Election 2010: what would a proportional parliament look like?

While we continue to enjoy/ endure the spectacle of the coalition negotiations, one of the key issues that remains is what will happen with regards to electoral reform, and, specifically, Proportional Representation.  While all this is going on, I thought it might be interesting to take a look at how different parliament would look if the numbers of seats each of the parties had was strictly proportional to their share of the vote.  So I made a table, taking the data from the BBC’s Election Results page:

(I encountered some difficulties in making this table – see the postscript below for the details.)

And, because I have way too much time on my hands, here’s the same information in the form of a couple of pie charts:

Perhaps the most striking thing about this is the amount of change there is – only two parties (SDLP and Alliance) received the number of seats their share of the vote  entitled them to, with every other party being either over- or under-represented.  The biggest losers under a proportional system would be the Conservatives and Labour, losing virtually the same number of seats each, and the DUP who would lose half of their seats.  The biggest winners are the Liberal Democrats, who ought to have getting on for 100 extra MPs; UKIP and the BNP also do well, transforming a total absence of representation into notable numbers of seats.  Amongst parties with an even smaller share of the vote, the Greens do substantially better, increasing their share of seats sevenfold, while a number of smaller parties would have an MP in the Commons.

In terms of the coalition arithmetic, there would be some change.  The Conservatives would still be the largest party.  The major difference is that a purely Lib-Lab pact would be viable – under a strictly proportional system, the two parties combined vote share of 52% would give them a workable overall majority of 28 seats; a Lib-Con pact would have a majority of 128 with a combined 59.1% share.

The existence of two easily viable outcomes would make the coalition negotiations now taking place rather more substantive.  Instead of being faced with a choice between whatever the Conservatives are prepared to offer and participation in an unstable Labour-led administration liable to collapse at any moment, the Lib Dems would be able to play one side off against the other, in order to arrive at a blended legislative programme that represented a genuine consensus.

Of course, there are caveats.  For a start, most systems of Proportional Representation would produce a result not altogether like this.  The table above assumes that seats are awarded proportionally on the basis of first choice across the country as a whole, where most systems of PR try to preserve a link between MPs and local populations, and also take into account the 2nd (even 3rd or 4th) preferences of electors.  Secondly, an election fought under a proportional system would almost certainly see a change in voting patterns, with many people who voted tactically for one party switching their allegiance to the party they actually support.  Experience from other countries suggests there would also be a proliferation of smaller parties, although UK experience in Scotland and Wales suggests these smaller parties may not have a major role in forming a government.

Postscript

Drawing up the table above was a lot more complicated than I thought it would be.  The first problem I encountered was that a percentage share of the votes doesn’t often translate into an exact number of MPs.  For example, Labour’s 29% of the vote entitles them to 188.5 MPs, but MPs obviously can’t be sub-divided – they come in discrete units of one.  I decided to follow the standard rule of rounding down decimals from 0.4 downwards, and rounding up decimals from 0.5 upwards, even though this made me a little uncomfortable – parties separated by only a few thousand votes could end up with different levels of representation.

Nevertheless, with this rule of thumb in place things seemed to be going along swimmingly – until I encountered the next problem.  This was the realisation that, with 650 seats to distribute, it takes a vote share of 0.154% (rounded to 3 decimal places) to secure an individual seat.  Given this figure, I realised that it would therefore take 0.077% of the vote to secure half an MP, and hence be entitled to have this rounded up to a single MP.  The problem here was that the BBC results site, when they calculated share of the vote, had rounded it to one decimal place, making it impossible for me to know which of the parties with a vote share recorded as 0.1% were due an MP, and which were not.  Luckily, the results page did include enough of the raw data – votes cast for each party, and the overall total of votes cast – for me to recalculate the share to the necessary 3 decimal places, and include the relevant data in the table.  (For the record, the party that came next after Traditional Unionist Voice was the Christian Party – they secured 0.063%, which translates to 0.410 of an MP, rounded down to none.)

I had hoped that this might have been the last of my difficulties, but when I had come to the end of the process I realised that I had still not allocated all the seats.  Following all the rules I had set myself, and pursuing all the way down the league of votes to the party that secured only 0.063% of the vote, I had only distributed 645 seats.  The remaining 5 were, presumably, the combined total of all the remainders of MPs that I had rounded down.  I found I was at something of a loss on how to proceed at this point because none of the potential solutions seemed fair.  I could have awarded the extra seats to those parties which had the largest remainders below 0.5, but this would mean giving an unearned MP to some parties while withholding them from others, which really didn’t seem fair.  And in any case, should it be the largest remainders amongst those parties that had already got an MP, or amongst those parties that hadn’t got an MP, or amongst all the parties?  Another possibility would have been to assign them randomly on the lot-drawing principle – this is what is used currently to decide who is elected in a constituency if two or more candidates are tied after several recounts – but again I couldn’t decide if the distribution would be among the parties without MPs, or the parties with MPs, or all the parties, and in any case using random methods is fairly profoundly undemocratic.

So, in the end, I decided to leave those 5 seats unassigned.  (You could argue 4 seats, since the Speaker isn’t included on either the proportional or actual lists, and he was elected on an apolitical ticket.)  In terms of a just-a-bit-of-fun illustration of what a parliament selected proportionately on the basis of votes as cast, it doesn’t really affect the picture, but I do come away with a greater insight into the problems there can be in designing alternative electoral systems.

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2 Responses to Election 2010: what would a proportional parliament look like?

  1. It’s funny. This is the second version of this blog post I have read. A friend of a friend did this too and it is strange to see you drawing the same conclusions – why the BBC haven’t done this themselves I don’t know.

    I think your remaining MPs is why there will always be a “top up” system for a PR government. You are also right that it would be regional if we actually did it here. You could also have an STV system like the Australian one, where the person has to have 51% of the vote to secure a seat – even if this is based on second, third, fourth preferences.

  2. aethelreadtheunread says:

    Hi intothesystem, and thanks for commenting.

    This is the second version of this blog post I have read.

    Well, i never claimed to be original… ;o)

    why the BBC haven’t done this themselves I don’t know.

    One possibility is that, if the BBC were to do this kind of analysis, they would be worried about being open to accusations of taking a view on the desirability or otherwise of electoral reform – the data in this post is more helpful to arguments in favour of electoral reform than it is to those against. Given that the grassroots of one party (the Conservatives) are pretty solidly opposed to electoral reform, the BBC might be worried that would be seen as party political bias. Then there’s the fact that PR is a big issue in the coalition negotiations, and the BBC will want to be very careful about doing anything that might be seen to prejudice those discussions. Personally, i’d quite like this analysis to get out more publicly – in the end, data is neutral, and the BBC could be scrupulously fair in allowing those opposed scope to argue against electoral reform.

    You could also have an STV system like the Australian one, where the person has to have 51% of the vote to secure a seat – even if this is based on second, third, fourth preferences.

    This is actually pretty close to the Alternative Vote system being promised to the Lib Dems outright by Labour, and subject to a referendum by the Conservatives, so this may well be what we end up with.

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