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The Fabulous Mr d’Hondt

To add to my European Election Primer of last week, this is a brief post to remind you how the four Welsh MEPs will be allocated after today’s election.

The voting system used for the European Parliament elections in Britain (Northern Ireland uses STV) is regional, closed-list proportional representation. For a further explanation, see this earlier post. Of the total number of MEPs the UK has in the European Parliament, Wales has been allocated four. Once all the votes have been cast, and counted, seats will then be allocated via the d’Hondt formula.

D’Hondt is one of several main proportional formulae used in elections around the world. It is named after the 19th century Belgian mathematician, Victor d’Hondt. Among the various formulae potentially available for allocating seats under PR, d’Hondt is generally agreed to be the one that most favours the larger parties. (Guess which parties decided that this is the formula we would use…). More pleasingly, perhaps, it is also one of the easiest to understand.

D’Hondt is based around the following, simple formula:

V/(S+1)

where V = the number of votes a party has won in the election, and S = the number of seats it has won so far in the election.

To allocate Wales’ four MEPs, this formula is then applied mechanically in four successive ‘rounds’ of calculations.

To illustrate how this works in practice, let’s walk through the example of the 2009 European election in Wales. To simplify things, I’ll only present the votes for the five largest parties; the number they each won were:

 

Conservatives: 145,193

Labour: 138,852

Plaid Cymru: 126,702

UKIP: 87,585

Liberal Democrats: 73,082

 

In Round 1, applying V/S+1 means simply dividing the number of votes for each party by 1 (ie, leaving each total as it is!) because nobody has yet won a seat. The first seat is then allocated to the party with the largest total – which can clearly be seen to have been the Conservatives. So they win seat 1.

For Round 2, we again apply V/S+1. That means leaving every party’s totals as they were, except for the Conservatives: as they have now won one seat, we divide their total by 1+1, i.e. 2. This gives us the following totals:

 

Labour: 138,852

Plaid Cymru: 126,702

UKIP: 87,585

Liberal Democrats: 73,082

Conservatives: 72,596.5

 

Seat 2 is then allocated to the party with the largest total – which is now Labour, who are allocated the second seat.

For Round 3, we repeat what the exercise again; only this time, V/S+1 means also dividing Labour’s original vote by 2; hence, the following totals:

 

Plaid Cymru: 126,702

UKIP: 87,585

Liberal Democrats: 73,082

Conservatives: 72,596.5

Labour: 69,426

 

Seat 3 then is then allocated to the party with the largest total – which this time is Plaid Cymru.

For Round 4, we – well, you are probably catching on by now. With Plaid’s votes also now being divided by 2, we have the following totals:

UKIP: 87,585

Liberal Democrats: 73,082

Conservatives: 72,596.5

Labour: 69,426

Plaid Cymru: 63,351

 

The party with the largest total remaining was UKIP, who won the final seat. Had there been a fifth Welsh seat, it would have been won by the Liberal Democrats. But, sadly for them, there wasn’t.

A couple of further points to note.

First, I’ve done the calculations here using vote totals (as the returning officers will do in the counts on Sunday night). You may, however, find it a little quicker and easier to do them on the percentages of the vote. That’s absolutely fine; the two calculations are mathematically identical.

Second, what do we need to look out for in terms of the allocations of seats? Well, to win two seats, the party coming first has to get more than double the number (or percentage) of votes won by the party coming fourth. To win three of the four seats, the party coming first would have to win more than three times the number of the party coming third.

Have some fun (?!) playing around with this week’s polling numbers, to see why things are looking so close for the third and fourth seats.

Comments

  • J.Jones

    Mr d’Hondt isn’t going to be the most popular Belgian…although he may become the best known in Wales, come the Assembly elections if UKIP take 8 list AMs.

    I have to say though that asking questions on Assembly voting intentions alongside MEP voting intentions and just before EU elections is dodgy in the extreme. Will UKIP be in the national news before the Assembly elections? Nevertheless d’Hondt is going to give us 4 major parties and one has-been a major party all representing a relatively small electorate. How many viewpoints within those 5 parties? Well, on some subjects, its UKIP v the rest.

    • Roger Scully

      I’m not sure I would accept that it is ‘dodgy’, Jon. Clearly there is potential for some people to answer the Assembly vote intention in a way which is influenced by the current political context of the European elections. But I think most people understand that, and realise that the political context for other elections will be different.

      More generally – one of the big questions for UK politics in the next few months will be whether UKIP are able to sustain or even build on their performance in these EP elections. After both the last two sets of European elections they faded away rather badly. But they are, perhaps, a rather more robust entity these days.

  • Hugh

    Roger, obviously your comment that d’Hondt generally favours the larger parties is correct, but in this particular instance, wouldn’t application of the Sainte-Lague divisor have produced the same overall result?

    Perhaps next week, when you comment on the outcome of today’s voting, you could give us not only how d’Hondt worked but also whether using Sainte-Lague would have produced a different result!

    • Roger Scully

      Good point, Hugh. I haven’t actually checked the maths on that one, although eye-balling it I think that is probably right. But at the margins the different formulae can make a difference – and in this election, those margins could be the difference between having a seat and not.

      I can just see the Sun headline now – IT WAS D’HONDT WOT WON IT.

      It is a neat irony that Britain uses Sainte-Lague to allocate seats between the regions, but d’Hondt to allocate the seats among the parties within each region…

  • Catherine Thomas

    Thanks for simple explanation of Proportional Representation.
    Waiting to see who represents Wales in Europe..

  • David Byers

    Somewhat pedantic, but to avoid confusion your formula should be amended to V/(S+1).

  • Martin Hughes

    D’Hondt seems to need a much larger number of seats to be a meaningful proportional representation system.
    We need a system that allows voters to express at least 2nd preferences to help ensure that votes for smaller parties are not wasted votes.
    Also in the case of a closed party list syterm, voters should be able to determine the order of the individual party candidates on the party list rather than have it pre-determined by the party.

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