Fun with numbers - splitting the Remain vote at the MEP elections

The MEP elections in Great Britain, to be next held on 23 May 2019, use the d'Hondt system for allocating seats in each of eleven constituencies/regions.

Whether the Remain parties (Lib Dem, Green and Change UK) have shot themselves in the foot (feet?) by competing over the same small pool of voters is an interesting question.

Let's treat this as an unofficial In-Out Referendum and assume votes cast are in line with current opinion polls and are the same in each constituency, as follows:

Leave
Brexit Party - 31%
UKIP - 4%

Remain
Lib Dem - 10%
Green Party - 10%
Change UK - 10%

Undecided - neutral - ambivalent
Labour - 22%
Tories - 13%

The more seats there are in a constituency, the closer the result is to proportional representation; the fewer seats, the closer the results are to FPTP.

If you crunch the numbers (or use Paul Lockett's fine calculator) for the largest constituency with ten seats (South East), the end result is the same whether the Remain parties had put up a single list or not - Leave 4 seats, Remain 3 seats and Undecided 3 seats.

The difference is that with a single list and 30% of the vote, Remain would win seats 2, 5 and 9; with three competing Remain parties, they will win seats 7, 8 and 9. So they will do relatively worse in smaller constituencies and relatively worse overall.

The reverse is true for Leave, only not as markedly. If Remain had put up a single list, Leave would win seats 1, 4, 8 and 10 of a ten-seat constituency. With the Remain vote split, they will win seats 1, 3, 5 and 10.
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To sum up, for various sizes of constituency with a split Remain vote, seats will be as follows:

3 seats = Leave 2, Undecided 1
4 seats = leave 2, Undecided 2
5 seats = Leave 3, Undecided 2
6 seats = Leave 3, Undecided 3
7 seats = Leave 3, Undecided 3, Remain 1
8 seats = Leave 3, Undecided 3, Remain 2
9 sweats = Leave 3, Undecided 3, Remain 3
10 seats = Leave 4, Undecided 3, Remain 3

As only five constituencies have seven or more seats, Remain have definitely messed up badly. With a single list Remain vote, seats would be as follows:

3 seats = Leave 1, Undecided 1, Remain 1
4 seats = leave 2, Undecided 1, Remain 1
5 seats = Leave 2, Undecided 1, Remain 2
6 seats = Leave 2, Undecided 2, Remain 2
7 seats = Leave 2, Undecided 3, Remain 2
8 seats = Leave 3, Undecided 3, Remain 2
9 sweats = Leave 3, Undecided 3, Remain 3
10 seats = Leave 4, Undecided 3, Remain 3

Just sayin'...

In case you were wondering how they calculate the number of MEPs each party gets in each region...

… I refer you to Paul Lockett's fine calculator here.

He set it up back in 2009, but the system doesn't seem to have changed and it still works.

The voting system at EU elections - the 'multi-member constituency'

This week's Fun Online Poll shows a clear preference for multi-member constituencies (only a minority support staying with first-past-the-post, see in particular these results). As it happens, multi-member constituencies form the basis of the d'Hondt voting system which is used for the elections to the EU Parliament, due again next Thursday, 4th June 2009, so we can cover both topics in on go.

(AFAIAA, the EU elections work on the basis of party lists, but this is not necessary. We could tweak it that each party puts up as many named candidates as it wants and everybody votes once for a single, named candidate, with each party's seats being allocated to their candidates in order of the number of votes they achieved personally.)

It's quite a neat system, actually, but the way the system is usually explained, while correct, is rather tortuous, so here's my crash-course in forecasting the results for any particular UK constituency, using the likely vote shares reported by PoliticalBetting a couple of weeks ago*:

1. Set up a spreadsheet, with parties and their votes in the left hand column (total votes do not add up to 100%, but that's the way they were reported). You don't have to arrange them in descending order, but it makes it a bit easier later on.

2. Type in the numbers 1 to 6 across the top of the columns, which is enough to cover most constituencies (unless the leading party gets a much, much larger share of the votes cast).

3. Divide each party's votes by the number in the top of each column (for example, Lib Dem, get 14% of the votes, so the result in the column headed '4' is 3.5%. Whether you use 14% or 140,000 votes out of 1,000,000 is irrelevant).

4. Allocating seat is then easy - you just look for the biggest X numbers, where X is the number of seats in the constituency. I've allocated the first ten seats because the largest UK constituency at the EU elections (the 'South East', excl. London) has ten seats (pdf); Northern Ireland and the North East, with much smaller populations only have three each. I've shaded the ten biggest numbers grey to make it easier to visualise:

The Tories get the first seat (28%); Labour get the next one (20%); then UKIP (15%); the next two go to the Tories and Lib Dem (14% each); then Greens (11%); then Labour (10%); then Tories (9.3%); then UKIP (7.5%); and finally Lib Dem (7%, assuming they manage to just pip the Tories by a fraction of a per cent).

Final result:
Tories: 28% of the vote, 30% of the seats
Labour: 20% of the vote, 20% of the seats
UKIP: 15% of the vote, 20% of the seats
Lib Dem: 14% of the vote, 20% of the seats
Greens: 11% of the vote; 10% of the seats

This worked example produces a 'fair' result, but noticeably 'fairer' to the Lib Dems than anybody else (unless the Tories had just beaten them to the final seat, in which case the Tories would have been laughing), but that's the fun part - smaller parties prefer larger constituencies (the more seats there are, the closer the relationship between % share of the vote and % share of the seats) but it helps you, relatively speaking, if your party is awarded the final seat...

For example, in this constituency, it would have suited UKIP if there were only three seats (they would have achieved 33% of the seats for only 15% of the vote) and it would have suited  Labour if there were only six seats (they would have achieved 33% of the seats with only 20% of the vote). With the benefit of hindsight, the Tories would have preferred the constituency to only have five seats (in which case they would have achieved 40% of the seats for only 28% of the votes), and so on.

I expect to spend the evening of Sunday 7 June in front of the telly with a lap-top while I process all this in real time.

I trust that this is of assistance, and remain.

* The results published today are far more interesting...