation.

There are two caveats, however. The first is that NP is far removed from, and least constrained by, assembly electoral systems, so the fit is not expected to be great (and is not). Second, we saw above that NV in this first Chilean election under the new rules was itself more distant from the prediction than NS was.

Under the old system, we would have predicted Np=2.40, so the actual mean for 1993-2009 was not far off (2.64). Under the new system, the SPM predicts 2.62. In the first round election just held, NP=4.17. That is a good deal more fragmented than expected, and we might not expect future elections to feature such a weak first candidate (37% of the vote). It is unusual to have NP>NV, although in the book we show that Chile is one of the countries where it has happened a few times before. Even the less constraining electoral system did not end this unusual pattern, at least in 2017.

In fact, that the assembly electoral system resulted in the expected value of NS, even though NP was so high, is pretty good evidence that it was not coattails driving the assembly election. Otherwise, Ns should have overshot the prediction to some degree. Yet it did not.

Brazil electoral rules changes: Will they make a difference?

Brazil has passed some changes to its electoral rules, according to the Economist. The changes mainly concern rules outside the “electoral system” in the way Taagepera and I delimit that term in Votes from Seats. That is, despite various proposals under discussion in recent years in Brazil, the assembly size, district magnitude, and allocation formula all remain unchanged. Instead, rules changes are focused on financing provisions and attempts to regulate pre-election coalitions. The concerns in Brazil are over the excessive fragmentation of the Congress, which is blamed on incentives to corruption resulting from the open-list, highly proportional, system in place.

In this post, I want to consider the extent to which Brazil’s existing extreme fragmentation is expected, or not, based on its electoral system. Knowing the answer to this question can help us understand if changes to electoral rules, outside the core system features, might make a difference.

The following graph is an authors’ original of one that appears in the book as Figure 14.3. It shows the number of parties winning at least one seat in each district of Brazil’s and two similar electoral systems: Chile and Finland. Each of these electoral systems is D’Hondt, open list, with rules explicitly permitting lists to be presented by multiparty alliances. In each system, all seats are allocated in districts, via applying the D’Hondt divisors to the total votes won by each list. The emphasis is important, as the electoral system does not operate on parties, it operates on lists. Sometimes a list is a party list, but in these countries it is common for it to be an alliance list. In such cases, the electoral system does not shape the number of parties, except indirectly. The number of parties winning will be dependent on how many winning candidates on the various lists happen to be branded by different parties. At the extreme, every candidate could be from a different party, even if they were elected from just a few lists (or one list, as happens in some Chilean districts, electing just two seats). This could mean that the number of parties–as distinct from the number of lists–winning seats is “unpredictable”. This graph shows that is not the case–there is still a predictable average pattern.

The thick dotted curve shows the predicted pattern. It says that the number of sub-alliance winning parties (again, whether winning on their own list or via having a winning candidate on a list in which they were one of two or more alliance partners) is the district magnitude, raised to an exponent designated “k”. You will need to read the book to see the derivation of k. I will give only the short version: k is the “embeddedness” factor, and captures the share of the total assembly seats that are elected in a given district. If a district elects all the seats in the entire assembly (as in Israel or the Netherlands), k=0.5 for reasons explained in the book (and also in Taagepera and Shugart 1993). When a district elects a smaller and smaller share of the total assembly, k increases and can be slightly over 1.00 when M=1 and the assembly is very large (as in the UK). What the embeddedness factor captures is the extent to which national politics enters the district level and makes district politics more competitive than it would be predicted to be, were there no extra-district politics. Specific to the case of Brazil, it tells us that we can expect higher fragmentation of the party system because of the electoral system–both the fact that the allocation rule is one of open alliance lists and that there are many large-magnitude districts embedded in a very large assembly.

What we notice is that the predicted curve, showing the expected number of parties winning at least one seat (on its own or on an alliance list) equalling Mk, fits the overall data cloud well. This is a deductively derived logical model, not a post-hoc data fit. The fit of the logical model to the data is confirmed by a regression test. However, the data plot also shows that Brazil’s very largest districts (with magnitude greater than 20 and up to 70) are even higher than the model predicts. So, for example, with M=55, we expect around nine parties to win seats. (The k formula here yields roughly 0.55, and so 55.55=9.1.) Yet Brazil’s actual districts in this very high-magnitude range all have more than nine parties, and sometimes more than twelve, represented.

Why is fragmentation so high? Without the logical model developed for these systems, we might have just said, well, they have high district magnitude. Maybe we would also have invoked country-specific features, and just said, “it’s Brazil”. Such statements about high M and Brazilian particularity remain valid, but what the model lets us see is that even if Brazil’s very largest districts “conformed” to the model–as indeed its more modest-sized ones do, on average–it would still be very fragmented. So, about those reforms…

The new electoral law amendment, according to the Economist, “outlaws election alliances among parties that do not share a programme.” That might be helpful, if it can be enforced, by eliminating alliances of pure seat-winning convenience. The amendments also impose a threshold (1.5% of the national vote or seats won in at least nine states)–not for winning seats at all, but for getting public campaign financing and and free television and radio time. That might matter more. (This ‘threshold’ rises to 3% by 2030.)

Perhaps it is the existing freedom to form alliances regardless of programmatic commitment with one’s partners and the promiscuous financing/publicity rules that cause some of Brazil’s districts to be above the predicted value. However, even if that is what is causing Brazil’s largest district’s to overshoot their expected number of seat-winning parties, the amount of fragmentation after these reforms would still be very high. In other words, Brazilians are likely to be disappointed by the impact of these reforms. The model says so!

If Brazilians wanted changes to make a more dramatic impact on fragmentation, what could they do? One thing would be to abolish alliance lists altogether. The lighter gray line in the graph above shows the expected number of lists to win at least one seat for a given district magnitude. It is equal to the square root of M. In the book we show that we do not need k for this; embeddedness does not push up the number of lists, on average, beyond the square root of M. If lists and parties are the same thing, as in many PR systems, then the number of parties winning at the district level is not systematically affected by extra-district politics. Other outputs of the party system are affected, the book shows: the size of the largest parties (both votes and seats) is systematically reduced, and the “effective” number of parties (again, both for votes and seats) systematically increased, by the extent of the district’s embeddnedness. The number of lists or party-lists is not. However, as shown here, the number of parties including those who win through alliance partnerships, is pushed up–systematically, in that it can be modeled.

Elsewhere in the book we show that the number of lists winning seats in Brazilian districts is consistent with the model (square root of M)–again, on average. So Brazil’s electoral system functions as expected–it turns list votes into list seats in a way consistent with PR systems worldwide. It also systematically increases the total number of parties through its alliance feature. Get rid of alliances, and the number of winning parties would surely drop (though probably not all the way to the square root of M, because at least some of these small parties could survive independently).

Of course, Brazil could do more dramatic things still, like redistrict to have smaller district magnitudes. But if the changes made this year, in advance of the 2018 elections, are the best Congress can enact, it is highly unlikely they could have done something that drastic! Given what was passed, perhaps the number of parties will come down–to the predicted value. That would still be a lot of parties!


Japan 2017

Japan has a general election this Sunday. Yes, again. It looks pretty uninteresting, as we almost certainly know the result will be a big majority for the LDP and its pre-election alliance partner, Komeito. Yes, again. The main question seems to be whether that majority will be two thirds or less.

When Japan had its election in 2014, I used it as an example of different ways a cabinet can be terminated. More specifically, I used it as an example of a case where there was no reason why an early election was needed, because the government has a solid majority. That is at least as true in 2017 as it was in 2014.

Japan’s electoral system for the House of Representatives is Mixed-Member Majoritarian (MMM). Those not familiar with the term might refer to my post on the 2005 election. Now, that was an interesting election. (2009 was interesting, too, and even 2012 was, sort of.)

The US Supreme Court gerrymandering case

I do not have time to dissect the arguments before the US Supreme Court in the case concerning the permissibility of the partisan gerrymander in Wisconsin. It clearly is a case of great importance to issues we care about at this blog. So, feel free to discuss here.

I highly recommend two pieces by Michael Latner:

Sociological Gobbledygook or Scientific Standard? Why Judging Gerrymandering is Hard (4 OCt.)

Can Science (and The Supreme Court) End Partisan Gerrymandering and Save the Republic? Three Scenarios (2 Oct.)



MMP weekend: Germany and New Zealand 2017

We are entering days of convergences. Over the next two days, the Jewish and Islamic new years and the first day of Autumn coincide. Then, on the weekend, we have the convergence of elections in the two countries that offer our best examples of mixed-member proportional (MMP) representation electoral systems: Germany and New Zealand. (Lest I be accused of hemispherism, let me hasten to note that in one of those countries, the election will be the day after the start of spring.)

In the case of Germany, which votes Sunday, there really has been no doubt for some time that the CDU/CSU alliance would place first, but it will be down from its 2013 result. There is also little doubt that the two parties that missed the 5% party-vote threshold in 2013 will clear it this time: the center-right FDP and the far-right AfD. The SPD, which briefly flirted with the lead in the polls some months after changing its leadership, looks like it may struggle to break 25% of the vote. The real question is what the coalition will be, after the election results are known.

I would expect the SPD to want a period of opposition to recollect itself after what looks sure to be another disappointing result for the party. Thus it may not be willing to renew the current CDU/CSU+SPD big coalition (what we should stop calling a grand coalition; my more direct translation of the German term is more apt). If the FDP has enough seats to combine with the CDU/CSU, we might see a return to the center-right combo that governed from 2009 to 2013, as well as in many past terms. There is just enough error in the projections from polling to allow for the possibility that this could be a viable combine. (Mouse over the numbers in the table at that link for the range of vote and seat projections for each party.)

However, the most likely result seems to me to be Jamaica! I will admit to rooting for this: CDU/CSU + FDP + Green. (The name refers to the parties’ colors.)

In New Zealand, the contest for Saturday’s election is much more uncertain. For months it seemed National, which heads the current multi-party governing arrangement, was cruising to another win. Then Labour changed its leader and surged (similar to the German pattern). By a few weeks ago, the two largest parties were running neck and neck, while the Greens stumbled badly and looked at risk of failing to clear the 5% party-vote threshold. This scenario was posing a potential difficult challenge for center-left voters: Do you vote Labour to bolster its formateur status (as the largest party, although there is no formal right of first attempt to the largest in New Zealand)? Or do you vote Green to ensure there is a viable partner for Labour other than Winston Peters and his New Zealand First (NZF) party? Given that the electoral system is MMP, you can do both: vote for Labour in your district (electorate) and vote Green on the list. However, while that might be a voter’s way of making a statement of preferred coalition, only the party vote affects the overall balance of seats in parliament. (Some exceptions to that statement, as I will get to below, but none likely relevant to the Labour-Green situation discussed here.)

In recent days, some polling suggests that National might be pulling ahead again. The result could be very close, and it could be a situation in which NZF is pivotal (although that may be less likely than it seemed some weeks ago). That is, assuming NZF makes it. The party has been tending downward and is hovering near 5%, as are the Greens . Here is where the electorate (district/nominal) vote comes in. The threshold provision for a party to participate in nationwide proportional allocation is 5% of party-list votes or one electorate. (Additional MPs elected beyond the electorate candidate are what I have termed “piggyback MPs“, not to be confused with that other MMP creature, the “shadow MP“.) The Greens do not have an electorate where they are viable, but NZF does.

Peters, the NZF leader, currently holds an electorate seat, Northland, having won it in a by-election in 2015. He is the party’s candidate again for the seat. If he retains it, his party would qualify for additional list seats, even if it fell below the 5% party-vote threshold.

The other electorate contests that matter include the one in Epsom, although it is not really a contest. The seat is safe for the one Act MP, David Seymour, who is quite certain to return. It is probably not likely that the Act party vote will be sufficient to earn the party a second seat, although I saw one projection a week or so ago that suggested it was possible. Act has been a governing partner with National since 2008.

Then there is Waiariki, one of the Maori set-aside seats. (Voters who claim Maori descent can choose to vote in their special Maori electorate or in the general electorate seat in which the reside.) Te Ururoa Flavell is fighting to hold the seat, which is the only way his party will retain a presence in parliament. That is quite a change for the party, which has been a National governing partner since 2008. In the past it has won as many as five electorate seats (in 2008) and in 2014 it had sufficient party votes to win a list seat for the first time, in addition to its win in Waiariki electorate. This time, it may end up with just one seat–or zero.

One electorate we know will not matter this time is Ohariu. United Future leader Peter Dunne resigned in August, after a 33-year career as an MP. This effectively kills the party, which has been a support partner to every government, whether led by Labour or National, since 2002. Only in 2002 did the party clear the party-vote threshold, and since 2008, Dunne has been its only member.

In an interesting twist on the Ohariu story, the Greens had initially decided not to contest the seat, in order to give the Labour candidate a chance to defeat Dunne and thereby knock a National partner out of the government-formation equation. When Dunne resigned, the Greens announced a candidate for the seat. With Dunne not running, there is no scenario in which this electorate will matter for the parliamentary balance, so there was no reason for the Greens not to have “local face” on the party (even though many of its voters will split their vote and give their electorate vote to the Labour candidate anyway). Running a candidate is thus another example of what I have called green contamination.

Two MMP elections in one weekend. Now that will be something to watch!