Magnitude and party advantage ratios

What is the relationship between district magnitude and a party’s advantage in seats, relative to votes?

Using the same district-level dataset that Rein Taagepera and I use for our forthcoming Votes from Seats (and which has its original source in CLEA), we can answer this question. The sample I am using here is simple PR systems–those in which the districts are the sole locus of seat allocation (i.e., leaving out two-tier systems).

The advantage ratio (A) is the best way to examine this; it is just a party’s percentage of seats, divided by its percentage of votes.The table below shows the average A for magnitudes (M) ranging from 2 to 7. The larger the A, the more a given party is over-represented. The table shows mean A values for the first, second, and third largest parties (by vote share in the district), as well as how many districts of a given magnitude are in the dataset .

M A, 1st A, 2nd A, 3rd Num. obs.
2 1.29 1.50 0.00 172
3 1.34 1.10 0.50 98
4 1.25 1.15 0.50 103
5 1.26 1.14 0.64 112
6 1.19 1.17 0.73 72
7 1.19 1.09 0.81 79

We can see that M=2 is the only case where the second largest party gains more than the largest does, on average. This result is well known from the experience in Chile. I had thought we might see a similar pattern at M=4. However, we do not. As with all other magnitudes except 2, the largest party at M=4 tends to have a bigger advantage ratio than the second, although the two largest parties’ A values are closer here than in odd M‘s just above and below.

Also of interest fro the same query to the dataset, we find that the lowest magnitude at which A<1.10 for the largest party is M=17. The average for the largest party never falls below 1.00. The second party first falls to A<1.10 at M=13 and then stays right around 1.00 through all higher values.

As for the third largest party, it stays, on average below A=1.00 till M=13, but falls below 1.00 again at several higher M values. The fourth largest party has to wait till M=20 (and likewise has some higher magnitudes where it falls below 1.00).

At higher magnitudes, these average values tend to bounce around a bit, mainly because the sample at any given magnitude is small and thus subject to vagaries of country-level (or district-level) factors (including allocation rules, although the vast majority of these are D’Hondt).

I have long “known” that 4-seat districts tended to under-represent the largest party, relative to the second largest. Well, apparently one should check what one “knows”. Thanks to Jack (on Twitter) for the prompt to investigate.

“Votes that count” in different electoral systems

Throughout the discussion on electoral-system reform in Canada, I have seen various social-media posts that purport to compare the percentage of votes that “count” in Canada vs. in existing PR systems. Typically, these posts will cite a figure of 50% of votes counting in Canada and 95% or more in PR countries.

The numbers seemed fishy to me. I do not doubt that votes are substantially more likely to “count” towards election of a representative under PR than under FPTP or other majoritarian systems. But the 95% figure seemed too high.

As I happen to have a dataset of district-level electoral results in many countries at my disposal, it was not too hard to subject the claim to a test. The harder part is knowing how to operationalize “count”. I chose two methods, based on my understanding of the complaint that reform advocates have against FPTP. The problem, it will be seen, as I suspect both methods are being used by these advocates, but different methods for different systems.

The first method is the one that I believe they are applying to Canada, which is: “did my vote contribute to the election of someone in my district?” Guess what–when your district elects one, for many voters the answer is “no”. (And this may be sufficient reason to want to ditch the system!) The second method is one that I suspect the authors of these posts apply when looking at PR systems: “Did the party I voted for win representation?” That is, I suspect a district-level standard is being applied to FPTP, but a national-level one to PR countries. My calculations seem to bear that out.

If we use the first method–district-level count of votes for parties (or candidates) that did not win in the district, we almost nail the 50% figure for the most recent Canadian election for which I have data. In 2011, I get 50.4% of votes across the country “counting” in the sense that they were cast for the winner in the voter’s district.

Across the 25 FPTP elections for which I have complete data, the average figure is 55.8%. The lowest figures are around 47% in several UK and Indian elections, with the highest being 62% or more in the US and Barbados. (What do these latter two countries have in common? Very few votes going to parties other than the top two.)

I then apply that same standard to PR systems. A pause is needed here. Canada is very highly unlikely to adopt nationwide PR, either with a single national district (which I think we can say is politically and constitutionally impossible) or with districts but also nationwide compensation (as in Germany or Denmark, among others). Thus I consider the relevant metric to be those PR systems that employ districts, plural, and no nationwide compensation.

Using the same standard–votes “count” when cast for a party that wins a seat in the district–the mean for (districted) PR systems is 87.2%. That figure is a lot higher than 50%, I will grant. It is also a good deal lower than 95%.

If we look at nationwide (single-district) PR, guess what? 96.5%! A few specific elections come in at 99%, such as the Netherlands, 2002, and Israel, 1951. (Most Israeli and Dutch elections are over 97%, but Netherlands, 1952, was at a paltry 94.7%.) That’s great! However, most PR advocates, unless they are real purists (and not at all realists) do not advocate the adoption of the Dutch or Israeli type of PR.

What about the second standard? Under this one, your vote “counts” if it was cast for a party that won representation somewhere (at least one seat), even if it did not win in your district. As I noted above, I suspect this is the standard being applied, at least implicitly, to the PR countries in the social-media posts I have seen.

By this standard, districted PR systems’ average percentage of votes that count rises to 93.7%. We are almost to 95%! For nationwide PR, it obviously does not change (there’s only one district). What about for FPTP? 97.1%. Canada, 2011, comes in at 99.1%.

I do not actually know if a Canadian voter feels “represented” if she voted NDP but the NDP candidate in her district lost. I suspect many do feel so represented, or else the NDP would not get more than trivial vote shares in districts where it has no chance of winning. Yet it does. Greens can also get votes near or above their nationwide percentage even in many districts that are totally hopeless for them. Perhaps they feel represented by Elizabeth May (the one Green MP) even if they reside in a different district or province. Not as well represented as if their own MP was Green, presumably, but my point is that voters probably tend to think of national party systems when voting, even in districted systems. Yes, even in systems in which districts have one seat apiece.

There may be many reasons to prefer PR over FPTP. I can think of quite a few myself. But the idea of a vote “counting” towards representation may not be one of the more meaningful criteria to use. Or, if it is used, it might be OK not to exaggerate. The difference between 50% (Canada, 2011) and 87% (mean for districted PR) is impressive enough, using the first (district-based) criterion. We don’t need to pretend that twice as many votes “count” under PR as under FPTP. 1.74 times as many is still a lot more!

Proportionality is such a difficult concept

I expect the mainstream US media to struggle with the concept of proportionality. But even FiveThirtyEight, which prides itself on brining quantitative methods to election coverage, can’t get this right.

Sure, far more delegates were at stake on Super Tuesday (595) than will be awarded March 15 (367), but the Super Tuesday delegates were all awarded proportionally. 
 
If that was the case, then I’d like to ask how it is that Ted Cruz got 2/3 of the Texas delegates on 43.8% of the votes. Or how Donald Trump got 73% of delegates in Alabama on 43.4% of votes. There are several other examples, but I hope these two suffice to make the evidently very difficult point.

The impact of M=96 and no legal threshold

The decision of the German Constitutional Court to invalidate the legal threshold for election of MEPs has been predictably consequential. Given the single 96-seat district, a very large number of parties has won at least one seat, and some have won with less than 1% of the vote.

There will be thirteen parties (counting the CDU and CSU separately) in the German delegation. Seven of them had less than the former 3% threshold; the biggest of the sub-3% parties had not even quite 1.5%. The German government reports the votes; seats are shown at Wikipedia.

Assuming the Wikipedia list is accurate (and it looks likely to be so), these parties that won representation thanks to the Court ruling are: Free Voters, Pirates, Human Environment Animal Protection, National Democrats (yes, a German neo-Nazi will be in the European Parliament), Family Party, Ecological Democrats, and some outfit called Die PARTEI. The last three of these have vote totals ranging from 0.69% down to 0.63%. The NPD’s vote percentage was 1.03.

Also noteworthy is that the Free Democrats continued their slide, winning only 3.36%. They had just missed the 5% threshold for the federal Bundestag elections last year. The Alternative for Germany (AfD), which also had just missed the threshold for the Bundetag won 7.04%.

Nationwide PR in a big country

Ukraine and the Russian Federation have represented, at various times, the only two examples I know of using a single-nationwide district with a magnitude greater than the 150 used in the Netherlands* and Slovakia. (Israel’s single district has M=120, Namibia’s M=72.) [But see JD’s comment for an intermediate example.]

As it happens, both Ukraine and Russia have used the same magnitude, 450, with closed lists, when they have had the single-national district. For Ukraine, such a system was used in 2006 and 2007; for Russia, 2007 and 2011. By contrast, in 1998, 2002, and 2012, Ukraine used a mixed-member majoritarian system (225 M=1 districts, and a nationwide non-compensatory M=225 district), as did the Russian Federation in post-Soviet elections before 2007.

Nationwide closed lists could have the effect of biasing representation towards the capital and other major cities, given the (potential) control of the lists by the central party leadership, and the absence of institutional imperative to offer regional or personalized representation. On the other hand, they could encourage parties to present candidates from even those regions where they are not strong, because a vote anywhere counts towards the party’s overall seat total, and because even in closed lists the presence of candidates from a region might signal to voters in the region that the party is responsive to their needs. In the only study I know of in the political science literature to address such questions, Latner and McGann find some bias towards the most important cities, but also an over-representation of peripheral regions in Israel and the Netherlands.

What about Ukraine? The pattern could be different in a much larger country, with clear regional divides in its politics. A blog post by Erik Herron, Univ. of Kansas, and one of my “Party Personnel” collaborators, offers interesting data on candidate and MP residency in the 2007 election.

Key point regarding 2007 winners:

Kyiv residency is dominant, accounting for more than half of all elected deputies. The Party of Regions is better represented through the reported residency of its elected deputies in some eastern areas (e.g., Donetsk) and the opposition is better represented in western areas (e.g., BYuT in Galicia). But, parties can also claim elected deputies who report residency in “enemy” territory.

Meanwhile, Russian Federation president Vladimir Putin today signed into law a return of his country’s electoral system to the mixed-member system. While the article is not explicit about the relation of the two tiers, I assume it will again be MMM (non-compensatory). Given the decline in the standing of the ruling United Russia, it makes sense that Putin would prefer a move towards a system that is both disproportional and favorable to “independents” who have local bases of support that exceed the popularity of the ruling party’s label. In this respect, it would be identical to the change in Ukraine prior to the 2012 election. That change worked strongly in favor of the Putinist forces of that country, buying them time to acquire the finest in home furnishings.

Now that Russia is moving back to MMM, and Ukraine is moving on from the Yanukovych/Party of Regions era, maybe Ukraine will go back to the pure PR system. If they ask me, I certainly would not recommend the single national district, however. Either districted PR, without too much variation in magnitude, or MMP would be my advice.

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* In a very technical sense, the Netherlands has districts for nomination purposes. But for all practical purposes, it is a single district. It also allows preference voting for candidates on the list (though list ranks are more important), as does Slovakia, and as Israel does not. Russian and Ukrainian lists have always been closed, as are Namibia’s, to the best of my knowledge.

The changed German MMP

With Germany’s federal election coming up within a week, Manuel has a very interesting post at Electoral Panorama about how the recently enacted changes to the electoral system work, and a simulation of their effect if they had been in place for the 2009 election.

I will not try to summarize it, but rather urge my readers to go over there, and then come back and discuss.

Thanks, Manuel, for the post.

Could proportional representation stop the popular Merkel?

One might think that the BBC would know the difference between the institutions of proportional representation (PR) and a parliamentary executive format. But one might be wrong.

On the Business Daily show on BBC World Service today, the host framed a program segment about Germany’s upcoming election around the following claim: Chancellor Angela Merkel (Christian Democrat) is vastly more popular than her main challenger, Peer Steinbrück of the Social Democrats. However, because of the electoral system she might not return as Chancellor.

For the record, if the most popular politician in the election does not emerge as head of the government after the election, it is because of the parliamentary system: Germany does not elect its leader directly. Its leader must have the consent of parliament (first chamber) to enter and remain in office. Just like Britain, one might note.

Later in the program, during an interview with two German election analysts, the host repeated a variant of this great threat to the popular Merkel emanating from the country’s electoral system, calling the system “unpredictable”.

If we redefined “electoral system” to mean “voters’ choices”, the host’s remark might have made some sense. He noted that many voters see less and less difference between the two big parties and are increasingly likely to vote for small parties, like the Greens. Indeed, even the popular Merkel is not going to lead her party to much more than 40% of the vote, assuming polls (which have been quite stable throughout the year) are accurate.

With only around 40% of the vote, the PR system will mean the Christian Democrats are short of a majority of seats–well short. The parliamentary system will mean she needs at least one partner. (One might point out to the BBC host: just like Britain; a minority government would also be possible but much less likely in Germany.) However, we can be fairly certain that the coalition will reflect how people actually voted. This is the value of PR. In fact, the highly predictable aspect of it. If 40% of voters have voted for Merkel’s party, and there is no conceivable alternative block of parties that has obtained a collective majority of votes, the government will be led by Merkel, in coalition with one of various smaller parties.

Despite the host’s best efforts to signal a looming crisis due to the German electoral system, both German guests calmly pointed out that Merkel was sure to return as Chancellor, most likely in the same coalition she has now–with the Free Democrats–or perhaps in coalition with Steinbrück’s Social Democrats. One of the guests said that the chance of the latter was increasing.

There actually is a good chance that the Christian and Free Democrats will be short of 50%. But that will be even less a crisis than when the same happened in 2005 (and that was not a crisis). In fact, given the new shape of German politics, with one party clearly dominant, it is time to stop calling the possible coalition of Christian and Social Democrats a “grand coalition”. But that is a theme for another planting.