Psephology series, part 4: why European elections are better under Sainte-League than d'Hondt

Earlier today, the full list of candidates for European elections in the UK was announced by each region.

Some opinion polls have been conducted on each of the largest seven parties (i.e. the Brexit Party, Change UK, Conservative, Green, Labour, Liberal Democrats and UKIP), who have submitted lists everywhere in Britain. However, seat projections should not be calculated at this stage as each party's regional support varies widely, as do the number of seats per region.

Which brings us to this interesting question in psephology: how would it look if we used Sainte-League instead of d'Hondt?

Sainte-League's key difference from d'Hondt is that when it comes to allocating seats to political parties, the divisor 2n+1, where n is the number of seats a party has already won within a round of allocation, is used instead of n+1. This means that when determining who gets the remaining seats in a PR constituency after the first set of seats have been allocated, the party's votes are divided by 3, 5, 7 etc. instead of 2, 3, 4, meaning that smaller parties are more likely to win seats.

How would this have affected European elections in Britain? Let us take the London constituency as an example, given that it had the most lists (17) in 2014:

Labour received 36.67% in that European Parliament constituency in 2014, the Conservatives 22.52%, UKIP 16.87%, the Greens 8.93%, the Liberal Democrats 6.73%, and the others polled too low to win a seat under any PR system.

With this, the d'Hondt allocation was:  4 Labour, 2 Conservative,1 UKIP, 1 Green.

1st seat: Labour (36.67%; 36.67/2= 18.335)
2nd seat: Conservatives (22.52%; 22.52/2=11.26)
3rd seat: Labour (18.335; 36.67/3=12.223)
4th seat: UKIP (16.87%; 16.87/2=8.435)
5th seat: Labour (12.223; 36.67/4=9.1675)
6th seat: Conservative (11.26; 22.52/3=7.506)
7th seat: Labour (9.1675; 36.67/5=7.334)
8th seat: Green (8.93)

The Sainte-League allocation, by contrast, would have gone as follows:

1st seat: Labour (36.67; 36.67/3=12.223)
2nd seat: Conservatives (22.52; 22.52/3=7.506)
3rd seat: UKIP (16.87; 16.87/3=5.623)
4th seat: Labour (12.223; 36.67/5=7.334)
5th seat: Green (8.93; 8.93/3=2.977)
6th seat: Conservatives (7.506; 22.52/5=4.504)
7th seat: Labour (7.334; 36.67/7=5.239)
8th seat: Liberal Democrats (6.73)

Making a hypothetical Sainte-League allocation in London: 3 Labour, 2 Conservatives, 1 UKIP, 1 Green, and 1 Liberal Democrat.

D'Hondt clearly favours larger parties simply because of mathematics, since they will get the extra seats first. In regional constituencies this can effectively disfranchise large numbers of voters.

There would be more Green MEPs under Sainte-League than d'Hondt at every election, especially in 2009, and in general the election would have been more proportional. Labour won half the European seats in London in 2014 despite winning only 36.67% of the vote, which is not that proportionate at all. Under Sainte-League, used in German elections, seats will be more evenly allocated. As coalitions are not necessary for European elections, they should be as proportional as possible. D'Hondt also makes smaller PR constituencies disproportional in practice, as seen in North East England and the East Midlands in particular.

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