Monday, 25 April 2011

Why Stop at 50%?

I've been too negative - pointing out inaccuracies in claims made in favour of AV, when nobody really cares how the system actually works anyway; it's about the spirit of the change.

So for this post and the next, I'm going to be more positive, and suggest some alterations to the electoral system that might in some small way improve things. (And for this first one, I'm indebted to Katie Piatt for setting me along this line of thought.) Let's begin.

A supporter of First Past the Post, a supporter of AV and a third-world dictator (I won't name them) are sitting in a pub (I will name it - the Good Companions, in Brighton).

The FPTP supporter says, 'Under my system, the winning candidate has the highest number of votes.'

The AV supporter says, 'Ah! But under my system I can guarantee that the winning candidate has more than 50% of the votes.'

The dictator says, 'That's nothing. Under my system I can guarantee that the winning candidate gets 100% of the votes.'

As it turns out, both the FPTP and the AV supporter are understating their positions.

In FPTP, we can make guarantees about percentages. If there are four candidates, then it is guaranteed that the winner will get more than 25% of the votes. If there are three candidates, then it's 33%. If two, then 50% (the equivalent of the last round of AV) and if there's only one, then you can guarantee 100% support (the dictator's system).

So if we want, as AV claims, more than 50% support for the winner but still have FPTP, that's easy - we just restrict the number of candidates to two. The problem is obvious - how do we determine those two?

AV is essentially an answer to that question. It manages it all in one election, but effectively takes multiple votes across a series of elections. If there are four candidates in total then we have a vote between those four. The loser drops out and their votes are transferred to the next round of three. At this stage we can only be sure that one candidate gets at least 33%, so again we drop out the loser, transfer the votes and now have an election of two in which someone (it's mathematically guaranteed) gets more than 50% and the result is called.

But why stop there? Why halt this repeated process of dropping out the losing candidate? Now the second place candidate drops out, his votes are transferred to the only remaining candidate, and the winner can be declared as having 100% support.

But that's silly. Clearly no one believes that the winner has 100% support, in just the same way that no one believes it in a dictatorship. The winner may be the most popular candidate, but the 100% support is meaningless - it's just an inevitable consequence of the mathematics.

But in just the same way, under AV as it is proposed, the 50% is meaningless - it's just as much an inevitable consequence of the maths, a statement which though true, cannot be false. I'd like to see a winner under AV who didn't get 50% of the vote.

I say that the percentage is meaningless, but perhaps a better term is 'not interesting'. If I were to tell you that the last five presidents of France all got more than 50% of the vote in the final round, it would not be interesting. And I use the term in a slightly technical sense - by 'not interesting' I mean it provides no information that you couldn't otherwise have inferred. French presidents have to get more than 50%, just as AV candidates do - that's the system.

However, if I told you that in 2007 Sarkozy won with 53%, whereas in 2002 Chirac won with 82%, that would (might) be interesting. Clearly there was something different about Chirac's election compared with Sarkozy's. (There was - Chirac was standing against the fascist Le Pen.)

But under AV, as currently proposed, we don't get that sort of information. If I were to tell you that in one constituency the winner was Smith with 53% and in another the winner was Jones with 58% the actual percentages tell you nothing of interest. Jones my actually be less popular than Smith.

Why? Well in Jones' constituency, voting went to the final round. Jones got 58% and his opponent got 42%.

But Smith reached the 50% finishing post while there were still three candidates left. He got 53% and his opponents got 20% and 27%. If the AV process had continued to the next stage and the third place candidate had dropped out then the redistributed results might have given 63% (or more, or less) to Smith and 37% to his opponent. Now Smith's 63% can be more fairly compared with Jones' 58%.

So why is this not the way AV is proposed to work? Why do we stop counting as soon as one candidate passes 50%? Well, it could be argued (I have done) that the purpose of elections is primarily to choose an MP, not to divine other related information. But I'd also argue that getting other information is useful, if it doesn't affect the actual result, which this doesn't.

It could be argued that counting every constituency through to the final round would be expensive, but we already know that there is no additional cost to AV elections, so even if my proposal proved to be twice as expensive, twice nothing is still nothing (and that's the simplest bit of maths you're likely to see on this blog for a long time).

It could be that proponents of AV realise that if this approach were followed then in some seats (safe seats under FPTP and still safe under AV) this extra transfer of votes might mean the winner getting maybe 80% or occasionally 90%, and that's getting a bit too close to the dictator's 100% and could give away the game that all the percentages are just artefacts of the system. I doubt it, because I doubt many of AV's proponents have thought it through to that extent.

But that's my proposal. If AV succeeds at the referendum, make a slight amendment to it:

In every seat, counting should carry on to the final round of two candidates, even if a winner can be determined earlier, so that comparison of winning percentages across constituencies operates on a level playing field.

Any takers?


  1. I can't see why this would be a bad idea. That worries me. I feel that you are leading with your left and then about to hit me with your right.

    Of course, in reality a distinction will be drawn, because it will be known which "round" of voting elected the MP. If you think that people won't be swanning around in Westminster gloating that they are "first round winners" and mocking those with a "ninth round" majority, you are insane.

    But, personally, I'd like to see the counting completed.

  2. No, I'm genuine in this. I don't much want AV, but if we have it, it should be like this.

    And you're right about the MPs gloating if this doesn't happen; I just think condensing that sort of comparison into a single percentage would be much clearer for everyone, rather than just an arcane measurement that MPs use amongst themselves.

  3. I'm happy with this, publishing the 'final round' winning percentage gives something comparable if people need something to compare, but I think I'm with @Sordel, being a 'first round winner' will be the aim and the thing they shout about.

  4. And, of course, they will choose the statistic that best serves them. A first-round winner who still only managed to get 51% after the final round will focus on the round, not the percentage.

  5. We're not sure yet how a declaration works: perhaps the information would be transparent anyway.

    Also, we don't know how these votes will come out in practice. The minor parties have so few votes that the likelihood of an election being settled by second, third, fourth votes will be, I imagine, low in many constituencies. It may well be that in the overwhelming majority of contituencies only once the third place party's votes are counted will the 50% line be crossed.

    If that guess is right (and it may apply even in the majority of what are currently regarded as safe seats) then the "rump" of seats without full counts may look even more anomalous, in which case your suggestion goes from being sensible to being virtually unavoidable.

  6. Hard to guess as you say, but I think your scenario is unlikely. At the moment there are several hundred seats where the MP has over 50% under FPTP. Other things being equal, those would be first round wins under AV, and therefore we learn more by continuing the count.

  7. I's surprised there are so many with the 50% margin under FPTP ... they are certainly called "safe" seats for a reason. It may be that the bandwagoning effect would be cut and that more people would vote in safe seats ... but, honestly, I'm not sure that either effect would be enough to cut very far into the winning margin on first votes in safe seats.

    There's so much we don't know, yet what do the media cover? In-fighting in the coalition.

  8. I suspect that, in practice, all preferences of all voters will be recorded before the "count" formally begins. Clearly, if voting is performed electronically, then the data will be recorded. If some sort of paper ballot is retained then error checking will be important. Any human or "robot" (OCR) counter will need to be clear that the scribble next to candidate "B" really is a "2" and this will need them to check that nothing that looks like a "2" is next to any other candidate etc. In a field of 6 candidates one would expect (assuming that all six numbers can be recognised with equal error rates) nearly 65 times fewer errors to be made by introducing the requirement that each number only occurs once, for example.

    If the data is available I think it should be published - for the political parties/media/voters to make of what they wish.

  9. You raise an interesting point about electronic voting. Representatives of the 'Yes' camp have generally been assuring us that AV will not require the introduction of voting machines. However, there is no 'Yes Manifesto' - all we get to vote on is the wording of the referendum, which doesn't go into such detail.

    What redress will the voters have if, having accepted AV, we discover that after all it is best implemented with voting machines, or if any other of the claims made by proponents proves to be false?

    (The same argument could be put against the 'No' camp, but since we already have FPTP, we're unlikely to be surprised by its implementation.)

  10. I am even more suspicious of the assurances of the Yes campaign than I am of the scaremongering of the No campaign. Basically, since very few of the potential voters in the referendum are going to examine the options even in superficial detail, both sides are feverishly misrepresenting the likely consequences of the referendum in order to win.

    I'm not sure that electronic voting machines are essential - it seems to me that distinguishing handwritten numbers is something that a human would do pretty well - but anyone easily discouraged by a more expensive voting system would do well to vote No. I for one will not be happy when it turns out the Lockheed Martin have just got the contract for implementing the counting process.

  11. I agree on the Lockheed Martin issue - unless they decide that the software needs to be done in C#.