French institutional reform proposals

French Premier, Edouard Philippe, has outlined plans for institutional reform, according to the FT:

“…the number of seats would be reduced from 577 to 404 in the National Assembly, the lower house, and from 348 to 243 in the Senate.”

“Proportional representation would also be allowed for 15 per cent of the seats in the National Assembly.”

The reduction of the National Assembly would be to almost precisely its optimum under the cube-root law (population about 67 million, the cube root of which is 406). Obviously, 15% of seats by PR is very minimal (especially if they are non-compensatory).

The FT article is short on detail. If anyone is following the French press coverage on this, please share anything else you might have seen that would flesh out these plans.

The Salvadoran result 2018: The electoral cycle counts!

[Note: the following has been revised based on updated voting results– 9 March, 17:17 PM PST]

Before the assembly election in El Salvador, I suggested that the FMLN should be expected to win 24.2% of the vote. I hedged, saying I thought the Salvadoran party system probably was still too rigid to allow one of its two leading parties to fall off that far. I should not have hedged, because the preliminary results show that the largest party will be the opposition ARENA, which won 42.3%. The FMLN got 24.4%. How about that. I was off by a tenth of a percentage point in my pre-election prediction!

Well, as nice as that would be as a story, it is more complicated than that…

now realize that I made an error in calculating my expectation of 24.2%. I based the expectation on the fact that the FMLN is the party of the incumbent president, that this election was being held with 80% of the president’s inter-electoral time lapsed, and the president’s own (first-round) vote total (in 2013). It was in the latter factor that I made a mistake, using 39.0%; that was the ARENA total, but the FMLN candidate, Salvador Sánchez Cerén, had 48.9%. Plugging that into the formula (shown below), I should have “expected” the FMLN to get 30.3% of the vote in this past Sunday’s assembly election. So the party actually did a good deal worse than the corrected expectation. And I did worse in my prediction.

Perhaps the party system is no longer so rigid; one of the leading parties can fall below a quarter of the votes after all. Alternatively, as I shall explore here, perhaps I made a second countervailing mistake, which was not to include a coalition partner. If we add the votes of GANA, a center-right party but one that has supported FMLN presidencies since 2010 and, importantly, did not compete against Sánchez Cerén in the presidential contest, we get 35.9%. That’s greater that my (corrected) expectation of 30.3%, but somewhat closer to it than the FMLN’s own vote. I will return to this issue of party vs. alliance later.

The FMLN’s 24.4% is its worst showing in the votes for assembly since its debut election in 1994 (21.4%); that election was concurrent with the presidential election and the party ran just behind its presidential candidate (24.9%) who was a very distant second. Since then, the party has won 33.0%, 35.2%, 34.0%, 39.7%, 42.6%, 36.8%, 37.2%, and now 24.4%.

The party’s high-water mark was 2009, the “counter-honeymoon” election that presaged the leftist, ex-guerrila, party’s first presidential win a few months later.* Then, holding the presidency, it slipped in 2012, an election held with about 60% of the president’s term elapsed. In 2014, it won the presidency again, then held its own in the 2015 election, held with 20% of the new president’s term elapsed.

GANA first appeared, as a split from ARENA, in 2010, just under a year after the election of the first FMLN president. It has now run in three assembly elections staring with 2012, and its votes have been 9.6%, 9.2%, and 11.5%. Interestingly, it gained in 2018 even while the FMLN lost badly. If we add the two parties’ votes together for the last three elections, we get 46.4% (not much less than Sánchez Cerén’s own percentage in 2014), 46.4% (yes, again) in 2015, and 35.9%. That is obviously a sharp decline in the two parties’ combined votes, even if one of the partners did experience an increase. FMLN and GANA will now will have around 40% of the assembly seats, whereas they held half the seats after both the 2012 and 2015 elections.

What led to the sharp decline this time? Many political factors, no doubt. But what really counts is the elapsed time–an election this late in a presidential term tends to be bad for the presidential party–or alliance. The FMLN in 2018 is just the latest example of an effect I first researched in my dissertation (1988) and published about in the APSR in 1995.

Now, via Votes from Seats, we have a formula:

Rp=1.20–0.725E,

where Rp is the “presidential vote ratio”– vote share of the president’s party in the assembly election, divided by the president’s own vote share (in the first round, if two-round system)–and E is the elapsed time (the number of months into the presidential inter-electoral period in which the assembly election takes place).

The key question around which this post is based is whether we should mean “party” literally as the party of which the president is nominee, or if we should include supporting parties that do not compete against the candidate. If you think it is cheating to use the alliance, I am being transparent and reporting the party totals. If you think it is OK to use the alliance when the two parties in question do not compete against each for presidency and cooperate in the assembly–despite running separately–we can compute the totals that way, too.

The formula above expects Rp=0.620 because E=0.80 for this election. Using only the FMLN assembly vote only, observed Rp=0.244/0.489=0.489. Using the FMLN+GANA vote, observed Rp=0.359/0.489=0.734. With the expected Rp=0.620, we get the previously mentioned expectation of 0.303 for the president’s alliance vote share. Obviously the president’s own vote does not change with these calculations, because any GANA-aligned voters who voted for the FMLN candidate are already included. This is why I think it makes sense to use the combined votes–not only because it makes the formula “work” better. (Honest! But F&V readers get to do peer review here!)**

This is the second nonconcurrent assembly election I have watched closely since Rein Taagepera and I developed the formula for our book (published in October, 2017). The other was in France. In April, 2017, I “predicted” that the brand new party of Emmanuel Macron would win around 29% of the vote. This was the day after the first round, and assuming he would win the second round (which he did, easily). At the time, much media commentary was of a hand-wringing character: Macron would be weak, maybe even face cohabitation, because he didn’t have any party to speak of. I said no, the electoral cycle will ensure he gets a good boost in votes in the assembly election. An elapsed time (E) of 0.017, an extreme “honeymoon” election, would almost guarantee it.

In fact, the election resulted in Macron’s party winning 32% of the vote. (And, a large majority of seats, due to the disproportional electoral system.)

So, that’s two elections in the past year called (more or less) correctly, within a few percentage points, based only on the elapsed time and the president’s own initial vote share.

I still hesitate to call this a prediction, because the parameters in the formula (1.20 and 0.725, above) are not themselves based on deductive logic. And perhaps I also should hesitate because of the ambiguity over party vs. alliance, as discussed in this post. But there just may be something to these electoral cycle effects, after all.

[Note: lightly edited since posting.]

______ Notes
* The 2009 presidential election featured only two candidates. So the party’s presidential vote was inflated due to the abstention of all but the two big parties from the presidential race that year. This is the only time smaller parties have not contested the first round. As I said at the time, the decision by the then-ARENA majority to shift from a concurrent to counter-honeymoon assembly election that year converted the assembly election into a “de-facto first round of the presidential election”. The right got spooked, perhaps, by the strong showing of the FMLN, and did not want to risk a division, even in the two-round election. The left followed suit and, with a sole candidate, narrowly won.


** In the 2015 election, based on the new president’s 48.9% of the (first round) vote in 2014 and elapsed time, E=0.20, we would have expected a votes ratio Rp=1.055. That would mean an assembly vote percentage of 51.6%. The FMLN itself won only 37.2%, but if we include GANA, as noted, we get 46.4% (Rp=0.949), which is a small under-performance. (Consequential, of course, as they failed to get the majority predicted.) How about one election farther back in the cycle? In 2012, GANA existed, but that party had not existed at the time the then-incumbent president of the FMLN was elected. So we certainly can’t include it in the calculation for 2012! For that election E=0.60, and so expected Rp=0.765. The president had won 51.3%, so we’d expect the FMLN to have won 39.2%. It actually won 36.8% (observed Rp=0.719), so it did only a little worse than the formula suggests it could have expected.

 

Italy 2018: Assessing the electoral-system effect

[Note: data calculations in this post are based on preliminary results. For some updated information, see the comments by Manuel below.]

The Italian election of 4 March produced an “inconclusive” result, as the media (at least English-language) are fond of saying when no party wins a majority. However, there are many aspects of the Italian result that are being reported with considerable confusion over how the electoral system works. In this post, I want to try to offer a corrective, based on the results published in La Repubblica.

These summaries will apply to the Chamber of Deputies only. The interested reader is invited to perform the equivalent calculations on the Senate and report them to the rest of us.

One common note of confusion I have seen in media accounts is insufficient clarity about the distinction between alliance (or “coalition”) and party. The design of the electoral system is fundamentally one that works on pre-election alliances, each consisting of one or more parties. Obviously, if an “alliance” consists of only one party, it is just that–a party. Rather than invent some encompassing term, I will use “alliance” when referring to the set of vote-earning entities (that would be a “more encompassing term”!) that includes pre-electoral coalitions, and “party” only when looking at the sub-alliance vote-earning entities. In the case of the Five State Movement (M5S), the “alliance” and “party” are the same thing. In the case of the other two main entities, they are different. Centrodestra (Center-right, or CDX) is a pre-electoral alliance consisting of the Lega, Forza Italia, and other parties. Centrosinistra (Center-left or CSX) is a pre-electoral alliance consisting of the Democrats (PD) and other parties.

No alliance has achieved a majority of seats. The M5S is the biggest party, while the CDX is the biggest alliance. As the table below shows, CDX leads with 263 seats, with M5S second on 222. The CSX has 118.

The breakdown is as follows, showing the three main alliances, plus a fourth one, Liberi e Uguale, which was the only other to clear the 3% threshold for individual parties or 10% for multiparty alliances:

Alliance % votes seats % seats
Centrodestra 37.0 263 42.5
M5S 32.7 222 35.9
Centrosinistra 22.8 118 19.1
Liberi e uguali 3.4 14 2.3
others 4.1 2 0.3

(There are two other seats indicated as being won by “Maie” [Associative Movement Italians Abroad] and “Usei” [South American Union Italian Emigrants]; no vote totals are given.)

The total comes to 619. Another summation from the same sources yields 620. I will not worry about the small discrepancy.

As an aside, I have seen at least two accounts of the result that have had phrasing referring to no party having won the 40% “required” to form a majority. There is no such requirement. It is true that no alliance or party attained 40% of the overall votes cast. However, the understanding that some authors (even one Italian political scientist writing on a UK blog) seem to have is that had someone cleared 40%, that alliance or party would have been assured of a majority of seats. That is incorrect. In fact, given the way the system is designed (more below), it is highly unlikely that an alliance with just over 40% could have won more than half the seats. Possible, but very unlikely (and we might say not significantly less likely had it won 39.99%). This “40%” idea floating around is just totally wrong.

The presentation of the overall result leads me to a second key point: the outcome is not terribly disproportional. However, it would be wrong to conclude from this observation that the electoral system was “proportional”. It is not designed to be such, and the disproportional elements of the design have significant consequences that I shall explain.

In terms of the Gallagher index of disproportionality (D), the result, based on alliances, yields D=5.40%. That is slightly greater than the median for my set of over 900 elections, and somewhat less than the mean of the same set (4.9 and 7.1, respectively). It is very slightly greater than the mean for PR systems (4.6; median 3.8).

Thus, based on the outcome measure of disproportionality, the Italian system looks like a moderately disproportional variant of PR. however, it is not a PR system! We do not ordinarily classify electoral systems based on their outputs, but on their rules. By that common standard, the Italian system is not PR, it is mixed-member majoritarian (MMM). It consists of two components–one that is nominal and the other than is list. The nominal component is plurality rule in single-seat districts, while the list component is nationwide PR (for alliances or parties that clear the threshold). Crucially the list seats are not allocated in compensatory fashion, but in parallel; this is the feature that makes it MMM, not MMP.

Unusually for MMM, but not disqualifying it from that category, the list-PR component is a good deal larger than the nominal (plurality) component. The nominal component is only around 35% of the total. However, the lack of compensation means that any alliance (or party) that can win pluralities in a substantial number of single-seat districts (SSDs) will be over-represented even after adding on all those list-PR seats. And such over-representation is precisely what happened.

If we look at the 398 list-PR seats and their allocation to parties (and here I do mean parties), we see a substantially more proportional output than overall. The Gallagher index is D=3.93%. This is, as reported above, right near the mean and median for pure PR systems. Just as we would expect! And most of the disproportionality comes from parties below the threshold, not from disparities among the over-threshold alliances. Around 4% of the vote was cast for alliances (or individual parties) that did not qualify for any seats. Some other votes are lost due to a provision that sub-alliance parties that get under 1% of the vote also have their votes wasted. If a party is between 1% and 3%, its votes are still credited to the alliance of which it is a part, even though such a party is barred from winning any seats in the list component.

Focusing on some of the major parties, we see that the major CDX partners were not much over-represented in the list component of the system: Lega has 17.4% of the vote and 73 seats (18.3%) for an advantage ratio (%seats/%votes) of A=1.05. Forza Italia has 14% of votes and 59 seats (14.8%) for A=1.06. The second largest alliance, the stand-alone party M5S has 32.7% of votes and 33.7% of seats for A=1.03. In the CSX, the PD is more over-represented, with 18.7% of the votes but 91 seats (22.9%), and A=1.22. I suppose this is because its partners mostly failed to qualify for seats, but the votes still get credited to the alliance (as explained above), and hence to the PD.

We see from these results that, with the partial exception of the PD, the parties are represented quite proportionally in the list-PR component of the MMM system. What gets us from D=3.93% in the list component to D=5.40% overall is precisely the fact that the nominal tier of SSDs exists and favored, as one would expect, the larger alliances. The following tables shows just how dramatic this was.

Nominal result
seats % seats % votes
Centrodestra 109 49.1 37.0
Centrosinistra 24 10.8 22.8
M5S 89 40.1 32.7
total 222 100.0

The vote percentages are the same as those shown in the first table, because there is no ticket-splitting between the two components. Each alliance presents a single candidate in each district, and the voter can vote for either a party list or an alliance candidate. Votes for a list are attributed to the candidate, and a vote for the candidate is proportionally divided among the lists in the alliance that nominated the candidate (with the previously noted caveat about parties whose national vote is in the 1-3% range).

The seats in the nominal component are distributed quite disproportionally: the largest alliance, CDX has nearly half of them, despite only 37% of the vote. The M5S is also over-represented, with about 40% of seats on just under a third of the votes. As is typical under SSDs with plurality, the third-place finisher, CSX, is significantly underrepresented, with a percentage of seats not even half its votes percentage.

Also as is typical, candidates often won their district seats on vote percentages in the low 40s or less. The mean district winner had 43.9% of the vote. For the M5S the mean was 45.4%, while for CDX it was 43.7%. As might be expected for a third force winning some seats, the CSX tended to benefit most of all from fragmented competition, with its mean winner having 39.2%. The lowest percentage for any SSD winner was 24.1% (M5S in Valle d’Aosta). Four winners had over 60%, including two from M5S and two from CSX; the maximum was 65% (CSX in Trentino-Alto Adige/Südtirol).

The media focus is on the “inconclusive” result, and many are blaming “PR” and the failure of any party (or alliance) to reach 40% of the votes for the lack of a “clear” verdict. However, we have seen here that the system is not proportional, even if the overall level of disproportionality is modest. If the entire system had been based on the allocation used in the list-PR component, we would be looking at CDX with 38.7% of seats, M5S with 33.7%, and CSX with 23.6%. However, given the actual MMM system, and its inherent disproportionality, the result is CDX 42.5%, M5S 35.9%, and CSX 19.1%. The non-PR aspect of the system thus has made a difference to the seat balance. The bargaining context would be difficult either way, but the two largest alliances are both boosted somewhat by features of the electoral system. Had the leader reached 40%, it would have netted only slightly more seats, surely still short of a majority, because–contrary to some claims circulating–there was no guarantee of a seat majority for reaching any given vote percentage. To form a majority of parliament, an alliance would have to win a very large percentage of the single-seat districts as well as some substantial percentage of the votes (probably a good deal higher than 40%). That the outcome is “inconclusive” says more about the divisions of the Italian electorate than it does about the supposed problems of a proportional system that Italy doesn’t actually have.


Thank you to Gianluca Passrrelli for sharing the link from which I based my calculations and for his excellent chapter in the forthcoming Oxford Handbook of Electoral Systems.

Italy, 2018

It is 4 March, and in addition to El Salvador, Italy has its election today.

It is especially interesting in that it is the first election under (yet again) a new electoral system. This system is MMM, although quite different from the MMM system in place for a few elections in the 1990s and early 2000s. Details of the system were discussed in an earlier thread. I offer this one for further discussion, in particular of the results as they come in.

Summary of new Italian electoral system

If you have been unclear on what the new Italian electoral system–to be used the first time this March–really is, there is a good summary.

Broadly, it is mixed-member majoritarian (MMM, and definitely not MMP, contrary to a few claims I have seen). But with only 3/8 of the seats elected from single-seat districts, it stretches the definition at least a little bit. Anyway, the components (nominal-district and list-PR) are allocated in parallel.

There are some complicated provisions regarding the relations of votes for district candidate and lists, having to do with parties running in alliances, but there is no way to split across alliances. There is no partial compensation mechanism as there was in the MMM system (which had a balance tilted more in favor of the nominal tier) that Italy used between 1994 and 2001.

Catalonia 2017 result

(Following up on the pre-election entry, where I said the electoral system could make a difference to the result!)

If we aggregate the parties’ votes and seats in this week’s Catalan regional parliament election by pro-independence and pro-union blocks, we find the election produced a plurality reversal. That is, the pro-union parties won more votes, but the way the separate parties’ votes were translated into seats by electoral system resulted in a pro-indepdence assembly majority. The voting result between the blocs was not even very close, those opposed to independence winning by about 4.6 percentage points. This sort of thing should not happen under PR, but can happen when the system is malapportioned and the geographical distribution of party support favors the over-represented side.

I thank David Lublin for pointing this out, via an email message, the contents of which I am sharing here, with his permission.

In this first table are the votes by party and electoral district (data from El País). The main pro-separatist parties are JxC, ERC, and CUP, and these together have 70 of the 135 seats (as the second table below shows), but only 48.3% of the vote.

Cs JUNTSxCAT ERC-CatSí PSC CatComú-Podem CUP PP
Barcelona 856382 615201 669108 491201 272632 141363 140786
Girona 79022 148702 87949 34898 16331 21539 11453
Lleida 40608 77695 63852 21618 9318 12052 10839
Tarragona 119870 95223 104057 51643 23443 17524 19976
CATALONIA 1095882 936821 924966 599360 321724 192478 183054

And here is a table David prepared of the same votes run through alternative electoral systems.

David looked at the outcomes considering:
(1) Malapportionment (actual system) v. Fair Apportionment;

(2) D’Hondt (actual system) v. Ste. Lague; and
(3) Four Districts (actual system) v. Single District.
As the following table reveals, the current setup greatly advantaged the pro-independence forces:

 

Back on 8 November, David had noted in a Monkey Cage post that the electoral system of Catalonia was “stacked” in the separatists’ favor. In that post, David said that Barcelona, which is the most pro-union of the districts, has 14 fewer deputies than it would have, based on its share of the population. (That would make its district magnitude 99! Of course, they could divide it into multiple districts.)

Manuel Alvarez-Rivera had previously noted the impact of the electoral system on the 2015 election, at which such a reversal also occurred. Manuel’s observations can be found both here at F&V and at his own blog, Electoral Panorama. The 2015 reversal was less severe than this year’s because in the earlier election the pro-union parties won the vote just 48.1% to 47.8%.

Catalonia and the rest of Spain need many things to work out their relationship (with or without separation). But one thing that clearly would help would be an electoral system for Catalonia’s own parliament that reflects how its people actually vote.

Catalonia 2017

I suppose it would not be an exaggeration to say that tomorrow’s election will be the most watched election ever for the regional parliament of Catalonia.

I certainly do not know anything about Catalonian politics, but indications are that the vote will be close between parties favoring secession and those favoring remaining in Spain (while perhaps advocating a new set of center-region arrangements).

The electoral system is quite proportional. At least according to the Wikipedia page on the 2015 election, the assembly size is 135. There are four districts, which makes for a mean district magnitude of 33.75. With a seat product of 135 * 33.75 = 4556.25, we should expect an effective number of seat-winning parties around 4.07. However, in 2015, the actual value was a good deal lower than that, at 3.60 (or 88% of expectation). This was due to a large leading party, which in that election was Together for Yes, with 62 seats (45.9%). Based on the seat product, we’d expect a largest party of around 35% of seats.

Naturally, with such a high seat product, the differences between percentages of seats and votes should not be large. Together for Yes had 41.3% of the votes (ignoring blank votes); overall deviation from proportionality is 3.78% (Gallagher index). While not especially high, that is a little more disproportional votes-to-seats translation than I would expect. There is a legal threshold of 3%, applied in each district. But with the smallest district having a magnitude of 15, this would not have much effect. Besides, the wasted vote percentage (non-blank votes for parties winning no seats) was only 1.1%.

So where does the disproportionality come from? Some of it is from the use of D’Hondt allocation, but with such a high seat product, even D’Hondt should not swing six seats to the largest party (the difference between a purely proportional result, to the nearest integer, and the actual result, for the largest party).

The small but potentially significant disproportionality of party votes and sats must be due to malapportionment. The largest district has 85 (!) seats. This is, of course, Barcelona. That makes it one of the very largest districts in use anywhere. Obviously smaller than the single districts in Israel (120), the Netherlands, and Slovakia (both 150), and formerly in the Russian Federation and Ukraine (both 450), but one of the largest in any recent time in a districted PR system. (I recall Indonesia used to have an 85-seat district; Brazil has one with 70*.) However, it is plausible that Barcelona’s 85/135 seats is under-representative of the capital district’s share of the population. The source I am using does not have vote totals, let alone populations, by district. Maybe someone reading this has that information.

It is actually pretty striking to see such disproportionality in a system in which the range of magnitudes is 15 to 85! Not that it is highly disproportional, but relative to what we might expect from such high magnitudes and seat product, it is on the distorted side. And, in a close election with a crisis over the territory’s status, the electoral system may prove decisive.

____

* Some Brazilian states have larger, statewide districts for their assemblies. (It may well be that no district has ever comprised a larger percentage of an assembly’s total seats, except where it is 100%.)