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.

Burkina Faso a-Blaise

Burkina Faso, a marginal democracy, perhaps, but one with competitive elections, is suddenly in the news. Government buildings are ablaze, and its president, Blaise, is in danger of overthrow. So my thoughts naturally turned towards the question of how the country’s parliament is elected.

Balise Compaoré has been president for 27 years. The trigger to today’s violence and declaration of a state of emergency, and reports of some soldiers defecting, was a meeting of the parliament to consider lifting a term limit that otherwise prevents Compaoré from running yet again in 2015.

The most recent presidential election was in 2010, and it was not exactly a close contest. Compaoré won 80.2%. He had won a similar total five years earlier, which was quite a decline from his 87.5% in the election before that.

In the election for parliament (which was dissolved late today), held in 2012, however, the president’s party was in a much less dominant position. The Congress for Democracy and Progress (CDP), won 48.7% of the national votes and 70 of 127 (55%) of the seats. No other single party was close–the two next largest parties each had around 11% of the vote and 18 and 19 seats–but the election results over the past fifteen or so years show a general, if slow, decline in CDP dominance.

The electoral system is unusual and interesting. As best I can tell, it is a parallel two-tier PR system. There is a national tier with a district magnitude (M) of 16, of which the CDP won 8 seats. This tier is quite clearly not compensatory: the seats won here are just added to the seats won in the provincial contests. It is in the latter that things get interesting. There are 111 provincial seats divided among 45 provincial districts. This works out to an average magnitude (ignoring the national seats) of 2.47.

Of the 45 districts, 37 have M=2. These 74 seats represent two thirds of all the seats in the provincial tier, and 58% of the entire parliament. This must be the highest share of two-seat districts of any country other than Chile (where all districts in both houses elect two members*). As we know from Chile, or from electoral-system theory, two-seat districts with a non-majoritarian formula systematically favor the second-largest party or alliance, in contrast to the usual rule that smaller magnitudes favor larger parties under proportional or “semi”-proportional allocation formula. Such over-representation was the explicit aim of the Chilean system’s designers, who were inside the former dictatorship and had evidence from the 1988 plebiscite that they would be the second largest political force in the country upon a return to fair elections.

I know nothing about Burkina Faso politics prior to what I have learned today, but it is hard to imagine that an electoral system with a majority of its seats elected in two-member districts was not deliberately designed to offer a boost to the second political force in each province. I can’t say the second nationally, as in Chile, because it appears that there is no single nationwide force in opposition to the CDP. Even so, the second largest party, the Union for Progress and Change, with 19 seats in the parliament, was significantly overrepresented: 14.96% of the seats on 11.1% of the national votes. (I should note that it is not clear to me whether voters get a single vote or separate national and provincial votes, although it seems that they might be separate; Adam Carr reports “voting for members elected from national lists” and that is what I am referring to here, until I turn to “voting for members elected by province” below). The 18 seats for the third largest party in parliament, the Alliance for Democracy, give it 14.17% on 11.2% of the votes. So the Chilean pattern is evident here, too.

Moreover, unlike Chile’s use of D’Hondt, in which a list wins both seats if it doubles the votes of the second list in the district, in Burkina Faso there are cases of the second list being well under half the votes of the CDP yet getting a seat. So not only the district magnitude, but also the formula, appear designed to boost the seat share of the runner-up. Take the case of Banwa province. Here the CDP had 55.6% of the vote and the Alliance for Democracy had 15.3%. That’s a votes ratio of 3.6:1. Yet each has one seat. There are numerous other examples of ratios of 2.5:1 or greater in the two-seat districts, but the seats splitting 1:1.

Of course, sometimes the CDP is not the largest party in a province, and the M=2 system then benefits it. For example, in Bougouriba, the CDP won 37.8% to 42.4% for the Union for Progress and Change. There are three other districts, all with M=2, where the CDP came in second place, but strong enough to get a seat. In addition, there were six districts, also all M=2, where the CDP managed both seats on vote percentages ranging downward from 88% to 60.3%.

What about the districts with magnitudes greater than two, aside from the national district? We have four cases of M=4, two of M=3, and one each of M=6 and M=9. Note the dominance of even magnitudes. Aside from M=2, the most favorable to parties other than the largest would be, of course, M=4. In each the four M=4 districts, the CDP got two seats on vote percentages ranging from 37.8% to 52.4%. In one of them, Yatenga, the runner-up won both of the other seats on just 35.5% of the vote (to the CDP’s 45.5%). This was one of only two provincial districts in which a party other than the CDP won more than one seat; the other was the one M=9 district. Even there, the second party was somewhat over-represented (2 seats on 20.2%).

The CDP’s 55% of the nationwide seats on 48.7% of the national list votes is, of course, over-representation. However, based on Adam Carr’s results showing different numbers of parties contesting some provinces than others, and often fewer than are reported in the national list results, there likely are separate ballots. If there are, it is possible that the CDP’s aggregate provincial list vote is more than 50%.** In any case, it is clear that the party would have won many more seats if not for an electoral system that systematically over-represents whichever list comes second in a given province.

It appears the district tier of the current system may already have been in place in 2007, with the parliament consisting of 111 seats, the same number as the 2012 sum of provincial seats.*** In that election the CDP won 59% of the votes and around 65% of the seats, but the second largest party was over-represented despite trailing far behind (14 seats on 10.7% of votes). In 2002, by contrast, the system had divided 91 seats among 13 regional districts (with no national tier). That means an average magnitude of seven; the range was 2-10, but only one district had M=2 in that election. The CDP then won 47 seats on 49.5% of the vote, an almost proportional result even if technically a manufactured majority. That’s at least three different electoral systems in three elections–stability in the presidency, but institutional instability for a legislature that is much less dominated by the ruling party.

Burkina Faso politics suddenly look interesting!


* Pending an in-progress electoral reform.

** The motivated reader is encouraged to convert the results to spreadsheet (or search for a source that has them in such a format already) and let us know in a comment.

*** Adam Carr does not show district-level results in 2007.