AV vs FPTP — the short(er) version

I am sufficiently out of touch (or perhaps simply part of the wrong generation) that when I saw that somebody on Twitter had described my previous post as “a prime candidate for tl;dr” I didn’t know what it meant. In case you didn’t either, it stands for “too long; didn’t read”. I realize that it was a bit long for a blog post: my defence is that (i) I thought that it would be mainly read by mathematicians, who are more patient than your average reader (if you want to know why, try reading a university-level mathematics textbook), (ii) I found that I had a lot to say and wanted to justify it carefully, and (iii) I tried to make it easy to skim-read by dividing it into sections and having slogans that summed up my points.

But the post has been read far more widely than I expected, which makes me think, with referendum day approaching rapidly, that I might be able to reach more people if I wrote a shorter version — I fully understand that not everyone has the time or inclination to read a 10,000-word essay. Of course, I have to compromise on the justifications, but they are there in the long version (which I would prefer you to read if you have the time and inclination). Another advantage of writing a second version is that it enables me to take account of some good points raised in the responses to the first. (If I don’t take account of yours, it doesn’t mean I didn’t think it was good.) One general criticism made by a couple of people was that I didn’t spend any time debunking bad arguments made by the YES2AV campaign (though that was before I wrote the supplementary post). I’ll try to put that right here, though it seems to me that the bad YES2AV arguments tend to be weak and unconvincing, whereas the worst of the NO2AV arguments are actually wrong.

A quick remark before I get going. I read an interesting article in the Guardian about the opinion polls, which are still suggesting an easy victory for NO2AV: they show a split of roughly 60 to 40 amongst people who say they are certain to vote. However, the article also said that the percentage who say they are certain to vote is much higher than most people believe will actually turn up to vote. This gives me a small straw-clutching hope. It seems to me that people who say they want to vote no to punish Nick Clegg can take that sort of view only if (i) they would have voted no anyway or (ii) they don’t actually care one way or the other about voting reform. It seems possible that people of the second kind will be less inclined to feel that it is important to vote. I don’t offer this as a completely convincing argument — perhaps there are lots of people who think that AV is a small improvement but in the end won’t make much difference, and perhaps they too will decide that it’s not the end of the world if they don’t vote. But leaving that aside, a low turnout is predicted, so your vote has more of a chance of making a difference than it might have. If you’re reading this, please, whatever your views, do go and vote. (That sounds admirably balanced, but it isn’t really: I think most people who read this post are sympathetic to AV, so if my plea makes any difference then it ought to favour the YES side.) One final thought about this is that even if NO wins as expected, the smaller the margin of victory, the more chance of getting the politicians to reconsider voting reform at some future date.

I thought about how to write this and eventually decided that a good way of keeping it short would be to write it in the form of a dialogue. The two characters are Q, who has lots of questions, and A, who provides answers. I’ve managed to get it down to about 3700 words (compared with 10000 for the previous one), which is longer than I hoped, but still a substantial shortening. If it’s still TL4U then scroll down to the bottom, where the whole thing is reduced to a series of soundbites.

Q. Can you explain what the two voting systems are that we shall be choosing between on May 5th?

A. Certainly. In both systems the country is divided into constituencies, and each constituency sends an MP to parliament. Under the First Past The Post system, or FPTP, each voter in any given constituency puts a cross by one candidate and the candidate with the most votes wins.

Q. That’s nice and straightforward.

A. Indeed it is.

Q. And what’s the other system?

A. It’s called the Alternative Vote, or AV. Under AV, you don’t just put a cross by one candidate, but rather you put all candidates in order of preference.

Q. All candidates? You mean, you have to decide whether you prefer the Official Monster Raving Loony Party or the Church of the Militant Elvis party?

A. No. Of course it’s not likely that both those two parties will be standing in your constituency, but in general you can put down as many or as few preferences as you like.

Q. I see. Well, that’s fairly simple too, but how are the votes actually counted?

A. You have a series of rounds. In each round, if a candidate has over half the votes, the contest stops and that candidate is elected. If no candidate has over half the votes, then the candidate with the fewest votes is eliminated and there is a new round. And in each round, your vote goes to the candidate who is highest on your list out of those still in the race.

Q. Is that it? I was told it was hard to understand.

A. I think all that means is that it is harder to understand than FPTP.

Q. Hang on, what happens if I haven’t expressed a preference between the remaining candidates?

A. Then you don’t get a vote in that round.

Q. Isn’t that a bit unfair?

A. No more unfair than the fact that people who don’t vote at an election … er … don’t get a vote.

Q. I think you may have oversimplified AV. Isn’t there something about the voters of the least popular party getting their votes redistributed first?

A. Yes there is, but that is to do with the implementation of AV rather than with AV itself. Suppose at the end of round one the least popular party is the BNP. In round two, everyone gets to vote between all the parties other than the BNP, who have been eliminated. So everyone who voted for a party other than the BNP can still vote for their first preference, while BNP voters must switch to their second preference. Since we have already counted all the first preference votes, there is no point in counting them again (though, if we were feeling perverse, we could). Since the only information we do not have is the second preferences of the BNP voters, that is all we need to count in this round. And so it continues.

Q. I have some more questions about AV, but first I’d like to ask why it’s called the Alternative Vote?

A. I don’t know. It’s a pretty bad name. But why do you think First Past The Post is called First Past The Post?

Q. It’s a horse-racing metaphor: the first candidate to get past the post, so to speak, wins the race.

A. OK, how does the metaphor work? In particular, what is the post?

Q. Well, it’s … er … hmm … I’m not sure.

A. The most obvious “post” would getting half the votes. So, weirdly enough, the metaphor “first past the post” is a better description of AV than it is of FPTP.

Q. Can I go back to the BNP question? I’ve been told that a disadavantage of AV is that some people, including BNP supporters, get more votes than others.

A. I’ve just explained how the system works. Did anyone get more votes than anyone else?

Q. I suppose not. But why in that case do people say that they do?

A. There is a confusion that some people have, and the NO2AV campaign is actively encouraging it. (David Cameron, with a first in Politics, Philosophy and Economics from Oxford, presumably understands AV well enough to know that he is talking poppycock when he talks about some people having more votes than others. It seems that when you are campaigning in a referendum, explicit dishonesty is allowed.)

First off, under AV each voter gets one ballot paper. So in that sense, obviously enough, nobody gets more than one vote.

Secondly, in each round, everybody gets exactly one vote counted (unless they have ceased to express preferences, but if so then that was their choice, and they presumably don’t care who wins out of the remaining candidates).

There is something that some people get more of than others. If you vote for an unpopular party, then more of your preferences will be taken into account. But think what that means. If only one of your preferences is taken into account in a given round, then you get to support your first-choice candidate. If four of your preferences get taken into account, then your first-choice candidate is eliminated, followed by your second-choice candidate, followed by your third-choice candidate. It is ridiculous to call this having four votes: it is having one vote that reflects lower and lower preferences as the rounds go on. A system that gives BNP supporters more “votes” in this sense is clearly a good system — sensible mainstream candidates get to support their first preferences and BNP lunatics have to make do with lower preferences.

A better word than “vote” in this context would be “disappointment”. If you vote for unpopular parties then you get more disappointments. It’s not unfair, and it’s not exactly an advantage for the BNP …

Q. I’ve seen advertisements that say that under AV the candidate who comes second or third can win. That sounds pretty ridiculous.

A. It would be if it were true. Under AV the candidate who wins is the candidate who is first under the rules of AV. Under FPTP the candidate who wins is the candidate who is first under the rules of FPTP. Sometimes the systems give different answers. If we were used to AV we would think it highly odd that under FPTP a candidate that 65% of the constituency hates can win with only 35% of the vote. We might say, “Under FPTP a candidate can be declared the winner without having won!”

Q. Yes, but that would be a silly argument.

A. True. It would be exactly as silly as the argument that under AV the candidate who comes second or third can win.

Q. OK, but why not just stick with the system we know, which seems to have served us pretty well.

A. It’s not so much whether it has served us well in the past that matters, but even in the past it is debatable whether it has served us well. It is a wildly non-proportional system. For example, in 1983 Labour got about nine times as many seats as the SDP/Liberal Alliance, when their shares of the vote were 27.6% and 25.4%, respectively. And the Conservatives, on 42.4% of the vote, got 61% of the seats, a landslide majority. In 1951, the Conservatives came second in the popular vote and got a majority. And I’m not just picking out extreme examples. Go and have a look at the UK General Election results over the last century or so and you’ll see that the number of seats parties gain has very little relation to the share of the vote they obtain.

Q. I see. So AV is a more proportional system.

A. Er, actually no. In fact, some have even suggested that it is less proportional.

Q. OK you’ve got me now. What could possibly be better about it?

A. Under FPTP there are two distorting effects. One is the lack of proportionality, which AV does little to address. The other is the fact that it often makes good sense under FPTP to vote for a party that is not your favourite party. The most common example of this is if your favourite party is the Lib Dems and in your constituency the Lib Dems are in third place to Labour and the Conservatives. Under these circumstances, the only chance you have of actually influencing the result is to decide which you prefer out of Labour and the Conservatives and vote for that party. So in that sense a vote for the Lib Dems is a wasted vote.

This leads to a strange situation where it might even be the case that everyone likes the Lib Dems best, but everyone judges that they don’t have a chance — and their judgment is correct because … enough people judge that they don’t have a chance that they decide not to vote for them even though they like them.

Under AV, if you like the Lib Dems best and Labour second best, you put the Lib Dems top and Labour second. If everyone secretly liked the Lib Dems best, then the Lib Dems get elected. If in fact it was correct that the Lib Dems were the least popular party they get eliminated and your vote, instead of being wasted, is cast for Labour.

So the big advantage of AV is that it encourages you to express your true preferences. In a funny way, FPTP is like AV in the following sense: if you support the Lib Dems and think they will come first, then you eliminate them yourself and write down your second preference. But the difference is that you have to play a silly and unfair guessing game under FPTP because you don’t actually know how the Lib Dems will do.

Q. So AV is basically a stitch-up to help out the Lib Dems.

A. I don’t see how you can call it a stitch-up, given that it takes account of people’s actual preferences rather than the vote they reluctantly make after trying to guess other people’s preferences. (This point is made crudely but effectively here.) Up to now it would certainly have helped the Lib Dems more than any other party. But there are plenty of seats where Labour or the Conservatives come third and their voters face a similar unnecessary dilemma.

Q. OK, so what would the effect of AV be?

A. That is difficult to say with any certainty, because we do not know how much people’s votes under FPTP have been a true reflection of their political preferences, and we also don’t know other important factors such as how much the Lib Dems have been damaged by their role in the coalition. So I’ll talk in more abstract terms.

Suppose you are in a constituency where there are two fairly similar parties and one very different one. And suppose the candidates from the two similar parties get 30% each and the candidate from the different party gets 35%, with other candidates getting the remaining 5%. Then 60% of voters want one kind of party and 35% want the other, but it’s the 35% who win the election.

To make it more concrete again, imagine you had to vote for a kind of biscuit. 35% want cheese biscuits, 30% want milk chocolate digestives, and 30% want plain chocolate digestives. Then 60% want chocolate digestives but under FPTP will end up with savoury biscuits.

This is not just a hypothetical situation: it happens all the time. For instance, there are many constituencies where the Conservatives win because the left is split between Labour and the Lib Dems. (Things may get more complicated at the next election now that more right-leaning people have taken over the leadership of the Lib Dems, but certainly this has been a good description of a lot of constituencies at a lot of elections in the past.)

Under FPTP, if you have two fairly similar parties, they both suffer. Under AV, this is no longer the case. See this article for a description of how this awkward feature of FPTP has been manipulated in Russia. See also this video, which does a good job of making the point I’m making here. Or if you haven’t got time for the video, then have a look at this poster.
AV poster

Q. Let me rephrase: what would be the likely effect on the numbers of seats for the major parties if we switched to AV?

A. In the short term, the Lib Dems would probably gain a little, but this might well be more than cancelled out by the amount they would lose as a result of their current unpopularity. If, as many expect, the Lib Dem vote collapses, then the outcome of AV would not be all that different from the outcome of FPTP. But assuming that they eventually recover, the longer-term outlook is probably that the Conservatives would get fewer seats, and Labour and the Lib Dems would get more. That assumes that by and large Labour voters would tend to put Lib Dem candidates second and vice versa. If that assumption turns out to be false, then all bets are off. Also in the longer term, once people start to realize that voting for smaller parties they like is not wasting their votes, the share of votes for such parties will probably go up.

Q. David Cameron says that FPTP makes it easier to get rid of unpopular governments.

A. He probably regards the Conservatives in the 1980s as popular. But there are plenty who would disagree with that assessment, and they won four elections in a row, always with the support of a minority of voters. In 2005, soon after the Iraq war, Blair was pretty unpopular after his lies about Iraq. As a result, his share of the vote dropped to 35.2%. The result: a comfortable majority and the coronation of Mr Popular himself, Gordon Brown. In fact, AV makes it easier to get rid of unpopular governments because those who are against the government do not get their vote split.

Q. You said earlier that in the short term AV probably wouldn’t have all that much effect on the outcome. In that case, why bother?

A. Two reasons. One is the practical fact that AV could well have a substantial effect in the medium or long term. The other is the matter of principle that a system that doesn’t put any pressure on you to vote tactically (that is, to put one party ahead of another party that you prefer) is more democratic.

Q. So AV spells the end of tactical voting?

A. Well, that’s an exaggeration, but it’s pretty close to the truth. Here’s a situation where tactical voting could in theory come into play. You have a constituency where the Conservatives are polling 35%, Labour 30%, Lib Dems 30% and UKIP 5%. You support the Conservatives. You’re pretty sure you’ll pick up almost all the UKIP second choices, which will get you to 40%. But you still need another 5%. You’re pretty sure you’ll be more likely to get those from Lib Dems than from Labour supporters. So it becomes more important to you that Labour beats the Lib Dems than that the Conservatives do well in the first round. So it actually pays you to put Labour as your first choice, even if they are in fact your third choice.

Q. Doesn’t that even mean that the Conservative candidate should ease off a little bit in the hope that a few voters will back Labour?

A. It could indeed. But it’s worth stressing that this sort of situation is quite rare, and that in practice one wouldn’t know enough about people’s voting intentions to know that one was in it. And if the Conservative candidate eased off, would those votes go to Labour rather than the Lib Dems? You’d have to do the easing off rather skilfully …

One other point about this. There have been actual elections under AV where this phenomenon has taken place. One example is a mayoral election in Aspen Colorado. It was noted afterwards that one party would have won if it had transferred some votes to its main rival. This was felt to be so unjust that they changed their system (not, I hasten to add, to FPTP).

But mayoral elections are not the same as general elections. The occasional anomalous result in one constituency is very different from the entire decision about who takes power being anomalous.

Also, anomalies occur the whole time under FPTP. Going back to the biscuits example, it could easily be that 60% prefer milk chocolate digestives to cheese biscuits, and 60% prefer plain chocolate digestives to cheese biscuits, but under FPTP it’s the cheese biscuits that are chosen.

Q. Look, you understand how AV works and so do I, but the fact remains that not everybody would understand the full implications of how their votes are counted. Isn’t that profoundly undemocratic?

A. It’s not ideal. But one should get this in perspective. Go back and look at my explanation of AV. It took four sentences of which the first was, “There is a series of rounds.” Anyone who wants to can take the trouble to understand this. Even so, I take the point that quite a lot of people will not in fact fully understand how their vote is counted. This does not, however, allow the people who do understand to get an unfair advantage: under AV it hardly ever pays to do anything other than put the parties you like in order of preference.

I have heard an interesting suggestion that the Lib Dems did considerably worse in the last election for London Mayor than they had done in the preceding opinion polls because people didn’t understand that putting them as first preference was not wasting their vote. This suggests that it would be important to explain to people that under AV there was no longer any need for tactical voting.

A final word on the subject of complication: have a look at this amusing flowchart produced by someone called Anthony Smith.
Voting flowchart

Q. I’ve also heard it said that AV helps the BNP.

A. Well, I’ve explained how it doesn’t give them more votes than other parties, just more disappointments. However, it does give them the opportunity to express their political preferences more accurately than they can under FPTP. For instance, one can vote BNP and still have a say in who wins out of the Conservatives or Labour. So it gives BNP voters more say than they have now.

Q. Isn’t that terrible?

A. No. It gives BNP voters more say because it gives all voters more say than they currently have. Was it a mistake to give women the vote because the BNP gets more votes as a result? Obviously not: all parties get more votes as a result, and the BNP probably benefits less.

Q. Some people suggest that AV will lead to a different kind of MP.

A. I would take all such claims with a huge pinch of salt. NO2AV campaigners say that it will lead to candidates who are bland and inoffensive, while YES2AV campaigners say that your MP will work harder and be more honest with their expenses. Well, for starters it will make no difference in safe seats where the leading candidate typically gets over 50%. It will also make little difference in marginal seats, where under both systems candidates have to reach out to floating voters or voters from other parties. In a seat that is safe because the opposition is split, it is not clear what will happen. Under AV it might become safe for another candidate. Or it could become a marginal seat. But do you really win a marginal seat by being bland? I don’t think so.

As for the expenses scandal, it’s true that it led some people to think that the whole system needed changing. But what needed changing were … er … the rules about expenses. The scandal could just as easily have happened under AV. I think connecting the two was a tactical blunder by the YES2AV campaign: people can see through it easily.

Q. One thing that confuses me is that the yes campaign says you need over 50% of the vote and the no campaign angrily claims that this is false. What’s going on?

A. Under AV, you need over 50% of the votes cast in the final round. This means that if a lot of voters have not expressed a preference between the remaining candidates then the final winner may not have 50% of the votes from those who voted in the first round.

It seems unlikely that this will be a major factor, since the parties that remain in the final round will almost always include big mainstream ones. But one can imagine situations where it occurs. For instance, perhaps at the next election there will be constituencies where the two front runners are the Tories and the Lib Dems, and where large numbers of Labour voters will be disgusted with both parties and will therefore not express a preference between them.

See this nice comment for a convincing argument that this 50% question is perhaps not all that important.

Of course, even if the winning candidate does get over 50% of the votes cast in the final round, some of these will be lower-preference votes, so it wouldn’t be entirely reasonable for the candidate to claim the support of half the electorate. In this respect, the YES2AV campaign is misleading. That’s a shame, because there is an important point here that is true. Currently, there are several constituencies where the winner can win by relying on core support (of, say, 40% of the electorate). Under AV, such candidates will need second-choice votes too, so they will have to appeal to a broader section of the electorate.

Under FPTP, you can be elected with 35% of the vote even if 65% of the electorate is bitterly opposed to everything you stand for. Under AV that is impossible.

Q. I’ve been told that AV means the end of safe seats.

A. It doesn’t. But it does mean a smallish reduction in the number of safe seats. And in the longer term, if AV has a substantial effect on the way people vote, it could lead to a larger reduction. But there are likely to be areas of the country that are solidly Labour or solidly Tory for a long time to come.

Q. Doesn’t AV lead to more coalitions and therefore political instability and weak government?

A. It probably would lead to a mild increase in the number of coalitions, though some dispute this (and so do others). Do coalitions lead to instability? Yes in some countries (e.g. Israel and Belgium) and no in others (e.g. Germany and Switzerland). It is very hard to predict whether coalitions would be stable in this country if they became more normal. Some would welcome a politics of compromise and an end to the polarization and lurches from one side to the other that we have at the moment. Others think that having a single party free to make unfettered decisions is more important than having a government that represents a majority of the population. There is room for legitimate debate here.

Q. Hmm … I see some sense in these arguments, but I feel so betrayed by Nick Clegg that I’m not sure I want to do what he wants me to do.

A. So you’d rather do what David Cameron and George Osborne desperately want you to do? Don’t confuse Judas with Satan.

And now for the really short version.

1. FPTP is unfair because it is very far from proportional.

2. AV is probably no more proportional than FPTP.

3. However, FPTP is also unfair because it puts pressure on large numbers of people not to vote for their favourite party. Under AV you don’t have to worry about wasting your vote. The right voting strategy is almost always to put the candidates you like in order of preference.

4. Under AV, everyone gets one ballot paper, just as under FPTP.

5. In each round of an AV count, everybody gets exactly one vote. It goes to their highest ranked candidate out of the candidates still left.

6. Under AV, if you vote for unpopular parties you don’t get more votes — you get more disappointments.

7. Under First Past The Post, there is no post. (FWIW, under AV there is.)

8. Under AV, the person who would have come second or third under FPTP sometimes wins.

9. Under FPTP, the person who would have come second or third under AV sometimes wins.

10. In so far as AV helps the BNP, it also helps everyone else. (The same could be said of women’s suffrage and votes for 18-year-olds.)

11. Anomalies can occur under AV.

12. There is no anomaly-free voting system.

13. Anomalies in a very small number of constituencies are very unlikely to affect who gets the power nationally.

14. AV doesn’t make your MP any more bland and inoffensive than FPTP.

15. AV won’t make your MP work harder.

16. AV wouldn’t have made any difference to the expenses scandal, which is in any case yesterday’s news.

17. AV might possibly lead to more coalitions but will not lead to a state of permanent coalition.

18. AV makes it easier to get rid of unpopular governments.

19. You think FPTP makes it easy to get rid of unpopular governments? Just look at the figures for 1987 and (especially) 2005.

20. Whatever system is in place, the Lib Dems will get a kicking at the next general election.

21. The Conservatives like FPTP so they can exploit the split on the left and often get a majority of seats with a minority of votes.

22. It is hard to predict what will happen in the future, but in the past AV would mostly have benefited the Lib Dems and Labour at the expense of the Tories.

23. It’s not true that bringing in AV would cost £250 million. The correct figure is more like £25 million (which is needed to explain to people that when the ballot paper asks them to put the candidates they like in order of preference, then they have nothing to gain by not doing so).

24. The outcome of the referendum will affect us for decades. Whichever way the vote goes, Nick Clegg will be forgotten about after five years. David Cameron and George Osborne want you to vote no and Ed Miliband wants you to vote yes.

78 Responses to “AV vs FPTP — the short(er) version”

  1. Sid Says:

    I think you should move the shortest version to the top of the post. Not everyone will skim the whole post before reading it in detail and for them having the short version at the end defeats the point of having the short version. Maybe even move it before the rationale given in the beginning for this post?

  2. Greg Martin Says:

    One nice point, which I heard from a different source but is presumably true, is that the Conservatives already use AV when internally selecting their party leader! (as do the other major parties)

  3. Jonathan Phillips Says:

    ” Under AV, you don’t just put a cross by one candidate, but rather you put all candidates in order of preference.”

    Erm… This describes Australian preferential voting in Lower House elections. You do correct yourself later, but it’s important not to let misconceptions arise at all.

    “Instead of a cross, you write 1 next to the name of the candidate who is your first choice. You can then write 2 next to the name of the candidate who would be your second choice, 3 against your third and so on, but as long as your first choice is clearly marked you don’t have to do so.”

    I’m pretty the process can’t be described in fewer words than this – but I also don’t think that more are needed. The point of marking alternative choices emerges from the description of the counting process – and the one you give here is one of the clearest and least ambiguous I’ve seen, especially in that it disposes immediately of the notion of some people’s votes being counted more often than others’. (Cameron can’t be an idiot, so he must be a liar. Comforting thought, that, isn’t it?)

    Why “alternative”? Because each choice you mark is your alternative (in whichever round) to your original first choice. It’s logically and linguistically perfectly correct to speak of a series of alternatives to an original first choice (even if your “first alternative” appears on the ballot paper as your second preference).

  4. Jonathan Phillips Says:

    And for Greg: There are systems that don’t involve putting numbers on a ballot paper which nevertheless allow voters to express an alternative choice. They just don’t happen to be called “alternative vote”.

    Two-round systems (used in many countries for presidential and legislative elections) are also a way of enabling voters to switch to an alternative.

    The Tories use a multi-round system to elect their leader – it lets voters switch votes between rounds even if their candidate hasn’t been eliminated, and it lets candidates drop out too. Tories tend to froth at the mouth if you tell them this is a form of AV, but whatever it is it is most certainly NOT “first past the post”!

  5. Jonathan Phillips Says:

    “Do coalitions lead to instability? Yes in some countries (e.g. Israel and Belgium)” “Lead to”? Better: Are coalitions necessarily associated with unstable government? Not in Germany or Switzerland (or indeed the Netherlands, Sweden, Spain…). And both Israel and Belgium are special cases.

  6. Johan Richter Says:

    Regarding the point about people not understanding the voting system it should be pointed out that in countries with PR very few of the population understand how votes are counted. Yet it does not seem to cause any problems.

    • gowers Says:

      I had a similar thought myself about the European elections. I think I could understand how my vote was counted if I wanted to, but the fact is that I don’t bother: I trust the system to be reasonably sensible and happily cast my vote.

    • Jonathan Phillips Says:

      Counting the votes in Euro-elections in GB (NI uses STV, which takes a little longer to explain…):

      Count up the votes cast for each list. To allocate seats to the lists follow this procedure:
      1. Imagine each party has won one more seat than it actually has, see which has the highest average number of votes per imaginary seat won, and give that party one real seat (to add to its imaginary seat).
      2. Imagine each party has won one more seat than it actually has, see which has the highest average number of votes per seat won (imaginary or real), and give that party one seat.
      3. Keep at it until all the seats have been allocated.

      The system (the method of the highest average) can be explained without reference to imagined seats but it takes longer. The point is to ensure that as far as possible every successful candidate is elected with roughly the same average number of votes. The larger the total number of seats in a given electoral region, the closer is the approach to “one person, one vote, one value”.

      With this type of PR all the voter needs to know is that seats are allocated to parties in line with the number of votes they have won. The mechanism is irrelevant.

      With AV you do need to know at least something about the mechanism in order to see the point of marking second and later choices.

  7. Gareth Says:

    Love your article(s). Can you phone Any Answers (following Any Questions) on Radio 4 in 30 mins to counter the inevitable nonsense… A way to reach Daily Mail readers who haven’t read your post 😉


  8. Anonymous Says:

    AV vs FPTP: A Very (Very) Short Summary

    AV is in a certain very reasonable sense more abstractly fair than FPTP, but no one really knows what practical effect this will have.

  9. Scott McKuen Says:

    Why is a real-world voting system being more proportional necessarily a desirable feature?

    I could see that you would want to maximize proportionality if the votes of people who know each other were uncorrelated: you want to ensure that all viewpoints are heard. But votes aren’t even *close* to being uncorrelated. Even in a strongly two-party system, extremely tight and extremely lopsided races are much more common than a binomial model of independent voters would predict, but I have read that the kurtosis is about what you would expect in a weakly-correlated model of voters. Given that it’s *possible* to influence your friend or neighbor before you all go to the polls, shouldn’t the voting system favor weak parties that are locally strong over weak parties that are weak everywhere, on the grounds that voters are already doing the first round of sanity-checks just by talking to each other?

    As I understand it, national parties of Scotland, Wales, and Ireland have a smaller UK-wide base than, say, the Greens or the BNP, but they win more seats because they’re all concentrated in a small area and focus on issues that affect their particular constituents. This seems like a feature, not a bug, to me. To the extent that AV helps minor parties succeed nationally when they can’t get traction locally, I’m not sure I am convinced that that is actually a good thing. If your issue is important enough, prove it – either convince a major party to take it up, or concentrate your electoral efforts in a few districts until you break through.

    That said, I’m American, so I’m very comfortable living with the results of a strongly two-party system over the long term, and that may be biasing my view of things. Our division of powers between Congress and the President and separated electoral cycles helps slow down the swings in policy after an election, so a major electoral blowout is of less consequence for us than for the UK.

    • gowers Says:

      Are you comfortable with Ross Perot handing the presidency to Clinton and Ralph Nader handing it to George W. Bush? The issue you discuss is not at all the only one.

      Also, it will be just as hard, if not harder, for a party the size of the Greens or the BNP to break through under AV as it is under FPTP. It’s when you get a large minor party with a broad non-localized base that you get a problem. I actually agree that strict proportionality is not demonstrably essential, but a voting system that can pretty well ignore, and sometimes has pretty well ignored, a quarter of the electorate takes some defending.

    • Jonathan Phillips Says:

      One problem with rewarding concentration is that social divisions become exacerbated. If one party is strong only in urban areas, then when it comes to power it will have little knowledge of rural areas and little interest in promoting their wellbeing. If the other is strong only in rural and suburban areas etc. etc.

      For a while the Liberal Democrats were able to win in both urban and rural areas throughout GB, but their future now looks bleak. The SNP has been able to win in both urban and rural areas in Scotland. The unsurprising concentration of the SNP’s support in Scotland does not contribute to the widening of social divisions, in Scotland or across the whole of GB; the concentration of Labour and Conservative support respectively in urban and rural/suburban areas does.

      AV would probably do little to alter this situation. A modicum of proportionality would. And oddly enough the effects of moving to a more proportional system would probably be easier to predict than those of switching to AV.

    • Scott McKuen Says:

      Ah – yes, we have no equivalent at all to the LibDems, so I can see where AV would have real consequences for the UK.

      In the U.S., it’s usually small progressive parties that push the AV (“instant-runoff” here), and they tend to dramatically overestimate how much they will benefit. In California all city-level offices are officially non-partisan, so there’s a single round with a unified ballot across all candidates from all parties – for example, in the Bay Area it’s normally two or more Democrats running for the same position alongside a smattering of other minor-party (including the Republicans) candidates. The nonpartisan ballot has tended to make AV even less effective as advertising for minor parties than you would think.

      Last year’s mayoral race in Oakland was our first bite at the AV apple: the incumbent retired, leaving the seat open. The initially-leading candidate, Don Perata, had something like 35% of the first-choice votes, with 24% going to the second-place candidate, Jean Quan. However, both of the second- and third- place candidates (field of 10) openly ran a “Vote for me, but if you can’t support me, at least don’t vote for Don” campaign, and managed to edge him out 51-49. The candidates that worked hardest to help people understand the new system ended up benefitting, which is probably appropriate.

    • Anonymous Says:

      Abraham Lincoln, widely viewed as the greatest US President, won the 4-candidate Presidential election of 1860 with only 40% of the popular vote, and would have been ranked last by a substantial fraction of voters. The South withdrew from the Union only months after the election. It’s thus conceivable that Lincoln would have lost the election of 1860 under AV, in which case the Confederacy would probably have won the US Civil War. Alternatively, the Civil War might not have happened.

      Determining the effect of AV on the presidential election of 1860 would require a detailed and difficult analysis, since US Presidents are elected by the Electoral College, not by popular vote. However, this example illustrates how unpredictable the effects of seemingly innocuous electoral reforms can be.

  10. Roy Langmaid Says:

    Really enjoyed your dialogue and posts on AV. I posted your brilliant beer or coffee? diagram to my FB page where I hope others will view it. On another matter, I am developing a course and an approach to teaching ‘insight’ work, and I know you did a piece at Cambridge recently on solving problems without thinking. Is there anywhere/way I can learn about your ideas on this topic?

  11. Clay S Says:

    As a mathematician, you could have done the economically rational thing, and just cited Bayesian Regret figures for the various voting system being considered.

    Instant Runoff Voting (aka “Alternative Vote”) is a bit better than Plurality (“FPTP”). However, it is still the worst commonly discussed alternative voting method.

    The best is called Score Voting, and it means voters simply score the candidates on a scale like 0-10 or 1-5. It is much simpler than IRV, and produces much more satisfying outcomes for the average voter. And, counter-intuitively, it is actually highly resistent to the negative effects of tactical exaggeration.

    But the bottom line is, mathematicians, if they are going to take the time to touch this issue, need to make Bayesian Regret the central unifying principle of social choice theory. It is THE “thing to be optimized”.

    Clay Shentrup
    The Center for Election Science
    San Francisco, CA

    • Jonathan Phillips Says:

      I don’t understand. If I award any points to candidates other than my favourite they will count against my favourite. What’s to stop me giving 10 to my favourite and none to anyone else? If everyone does that, we might just as well go back to voting with crosses. And if I’m forced to score all the candidates, what will my vote be worth? Zero?

      I’m also mystified as to how awarding point scores might be simpler than ranking candidates, as few or as many as I like, in the order of my choice.

      People have been looking at alternatives to election by plurality for the best part of 200 years. On the other side of the North Sea is the Netherlands, where since 1918 there have been no local constituencies and parties win seats precisely in proportion to their share of the vote; in this country all MPs are elected from local constituencies and there is no link between total votes and seats won. Both claim to be democracies. In the Netherlands voters have some power to determine which candidates are elected from a given party list; in this country we have none, since each party list has only one name on it. Since the early ’20s Ireland has had multi-member constituencies but no party lists and voters can pick and mix to their heart’s content. Another democracy.

      Are there any functioning electoral systems which do not fit somewhere into this triangle? Do we need to come up with new and untried systems that do not fit into it, whatever their apparent theoretical appeal?

    • Gil Says:

      Clay, Thursday UK referendum is just about AV vs FPTP leaving more or less the constituencies system. (I say more or less since part of the deal is moving from 650 to 600 constituencies and this can also be a big deal in terms of the effect on the outcomes (especially if biased towards some goal.)) (The AV vs FPTP question is complicated and rich enough to make mathematicians happy.)

      There are many forms of democracy and certainly general elections based on proportional representation is a simple and quite effective form. (In fact, I regard the Israeli election method as fairly good and rather stable.)

      The crux of matters is how to model preferences/utilities/choices of a single voter. Every method based on ranking allows to take more delicate voters’ considerations into account but at the same time put a more complicated task on the shoulders of (even non-tactical) voters. Range voting put an even more complicated task on the voters. (It is a bit better for approval voting namely {0,1} range.) The analysis often take into account that the voters has an order relation on the candidate or even a utility function for each outcome. These assumptions are rather problematic.

      I am not sure we need to make Bayesian Regret the central unifying principle of social choice theory. But it is certainly of interest.

    • gowers Says:

      I don’t blame you for not reading through over 400 comments on the first post, but in fact we have had this conversation. You can find it by searching for Warren B. Smith, who strongly advocates range voting. As Gil says, the referendum on Thursday is between AV and FPTP, which is why I didn’t discuss voting systems more broadly.

  12. Best post ever on “Is AV better than FPTP?” by Timothy Gowers | starshaped Says:

    […] A shorter version (with an even shorter version at the bottom of the post) is at: https://gowers.wordpress.com/2011/04/30/av-vs-fptp-the-shorter-version/ […]

  13. OldBloke Says:

    So it seems one of the NO camps arguments has been proved correct; ‘it’s too complicated to understand’, at least to a simple person like me.

    I never knew just how complicated, and interesting, voting procedures were. Regrettably, your shorter version posting will still be too long for me to present directly to people in my community. However, with the much appreciated help of your articles and replies of you readers, I at least have a solid base from which to argue. I have achieved some progress with simple diagrams explaining AV and an anomaly with FPTP together with a simple point by point criticism of the NO to AV leaflet distributed nationally.

    Unfortunately my community is mainly ‘I’M BLUE, MY MINDS MADE UP’ but if they can be made to think for themselves – who knows! My main aim is to get people to think before they vote; did I hear you laugh?

    Could you produce a point by point criticism of the No to AV leaflet keeping to a limit of about 300 words? Armed with your words, I might be able to get more people to think.

    On the subject of cost, I think there is cause for confusion here. Are we talking about the cost of the Referendum or the cost of voting in an AV election or even the extra costs of an AV election over a FPTP election? Somewhere I read that a recent general election cost about £40 million. An AV election must cost more than this due to the extra counting. So is point 27 in your ‘really short version’ approaching truth?

    • Jonathan Phillips Says:

      May I (arrogantly) suggest these:

      Ourtown Votes – a fable for election time: http://bit.ly/fldUMZ
      The Voter’s Dilemma – http://bit.ly/fgHxR0
      How to Vote – http://bit.ly/hctTGk
      Counting the Votes – http://bit.ly/dSMTYV
      The Alternative Vote: A Better Choice – http://bit.ly/eddJWZ

      There are also some brilliant videos out there.

      Incomparably the best is:Is your Cat confused about the referendum on the voting system? http://bit.ly/jOrj0d

      A very precise explanation of the counting system, demonstrating that no-one’s vote gets counted more times than anyone else’s: http://bit.ly/myadHY

      Dan Snow explains AV at http://bit.ly/g73aDr and gives a historical perspective at http://bit.ly/fBJXA8

    • OldBloke Says:

      Sorry, I meant point 23.

    • gowers Says:

      OK, here are NO2AV’s reasons for suggesting you vote no (taken from their website).

      1. AV is costly.

      Response: they use a vastly inflated figure that includes the cost of the referendum itself and makes the false assumption that we would need electronic vote-counting machines.

      2. AV is complex and unfair.

      There is nothing complex about putting your candidates in order of preference. The system is different from FPTP but that does not make it unfair. It can lead to some anomalies, but all voting systems lead to anomalies (this is an actual mathematical theorem) and the anomalies in FPTP are worse.

      3. AV is a politician’s fix.

      Response: The argument here is against coalitions. But we get coalitions and minority governments under FPTP and will continue to do so if the Lib Dems ever recover. AV will lead to at most a small increase in their frequency. And some would argue that a coalition better represents the views of the electorate than a single party with under 40% of the vote. In addition, the major parties contain many people with a wide range of views. Does anyone honestly believe that there aren’t “politicians’ fixes” going on the whole time?

      In leaflets I’ve seen the following statements.

      4. Under AV the candidate coming second or third can win.

      Response: This is silly: the candidate who comes second or third under the rules of FPTP can win. Similarly, under FPTP the candidate who comes second or third under the rules of AV can win.

      5. AV gives more votes to the BNP.

      Response: This is nonsense. There is a series of rounds and each voter gets one vote in each round, unless they have ceased to express a preference. Voters for unpopular parties are forced to switch to lower preferences, so they do worse (not better) than voters for mainstream parties, who can continue to support their first choice.

      By the way, there’s a confusion that the NO campaign cleverly exploits, which is there is a difference between the following two apparently similar statements.

      1. The ballot papers of the BNP ARE COUNTED more than the ballot papers of supporters of the Conservatives and Labour.

      2. The ballot papers of the BNP COUNT more than the ballot papers of supporters of the Conservatives and Labour.

      The first statement is true and the second false. The first statement is true because when a party is eliminated, although all ballot papers still COUNT once, most of them have already BEEN COUNTED. It’s only the ones supporting the party just eliminated that have to BE COUNTED again.

      This gives the NO campaign a useful way to lie without lying: they say “votes for the BNP are counted more often” and rely on the reader to misinterpret that as “votes for the BNP count more”.

      I hope that gives you a little bit of ammunition …

    • gowers Says:

      PS As I understand it, counting in elections is done by volunteers. But I may be wrong about that.

    • David Craven Says:

      The current method of counting is done by volunteers, but will have to change of course.

      One method (in fact the only method I can see) working using hand counts is the following: sort all ballots into piles according to each candidate and count, then put that on a big board. Then go through each loser pile, moving the ballot papers to other piles and adding that total on the board.

      Without using electronic voting in the beginning, this would be quicker than feeding the results into a computer manually I would think, and more accurate. OCR would be worryingly inaccurate for this so a scan is out. Maybe a tick-box system like multiple choice question sheets?

    • Jonathan Phillips Says:

      For David Craven: you can find an example of how the full results are set out at http://electionsireland.org/counts.cfm?election=2007B&cons=85&ref. (This is for a by-election in a Dublin constituency.)

      Wherever STV is used in “all out” elections (all elections in the Irish Republic, local, Assembly and Euro elections in Northern Ireland, and local elections in Scotland) to elect several members per constituency or ward, AV is used in by-elections to elect single members.

    • David Craven Says:

      @ Jonathan Phillips: I tried to reply to you but that didn’t work, see below…

    • OldBloke Says:

      In trying to get my contemporaries to consider the pros and cons of AV reaction has varied from total indifference to naked aggression.
      However, I have had a success, a 97 year old – unfortunately she had already voted by post.
      I think the jury are now considering their verdict, any more effort is now superfluous. I fear the NO campaign will win, because there are too many old people.

      My Response to Points Raised on the NO to AV Website, with thanks to gowers and Jonathan Phillips( I don’t see why you should be worried about getting BNP votes, they would only help you.) et al.


      AV is costly:
      £250 is really a gross overestimation. It is a one off cost and should be discounted over future years. The case for the use of voting machines is not proven.
      Quote from ACE – ‘Whilst mechanical voting or computerization may enhance accuracy, this must be balanced against the resulting apparent loss of transparency.’
      Vote counting is generally an unpaid volunteer job. (No doubt expenses are allowed.)

      AV is complex and unfair:
      AV is not complex although the arguments for fairness in both AV and FPTP may be complex.

      AV is a politician’s fix:
      There is no proof that hung parliaments will result. Responsible research suggests little will change. Coalitions may be the price of freedom and democracy.

      Vote NO to AV on 5 May 2011:
      Substitute YES for NO and this is exactly the same comment the Yes campaign can make.


      It creates strong governments.
      There is no proof that coalitions will increase and reduce strong accountable government. If horse-trading by politicians behind the scenes goes on now it will most certainly carry on under any other system. AV is more proportional than FPTP because it allows voters to express preferences.

      It’s fair.
      AV is exactly the same as FPTP, ‘one person one vote’. The voter only gets one voting form. The ‘transfer preferences’ of supporters of fringe parties actually add to the candidates of the mainstream voters, so mainstream voters gain.

      It’s simple to understand and easy to implement.
      What is difficult about putting 1,2,3 against candidates’ names in ‘your’ order of preference.

      It excludes extremist parties.
      What has the BNP to do with the Australian One Nation party? Here, the chance that they could get any seats under AV let alone control this country is far removed from reality. If you don’t want BNP don’t vote for them.

      It’s the most widely used system in the world.
      Maybe, but there are over 200 countries in the world, 193 of them recognised by the UN, so what do the other 75 %, the majority, use? However, it does not follow that it has to be the best. Other countries also have problems in selecting the best voting system. Many countries use some form of proportional voting, including Canada and the USA; all have opponents.

  14. David Craven Says:

    I was thinking the actual mechanics of it, how you would physically do it, and not just what the resulting table would look like. This point is the important one for questions of cost.

  15. Jonathan Phillips Says:

    In a post in Gowers’s Weblog Denis Cooper writes as follows (concerning that Dublin by-election):

    “There were nine candidates and it needed eight counting rounds to finally identify the winner… In the first round, the count of the first preference votes, the tellers had to sort and count all 28,412 valid ballot papers, just as in the single count under FPTP. Because of AV they had to carry out 16,878 additional sorting and counting operations in the subsequent seven rounds, an increase of 59% over those needed for FPTP.”

    So an extra 59% teller-hours in what would seem to be something like a “worst case” scenario in the UK. In maybe a third of UK seats the initial tally would produce a result; in quite few more a small number of transfers (e.g. from Ukip to a Tory who was within five points of the 50% mark) would give a result. In those constituencies where the candidate leading in the initial tally was well short of the 50% mark more recounting would be needed.

    Cooper’s estimate is that overall the cost of counting services in a UK general election would rise by maybe £2m, assuming tellers are paid £16 p/hr.

    Sorry – I kept the text of Cooper’s posts but but not the URL.

    By-election counts using AV in Ireland, north and south, and in Scotland (council elections) are all conducted by hand. Google will find you accounts of the process.

    (The STV counts used in “all out” elections are also conducted by hand, an altogether more fearsome process.)

    If we continue to use paper ballots and to count them centrally, then computerisation of the count would require machine-readable ballot papers. Possible, but only at the cost of making the ballot papers almost impossibly clumsy: candidates in a column on the left, then a series of columns for first, second etc. choice, and voters having to block in a circle in the first column in the same row as their first choice, in the second column in the same row as their second choice, etc. I have a notion that this is done in STV elections in Cambridge Ma, but I’ve been unable to turn up a reference.

    The drawbacks greatly outweigh the benefits, especially since the counting machines would be used only every four or five years.

    And watching the physical processes involved in counting and transferring votes is interesting in itself – much more so than just seeing numbers flash up on a screen. (Now… who’s going to get those BNP votes when they are transferred – oh please God not me!)

  16. Nicola Says:

    I like the really short version! Makes more sense than most of the official stuff out there on the referendum!

  17. Neil Wilson Says:

    What’s interesting about all this debate is that it is beside the point.

    The system we have in the UK is a virtual dictatorship consisting of front men who are graduates from very particular universities and schools running parties who are all funded by the wealthy in their interests.

    The only choice given to the people is a choice of colour. Ultimately a politician always wins.

    • Jonathan Phillips Says:

      Don’t vote – it only encourages them!

      The trouble is that our not voting doesn’t discourage them in the least. Low turnouts are simply ignored.

      There are reforms that might help. How about a turnout requirement, less than 50% being equivalent to “none of the above” and requiring a rerun with different candidates?

      There’s no doubt that STV puts more power in the hands of the voter and thus at least opens up the possibility of electing people who are not machine politicians.

      Then radical decentralisation, bringing politicians much closer to the people, and making it more likely that politicians will actually b e people.

      Then giving some substance to the notion of the “big society” – replacing it with “many small societies” for a start – making possible some form of direct democracy within smallish groups (’60s hippy talking).

      Sadly, we can whistle for it. But still better some reform (Yes to AV) than none, not now, not ever…

  18. sam Says:

    How about this for a short way of describing what we are trying to do with AV?

    AV is not unfair to the first preference of a minority of people (current system), AV is fair to the consensus of the majority of the people.

    • David Craven Says:

      Alternatively, AV gives you the candidate that the majority of the people don’t hate. It’s the “unhappy compromise” candidate. Both statements are the same thing, it just depends on your spin.

    • Jonathan Phillips Says:

      @ David Craven: … while “first past the post” can actually let the LEAST popular candidate win – which is the greater defect?

      And why assume that a compromise is “unhappy”? – wasn’t compromise once said to be part of the British genius?

      It’s perfectly possible anyway that a majority might be happy to agree on (line up behind) a candidate whom few would regard as a “compromise” – Ken Livingstone, maybe – because they combine a distinctive message, a strong personality and the sense that “you know where you are with them.” Better someone I disagree with but trust than a slippery customer who happens to make all the right noises.

  19. sam Says:

    @ David Craven. I would disagree, your statement doesn’t defend FPTP t only suggests an alternative is wrong.

  20. Oliver Cottam Says:

    Hi i was pointed in the direction of your blog by a friend studying your maths course, i like your 24 points however i think there is one key point that doesn’t seem correct: “AV makes it easier to get rid of unpopular governments”.

    You mentioned the 2005 election, saying labour were unpopular after the iraq war and got a majority with only 35.2% of the vote, but managed to get a majority with 356 seats. Research suggests they would have had 364 seats under AV – far from making it easier to get rid of them.

    In addition the British Election Study data suggests that in 1987, the total conservative seats would have risen from 376 to 383 (where they got 42.2% of the vote).

    So i don’t think AV can be considered better at getting rid of unpopular governments.

    • Jonathan Phillips Says:

      “So i don’t think AV can be considered better at getting rid of unpopular governments.”

      Of course it can’t, though I can’t see that it’s worse than “first past the post” in that respect.

      What it clearly is good at is getting rid of unpopular MPs. Any MP who p*sses off a sufficient proportion of his/her constituents is going to find them ganging up on him/her.

  21. RAB Says:

    Re 12. There is no anomaly-free voting system.

    (As far as I understand) Arrow’s theorem assumes that each voter ranks all the candidates. But under the AV proposals, this assumption doesn’t hold; I don’t have to rank every candidate, so I am free to not rank the parties I hate.

    Does this mean that anomalies are less likely? And are there any mathematical theorems relating to systems where I am free to rank as many of the candidates as I wish, but am not forced to rank them all?

  22. Anonymous Says:

    I don’t see how AV could do much more than give some small set of political opportunists more power to form a coalition with one of the two major parties. Perhaps this would damp some of the oscillations described by Prof. Gowers a bit, but I”m skeptical that AV would substantially alter the trajectory along which British society seems to be evolving. The actions of the current coalition government seem to support this view.

    • Anonymous Says:

      The main effect of AV would seem to be to add a random perturbation to the more deterministic oscollation described by Prof. Gowers.

  23. Tom Leinster Says:

    Tim, I’ve enjoyed your posts on this very much, and I think they’re a valuable public service.

    I just wanted to make a comment on something tangential to your main theme (and closely related to Rab’s point just now). I would say that Arrow’s theorem isn’t directly relevant to our real voting systems for two reasons.

    One is that, as Rab said, in Arrow’s theorem each voter puts a total order on the whole set of candidates. In reality, we totally order a subset. So the “input” doesn’t match our reality.

    The other is that in Arrow’s theorem, the outcome is also a total order on the set of candidates. In reality, the outcome is a single selected candidate. So the “output” doesn’t match our reality either.

    I know people have thought about no-go theorems involving structures other than total orders: e.g. putting a preorder on the set of candidates. This means that you can rank several candidates equally (as in LMS committee elections). Included in this, implicitly, is the possibility of leaving some candidates unranked: they should be regarded as bottom equal.

    I wrote a blog post about this kind of thing here. It has a little about the fantasy of being able to put a non-symmetric metric on the set of candidates, to say how much you prefer one candidate to another.

  24. WJ Says:

    I was somewhat saddened to see this page – http://www.bbc.co.uk/news/uk-politics-13229787 – where the YES and NO campaigns each gave what are supposedly the five best arguments in favour of their point of view. As far as I can see, the opposite is true.

    If you had to come up with the five top arguments for each side, what would they be?

    • WJ Says:

      By the way, here are my top five arguments for each (where a criterion is given, it is a criterion satisfied by the voting system it is supporting and violated by the other system):

      YES to AV:
      1. Near elimination of tactical voting (the best tactic is nearly always to vote sincerely.
      2. Condorcet loser criterion – FPTP can, and frequently will (if the BNP isn’t standing), elect the candidate who would lose in a two way election against every other candidate.
      3. Independence of clones criterion – if a new candidate decides to stand who is exactly the same as one of the existing candidates, they will not harm that candidate’s chances under AV, but will under FPTP.
      4. Mutual majority criterion – If there is a subset S of the candidates such that more than half of the voters strictly prefer every member of S to every candidate outside of S, and this majority votes sincerely, then the winner must come from S. This criterion is violated by FPTP.
      5. MPs need to get wider support, not just from a few voters in swing-seats.

      No to AV:
      1. Monotonicity criterion – quite a serious shortcoming of AV relative to FPTP, though I think it is pretty much cancelled out by the relative shortcomings of FPTP.
      2. Participation criterion – under AV, you can (occasionally) help your favourite candidate by not voting at all. Under FPTP, this is never the case.
      3. Extra expense, I suppose…
      4. ?
      5. Under AV some people get more votes than others.

      I’m still trying to think of a good fourth and fifth argument against AV, but I’m not sure if they exist.

      What do you think?

    • WJ Says:

      By the way, point number 5 on the no to AV list was a joke: I tried to put faux-HTML tags on it but they didn’t come out.

    • gowers Says:

      I think it’s worth stressing that FPTP has its own form of non-monotonicity. If you campaign successfully for certain causes, you can harm those causes. For example, Ralph Nader campaigned on green issues in 2002: if he hadn’t, Gore would have won the election instead of Bush. Similarly, one can imagine that if UKIP had a particularly successful general election (in terms of vote share) then it might hand the election to Labour, who tend to be less anti-Europe than the Conservatives.

      We’re so used to this particular non-monotonicity that we almost don’t notice how problematic it is. I think it completely dwarfs any non-monotonicity problems that arise under AV.

    • WJ Says:

      Oh! I forgot:

      4. AV is more complicated to understand (though I very much enjoyed the flowchart in the post: it’s so true).

    • Jonathan Phillips Says:


      ☹ Most of us are represented by MPs we did not vote for, MPs chosen for us by other people.

      ☹ MPs can slide in with under a third of the vote. For every three people that voted for Norwich South’s MP, seven would have preferred someone else.

      ☹ In a three-way contest it is perfectly possible for the LEAST popular candidate to win, just because the opposing vote is split.

      ☹ People who want to support a party which cannot win in their constituency have no influence over the result: their vote is simply wasted.

      ☹ There isn’t any post!



      ☺ Far more of us get a say in who represents us.

      ☺ MPs have to gather the support of a real majority of voters to gain election.

      ☺ Unpopular candidates cannot win.

      ☺ No-one’s vote need go to waste.

      ☺ There IS a post: the first candidate to pass 50% in any round of counting has won!

      Will that do?

    • David Craven Says:

      @ Jonathan Phillips: just to play Devil’s advocate, I can’t help but notice that your first and second points are identical (the majority of people don’t normally vote for the candidate, MPs are elected normally by a (significant) minority), and the third point is heavily related to these. I’m not even sure whether 5 is meant to be serious, so that can be ignored. So you have two problems with FPTP really.

      My real worry with AV is that (I believe, I don’t know for sure) that it essentially hands the election to Labour every time. I don’t think there’ll be more Lib Dem voters than Labour voters in most constituencies, so the Lib Dem candidate will be eliminated, and most of the votes that way will slide to Labour. If that’s the will of the people then fine, but I feel that an almost-default Labour victory will be seriously damaging to our politics.

    • Jonathan Phillips Says:

      @ David Craven.

      “Default Labour victory.” Do you think that could be why the whole Tory party and its megabuck donors have thrown every kind of mud they can find at AV? Though it doesn’t explain why the likes of Straw, Prescott and Beckett are happy to take the tainted cash. Perhaps they’re just stupid.

      Once upon a time (see Keynes writing about politics in the ’20s) the Tories were widely regarded at the Stupid Party. Since the ’80s they’ve been seen more as the Nasty Party. It’s true that AV enables voters to punish parties they don’t like more effectively than does FPTP, so perhaps the Tories would suffer.

      On the other hand, in 1974-79 Labour began to appear thoroughly incompetent and by 1983 it had turned itself into the Insanity Party. In the circumstances it would not have gained many second preferences from minor-party supporters (who might well have refused to mark any second preferences at all, given the choice on offer).

      As a lifelong (but no longer) Liberal (Democrat) I would certainly have given my second preference to Labour at every election from 1992 onwards (though I would have had to hold my nose in 2005 and 2010) – but there are no doubt many LD supporters who would not have done so. Going back to earlier elections, from 1966 to 1974 the Tories would probably been my Number 2s (ho ho). 1979-87 would have been a “plague on both your houses” period. So here is at least one voter who, on past evidence, couldn’t be guaranteed to contribute to a Labour victory.

      What LD, Green and Ukip voters would choose to do with their second preferences (if they chose to mark any) is uncertain. And what would be the role of Plaid Cymru and the SNP and their supporters? Much depends, as always, on the image, personalities and policies of the main parties: get them right and victory will follow. A Conservative party led by someone of the calibre of Harold Macmillan (a toff, certainly, but one who had lived through wars and depressions and was keen that no-one should suffer that kind of deprivation again) might fare considerably better than the C. party of today. There were once caring Conservatives, really there were!

    • David Craven Says:

      Don’t get me wrong: I am going to vote Yes tomorrow, but on the basis that it will hopefully lead to something like STV with constituencies of 3-4 MPs, my preferred solution, as it blends PR and the constituency link. The extra cost of AV, which is a few more hours counting time, will be offset by the reduction to 600 MPs, so that isn’t really an argument. Some much-needed reform trumps my Labour-default-winners concern about AV, but I don’t buy arguments like “it will make MPs work harder”, because the truth is that the majority of people will vote for parties, and only a few people, and a few constituencies, vote for the MPs themselves. If Yes wins, it would be an interesting first election under it though!

    • Jonathan Phillips Says:

      @ David Craven – the Yes arguments have been feeble and tangential, the No arguments fraudulent.

      A problem with multi-member constituencies is that each member represents the entire constituency (population and geography) – even if you kept to 3-4-seaters this would be quite a load. No problem in local elections, where 3-member wards are common anyway, and no problem in Ireland (166 TDs to a population of 4.5m – you can hardly move without bumping into an MP). There’s no doubt that STV maximises voter choice and voter power, but perhaps at the cost of making MPs excessively patch-minded, rarely raising their eyes much above local concerns. But it is the only system that comes at all close to eliminating safe seats and “jobs for life”.

      Which leaves me chronically undecided as between STV primarily in 3-member constituencies and Roy Jenkins’s ingenious AV+ scheme (http://bit.ly/emjgB2 if you haven’t seen it), which is more “mitigated majoritarian” than proportional, even to the limited extent that STV in 3-member constituencies would be.

      Of course AV now could take us in either direction later on (as well as to STV in local elections), while a No vote means we get nothing, not now, not ever – and since I’m already pushing 70 I really don’t have that long to wait.

      Given the speed with which C&C reached agreement I’ve begun to suspect it was actually a stitch-up – or at least that the Cons had worked out the scenario beforehand and Clegg walked into their trap. Even in countries where coalitions are the norm, even in circumstances where parties’ preferred partners are known in advance (FG and Labour in Ireland, CDU/CSU and FDP in Germany) it takes more than five days to reach agreement on a programme of government and the division of cabinet seats.

      AV – a better choice, a stronger voice. Now why didn’t someone think of that a couple of months ago?

      And if Clegg was going to go for some kind of quid pro quo, why didn’t he insist on STV in local elections? – the case is very strong, and it wouldn’t have needed a referendum.

  25. Alternatives « Notes from a small field Says:

    […] AV vs FPTP — the short(er) version (A follow on from Is AV better than FPTP? and AV vs FPTP — a supplementary post) […]

  26. WJ Says:

    By the way, point number 5 on the no to AV list was a joke: I tried to put faux-HTML &ltjoke&gt &lt/joke&gt tags on it but they didn’t come out.

    • WJ Says:

      Sorry; I appear to have posted the same comment twice. Could you remove these two please?

  27. Why you should vote Yes to AV - Jonathan's Blog Says:

    […] also has a shorter (here meaning 5000 words!) post, making much the same points, but (slightly) more concisely — there’s also a summary in […]

  28. Dr. Axel Ridder Says:

    Your explanation of the two voting systems FTPT and AV is excellent, but what would you think about another choice? This is my comment on the opinion of “The Economist”of April 30th-May6th. http://is.gd/PhD9Z4

    The British Referendum on May 5th asks: FPTP ( relative majority voting in a one-person constituency) plus AV ( alternative voting or preference vote like in Australia) YES or NO? The Economist says NO and proposes: FTPT plus 20% PR (proportional representation).
    I say: FTPT in three-persons-constituencies plus American Primaries plus AV plus 33,33% PR for women or men. I have extensively elaborated on my web page http://www.2009-de.com .

    My website http://www.2009-de.com proposes a slight improvement of the Westminster model which makes it superior to the American gridlock. My new idea is: Reform of the one-person-constituency (“winner takes all”) to a three-persons-constituency with relative majority voting and a list of 2 candidates for every party ( party A = 2 seats of parliament, party B = 1 seat of parliament; parties C, D, E, etc. get nothing or “everything” in another constituency, as is normal in relative majority voting, invented by the ingenious Greeks. )
    In a time of transition it is advisable to have a two-persons-ticket of a man and a woman or a woman and a man plus the Australian “preference vote” ( AV ).

    The heaviest argument against the Economist’s NO is: Nobody understands why 20%, not 21% or 17% or 5% or 30% or50%???? It smells manipulation, no clarity, no simplicity or no functionality. Look to Italy and the whole Berlusconi nightmare!

    I do not say YES to the British proposal but say: Make the referendum better!

  29. Hughes. Says:

    Yet another pro-AV argument that tries to gloss over the fact that the least popular candidate’s supporters have a disproportionate influence over the result.

    If 2nd, 3rd, 4th and 5th preferences have equal weight, then everybody’s preferences should be counted in the subsequent counts. That would be a genuinely fairer system, and that is NOT the system being proposed.

    • tim ellis Says:

      Everybody’s preferences are counted in subsequent rounds. In each round your highest ranking preference for a candidate that is still eligible is counted. If you voted for the candiate currently in the lead your first preference vote is counted in the second round. If your second preference was counted you would be voting for someone else, so your first choice might not win – In what way would this (a) be fairer or (b) even start to make sense?

    • gowers Says:

      Let me put the point again, with an example.

      Suppose you are a Conservative supporter and I am a Green supporter. Suppose I put the Greens first, then the Lib Dems and then Labour. And suppose that in the particular constituency the Conservatives and Labour are battling it out for first place, with the Lib Dems third and the Greens fourth. Finally, suppose that three rounds are needed for the count.

      Then in the first round we both get to support our first preferences. In the second round, the Greens are eliminated. You still get to support the Conservatives, but I have to settle for the Lib Dems, my second choice. Then the Lib Dems too are eliminated. In the third round, you still get to support your first choice but I have to go down to my third choice. Which of us is in the better position?

      True, your second and third preferences are not counted, but your first preference is counted three times. That’s BETTER not WORSE. It gives you MORE influence not LESS. (Just to be clear that I’m not accidentally arguing against myself, it gives me, the Green supporter, LESS influence, not MORE.)

      The pro-AV campaign has shot itself in the foot here. It could have calmly pointed out that if a BNP supporter gets more than one vote, then so does everyone else.

      If you still don’t see it, then perhaps you’d like to explain in detail how your “genuinely fairer system” would work.

  30. Maggie E Says:

    I lived in Australia for 30 years and have recently returned to the UK in retirement. Summing up my Australian experience, just a few points:

    1. Australians are happy with AV. It has been said that Australia is thinking changing their system. I am not aware of this but, if it were, it would not be to return to FPTP.

    2. I find voting in Australia much more empowering than in the UK. You can vote for the person you want without any feeling of wasting a vote. It works best when you do express your preferences fully. In that case, when the election comes down to two candidates you know that your vote is still in the hunt and is sitting on the pile of the person you prefer of those two.

    3. It should not be much more expensive or slow to count than FPTP. In most consituencies little redistribution is needed.

    4. The information acquired from the statistics after the election are very useful in understanding trends in public opinion. For example the Greens are gaining votes in Australia. The ALP candidate won in this electorate because of Green preferences despite losing the first round (http://results.aec.gov.au/13745/Website/HouseDivisionDop-13745-193.htm – thanks to the poster above who gave this link). This means the Liberals need to do more to be green in order to do better in future. Under FPTP the Liberal would just have won.

    5. AV makes tactical voting difficult for individual voters but it is worth the while of a party to influence the preferences of the voters as a whole. So distribution of how-to-vote cards should be disallowed.

    I voted (legitimately!) in both the UK and Australian elections last year. The second was a much better experience. But I am not at all hopeful for this referendum.

  31. Anonymous Says:

    Please please please edit this blog post to put the bullet point list on top, or put it in a post of its own. It is a great summary of your points, and if people are interested they can always read the longer versions.

  32. Robin Saunders Says:

    Two things I would have changed:

    Tactical voting is not the only serious thing wrong with FPTP (other than lack of proportionality). Vote splitting is a big problem – you mention it in the body of your post, but I think it belong up there near the top. Not only is it a deficit that AV fixes, but it is in a sense partly responsible for the aforementioned lack of proportionality.

    For what it’s worth, my ideal parliament would be composed of individual candidates ranked by the Schulze method.

    • gowers Says:

      I agree with you. It’s right up there in the top of my mind, but I didn’t reflect that enough in the post. Since then I’ve made a few comments about Ralph Nader losing Al Gore the 2002 presidential election, an example of non-monotonicity under FPTP (because by campaigning successfully on an environmental ticket he brought in a climate-change denier instead).

  33. Robin Saunders Says:

    I missed the second thing that I would have changed, although it’s more tongue-in-cheek:

    “Q. Look, you understand how AV works and so do I, but the fact remains that not everybody would understand the full implications of how their votes are counted. Isn’t that profoundly undemocratic?”

    Look, you understand how FPTP works and so do I, but the fact remains that not everybody understands the full implications of how their votes are counted.

  34. AV, BNP and Stephen Fry: more reasons to vote on Thursday | Inside Croydon Says:

    […] AV vs FPTP – the short(er) version (gowers.wordpress.com) […]

  35. Raffaella Sirletti Says:

    This has helped me enormously with my vote tomorrow, I have been debating long and hard with myself but have got there now.

  36. Charles Roddie Says:

    This shorter “version” is much much better than the long one. A completely different article. Presents facts without much explicit atempt to conclude what is morally better, which was creating problems of multiple inconsistent points of view with the long version.

    It starts to make clear why you don’t like tactical voting. Or maybe this has just become clear to me. You don’t like tactical voting because under systems that require tactical voting, people don’t vote tactically enough. This makes the outcomes of FPTP “unfair”. For example it causes the “wrong” choice of coffee in the picture you linked to because the beer drinkers are not voting tactically.

    Of course it could be that you don’t like tactical voting because it’s complex but I’m not sure why you think that is a disadvantage.

    Your idea about fairness seems to have more to do with who gets the seats than who gets the majority. But seats have little importance beyond determining a majority. If for example AV would not have historically increased the chance of coalitions then the claim that the Liberal Democrats historically got an unfair deal doesn’t stand up. So to make the claim of fairness I think you need to be more definite about the connection to coalition governments.

    The fact that AV is being used at a local level and the outcome is government formation at a national level is an essential consideration.

    There is an explicit recognition that while “There is no anomaly-free voting system”, we can minimize the anomolies. I am perplexed by this reaction to Arrow’s theorem, which is quite a common one. Doesn’t Arrow’s theorem indicate that the properties that some people wanted were inconsistent, so that we should look for another approach altogether. I guess the alternative approach will be formal modelling of different systems and their outcomes but this also gets stalled by the intractability of voting with multidimensional preferences. Empirically democracies seem to do better than despotisms, but I don’t think the literature is not at the point of distinguishing between different types of democracy or looking at different systems.

    So maybe after this is over we can get back to more tractable questions.

  37. OldBloke Says:

    The referendum is really about FAIRNESS, in particular through the mechanism of PREFERENCES – is one voting system fairer than another?

    My Parthian Shot is:

    IS ONE MAN, ONE VOTE fair?

    Consider this: A 97 year old female, with a life expectancy of 2.81 years, ‘will have fallen off the perch’ by the time one of the referendum choices could be applied, whereas an 18 year old female, with a life expectancy of 62.93, will still be around for a considerable number of years.
    Is it fair that the 97 year old will have totally negated one of the younger voters PREFERENCES?
    We are told our society is growing older and this must skew the plot of Age/Voting Population to the right (could also be that we become more ‘conservative’ with age). Should we not, therefore, introduce a mechanism of weighted voting depending on age?

  38. Narjas Mehdi Says:

    I loved the diagrams, and would have liked to see them nearer the top.

    The beers vs coffee FPTP graph finally explained what AV was trying to avoid WITHOUT using 1000 words, and in a way that I understand. Thank-you thank-you thank-you.

  39. yikaozhu Says:

    Thank you very much,I love this post.

  40. demotivator Says:


    […]AV vs FPTP — the short(er) version « Gowers's Weblog[…]…

  41. Getting into norms | Out of the Norm Says:

    […] happened on a national scale earlier this year, with the UK deciding it didn’t want a slightly more complicated but better voting system, with both sides of the debate generally arguing “vote for our method or X will […]

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