Is AV better than FPTP?

On May 5th the UK will vote in a referendum for only the second time ever. (The first time was in 1975, when we voted on whether to remain in the EU, or the Common Market as it was then called.) Now we have a chance to decide whether to retain our current voting system, misleadingly known as First Past The Post, or whether to switch to the Alternative Vote. Let me come clean straight away. Although in this post I shall try to write dispassionately about these two voting systems, my actual attitude is anything but dispassionate: I have yearned for a better voting system ever since I have had any political awareness at all, and am steeling myself for what is probably going to be a huge disappointment when the country votes for the status quo. And I am writing this post in the genuine hope of making a difference. Since it is extremely hard to change anybody’s mind in politics, I think the best I can hope for is to persuade somebody to vote yes (the question will be phrased in such a way that “yes” means you want AV and “no” means you want FPTP) who might otherwise not have bothered to vote at all. This is a mathematics blog, so I will give this post a mildly mathematical slant, but all I really mean by this is that I know when I write that a typical reader of this post will be mathematically literate, which may make the post different in tone from how it would be if I were writing for a more general readership.

A little history.

Let us look at the election results from 1979, when Margaret Thatcher first came to power, to 1997, when Tony Blair first won. These are results of elections held under FPTP, the system where the country is divided into constituencies, each of which gets a seat in parliament, and the seat goes to whichever candidate gets the most votes in the constituency.

In 1979 the results of the three main parties were as follows:

Conservatives, 43.9% of the vote, 339 seats

Labour, 36.9% of the vote, 269 seats

Liberals, 13.8% of the vote, 11 seats.

So the Conservatives got a little over three times as many votes as the Liberals, and just over thirty times as many seats. To put that another way, it took about ten times as many votes (on average) to elect a Liberal MP as it took to elect a Conservative MP.

The next election was an interesting one. A couple of years into Thatcher’s premiership, a new political party, the Social Democratic Party, was formed by moderate Labour Party politicians who did not like the lurch to the left that had taken place under Labour’s then leader Michael Foot. Within a short time, they were coming top in opinion polls, but this did not last until the General Election, largely because the Falklands War gave Mrs Thatcher a huge boost to her popularity. It was clear that the Social Democrats had a lot in common with the Liberals (with whom they were later to merge), so they agreed not to stand against each other at the 1983 General Election, instead forming the Alliance. The results of the election were as follows:

Conservatives, 42.4% of the vote, 397 seats

Labour, 27.6% of the vote, 209 seats

SDP/Liberal Alliance, 25.4% of the vote, 23 seats.

Let us note a couple of anomalies in this result. Most strikingly, the Alliance got almost as many votes as the Labour party but Labour got roughly nine times as many seats. Second most strikingly, the Conservative share of the vote went down slightly, but they now had a truly thumping majority, much higher than after the previous election.

How was this possible? Well, under FPTP, if you want to maximize the number of seats you will get for a given share of the vote, then there are two things you must avoid. Most importantly, you don’t want to spread your vote about too evenly: if you get 28% of the vote in every single seat, you probably won’t win a single seat. So FPTP penalizes parties that have a uniform appeal throughout the country. This suggests that what you want is for your support to be geographically concentrated, and indeed that is the case up to a point, but you must also avoid having too many seats where you have an overwhelming majority: if you get 90% in a seat, then at least 40% of those votes would have been more useful to you if they had been cast in other constituencies. So FPTP favours parties with support that is geographically concentrated but not too concentrated. The Alliance’s support was dispersed, and the consequences for them at the election were disastrous.

The second anomaly — the hugely increased majority for the Conservatives despite a drop in their share of the vote — was a consequence of a phenomenon that frequently arises in this country under FPTP, the splitting of the left. At that time, both Labour and the Alliance were clearly on the left (the Alliance was much less so, but they were certainly not in favour of the Thatcherite programme that the country officially voted for) so there was a clear majority in favour of broadly left-wing politics. However, that majority was roughly evenly split between two parties, so there were many constituencies where the Conservatives won the seat with well under half the vote.

The next election, in 1987, was similar but less extreme.

Conservatives, 42.2% of the vote, 376 seats

Labour, 30.8% of the vote, 229 seats

Alliance, 22.6% of the vote, 22 seats.

In 1990 Margaret Thatcher resigned and John Major took over. The next election was in 1992 and the results were as follows. By this time, the SDP and the Liberals had merged to become the Liberal Democrats.

Conservatives, 41.9% of the vote, 336 seats

Labour, 34.4% of the vote, 271 seats

Liberal Democrats, 17.8% of the vote, 20 seats.

Something odd happened here too: the Conservative vote dropped by 0.3% but their majority went down very substantially (which led to numerous rebellions throughout the parliament, particularly on the thorny subject of Britain’s relationship with Europe). The explanation is that the split on the left, which still existed, was less severe.

Next was 1997, the year that Blair was elected.

Labour, 43.2% of the vote, 418 seats

Conservatives, 30.7% of the vote, 165 seats

Liberal Democrats, 16.8% of the vote, 46 seats.

Again there are some strange aspects of this result. The Liberal Democrats had their best result for many decades despite their lowest vote percentage in all the elections I have discussed. (However, their share of seats was still significantly lower than it would have been under a proportional system.) Labour got about two and a half times as many seats as the Conservatives for under one and a half times as many votes, and got a massive majority with only 43.2% of the vote.

Does FPTP reflect the will of the voters?

It is very easy to slip into thinking that the answer to this question is yes by definition: whatever the result of an election, the interpretation given to it by the media will be that “the voters have said” whatever FPTP deems them to have said. For instance, when I think back to the election that John Major won, my impression of it is that the mood of the country swung against the Tories, but not by enough to unseat them. I had completely forgotten that the Tory vote remained virtually unchanged from the previous election and that it was only the change to how the votes on the left split that caused the Tories to lose seats. So a more correct interpretation of the result is that the Labour party had become more electable again, improving its appeal relative to that of the Liberal Democrats.

I don’t think it is possible to defend the view that the 1983 election reflected the will of the voters: over a quarter of voters ended up being represented by about 3% of MPs, and the representatives of just over 40% of voters were given free rein to continue with a program that was (I am pretty sure) bitterly opposed by the majority.

It is reasonable to say that when Tony Blair was elected, the result reflected the national mood to some extent: the Conservatives had been in power for 17 years and John Major’s government had lost the country’s respect after Black Wednesday, from which it never really recovered. However, it is not reasonable to say that the size of Blair’s majority — he had almost two thirds of all seats — reflected the national mood. The large swing was reflected, but in a distorting mirror that greatly expanded it.

Similarly, since the Liberals, or Liberal Democrats, always come a distant third in elections, one naturally thinks of them as a minor party, but their share of the vote, often over 20%, is anything but minor.

And I haven’t mentioned elections from further back that were won by parties that did not get the most votes. In 1951, the Conservatives under Winston Churchill won an absolute majority of seats (though a small one) with 48.0% of the vote. In the same election, Labour under Clement Attlee got 48.8% of the vote.

Do people’s votes reflect the will of the voters?

This question looks a bit silly. Is the answer not trivially yes?

No it isn’t. Under FPTP, we often receive election literature that looks something like this.

That was a bar chart put out by the Liberal Democrats in Cambridge at the last general election. They reasoned that Conservative voters would prefer the Liberal Democrats to Labour, so tried to persuade potential Conservative voters to vote Liberal Democrat on the grounds that voting Conservative might well let in Labour. It is only fair to say that this argument has been employed much more often in the past against the Liberal Democrats. The slogan, “A vote for the Liberals is a wasted vote,” used to be heard frequently at elections.

But the general point is that under FPTP it is often rational to vote for a party that is not your first choice. This is a very important point, since it hugely weakens one of the main arguments of those who are campaigning against AV. I will come back to this later.

(In parentheses, let me remark that the result in Cambridge at the last election was

Liberal Democrat 19,621 (39.1% of vote)
Conservative 12,829 (25.6% of vote)
Labour 12,174 (24.3% of vote)
Green 3,804
UKIP 1,195
others 507

So it seems that Conservative voters were not persuaded to vote tactically.)

Going back to some of the results under FPTP, one cannot know how many people voted for parties that were not their first choice. However, all the main political parties urge people to vote tactically in individual constituencies (even if the senior politicians do not always admit it), and it is obvious that many people heed the call. I cannot prove it, but I find it pretty obvious that some of the results from the 1980s that were so unfair to the Liberals, the Alliance and the Liberal Democrats were in fact more unfair even than they looked, since many people would have voted for them if they had not been persuaded by the wasted-vote argument.

Is AV any better?

So far all I have done is discuss some of the deficiencies of FPTP. (OK, perhaps “deficiencies” isn’t a neutral enough word. I have been discussing some of the interesting phenomena that can occur, and often have occurred, under FPTP.) But does AV do any better?

The first thing to say is that AV is not proportional representation. Under AV it is still possible for a party to get a share of seats that is very different from its share of the votes. Before I say any more about AV, let me quickly say what it is (though I imagine that most people interested enough to get this far know already). Under AV, you don’t just vote for one candidate. Instead, you number the candidates 1,2,3 until you no longer wish to express a preference. For instance, if you are a UKIP supporter (the United Kingdom Independence Party is a right-wing party that wants Britain to leave the European Union) then you might put UKIP first and the Conservatives second, but not express a preference between Labour, the Liberal Democrats, the Greens, etc.

When the votes are counted, the following algorithm is applied.

1. Count all first-preference votes not yet counted.
2. If some party has over 50% of first-preference votes, then HALT. (That party then wins.)
3. Take the party with the smallest number of first-preference votes and change each vote for that party by removing the first-preference votes and turning th-preference votes into th-preference votes for each
4. Remove that party from the list of preferences of all other voters.
5. GOTO 1.

As an example, suppose that the parties in your constituency are Labour, the Conservatives, the Liberal Democrats, UKIP and the Greens. Suppose that your preferences are Green, Lib Dem, Labour, Conservative, UKIP in that order. Then if no party has over 50% and UKIP comes bottom, nothing happens to your voting paper. If after the next count (when the UKIP second preferences have become first preferences) it is still the case that no party has over 50%, and this time the Greens are eliminated, then your preferences are shunted up by 1, so they now read Lib Dem, Labour, Conservative (UKIP and the Greens having been eliminated). Perhaps by this stage Labour have reached the magic 50% (with a boost from those Greens who put Labour as their second choice). Or perhaps no party has and the Liberal Democrats are now third. In that case, your preferences become Labour over the Conservatives, and one or other of those will now have over 50%.

One of the criticisms of proportional representation is that it weakens the constituency link: it is hard to have a fully proportional system where each MP represents his or her constituency. AV does not suffer from this defect, since there is still a constituency system. But the price for that is that there is no obvious reason to expect AV to be proportional. So why is it any better than FPTP (from the point of view of representing the will of the voters)?

The reason is that under AV there is far less reason to vote tactically. Under AV, a vote for a minor party is not a wasted vote: you can express your preference for the minor party while still having an opportunity to decide which of the major parties you would prefer. For instance, you could vote Green and not worry that you were letting in the Conservatives, or you could vote UKIP without thinking that you might let in Labour. And if you are an anyone-but-the-Tories person, you can express that sentiment without being forced to guess which party has the best chance of defeating them.

Is tactical voting eliminated under AV?

The scope for tactical voting is greatly reduced under AV, because the wasted-vote argument no longer applies. But it is possible to come up with circumstances under which it would make sense even with AV to vote tactically. I’m not sure these circumstances would be relevant: typically they would require voters to know more about the preferences of other voters than they are ever likely to in practice. But let me give what I think is the simplest situation where tactical voting would in theory be rational under AV. To make it easier to understand, I’ll use actual parties, and will try to make people’s second preferences as plausible as possible given their first preferences.

Suppose you are voting in a constituency where the Conservatives typically get around 40% of first-preference votes, Labour get around 30%, the Liberal Democrats get around 30%, and the other parties get almost nothing. (This is not entirely realistic, but it could well be the situation after all but three parties have been eliminated.) Suppose you are an ardent supporter of the Conservatives. What should you do? Well, you might judge that Liberal Democrat voters are more likely to put the Conservatives as their second choice than Labour voters are. If that is what you think, then paradoxically it might make sense to vote Labour (the party you like least out of the three) so that when the second-choice votes are counted the Conservatives will get enough to push them over 50%. To see how this could work, imagine that the second-preference votes for Labour split 5:1 in favour of the Liberal Democrats (that is, 25% of voters have Labour first and Lib Dems second, and 5% of voters have Labour first and the Conservatives second), while the second-preference votes for the Lib Dems split 3:2 in favour of Labour (so 18% of voters have Lib Dems first and Labour second, while 12% of voters have Lib Dems first and the Conservatives second).

Labour and the Lib Dems are neck and neck. If the Lib Dems come second, then Labour will be eliminated and the total percentages of votes will be 45% for the Conservatives and 55% for the Liberal Democrats. If Labour come second, then the Lib Dems will be eliminated and the percentages will be 52% for the Conservatives and 48% for Labour.

So in a situation like this, we have the strange phenomenon that it may be in the interests of some Conservative voters to put Labour as their first preference in order to gain a substantial block of Liberal Democrat second-choice votes.

However, there are some pretty serious problems with actually voting tactically in this situation. Obviously if all Conservative voters were to do so it would be a disaster for the Conservatives. And you can’t coordinate your votes. So how do you decide what you, an individual Conservative voter, should do? If you are a mathematician, then you will probably toss a coin a few times and make a probabilistic decision, but something tells me that that practice is unlikely to catch on. And of course, it is ridiculous to suppose that you will know what proportion of Lib Dem voters are likely to put the Conservatives as their second choice.

To get an idea of just how much less tactical voting there would be under AV, try to imagine a slogan as punchy as “A vote for the Liberals is a wasted vote.” You won’t get very far with “A vote for the Conservatives might let in the Lib Dems with the help of Labour second preferences, whereas a vote for Labour will help the Conservatives win with the help of Lib Dem second preferences, but could only a few people pay attention to this please?” In practice, hardly anyone will have a good reason to do anything other than put in order of preference the parties that they have a view about.

Is the First Past The Post system the First Past The Post system?

This is another question that seems to have a trivial answer but actually doesn’t. Presumably First Past The Post is a metaphor. Indeed, it is a metaphor — from horse racing. So let us try to work out how the metaphor works. Presumably there should be a post somewhere. So what is the post? Hmm … it’s hard to say.

A natural answer might be that you pass the post when your party reaches 50%. That is, you would have a sort of race, and the first party to get over 50% would be declared the winner. Are there any systems like that? Oh yes, AV. (And not just AV, but that is the one we have the chance to choose.)

For the most part I want to stick to rational argument, but sometimes it’s quicker and more effective to use slogans. Here’s one I like:

FIRST PAST THE POST IS NOT FIRST PAST THE POST!

And to those who think it is, how about

WHAT IS THE POST?

(Under some circumstances, the first word might perhaps be replaced by “wtf”, but not on this nice family blog.)

If I want to vote selfishly, then how should I vote?

Suppose that you firmly support one political party and your only interest is to do what will best serve that party, ignoring all questions of fairness, democratic principle, etc. How should you vote in the referendum?

If you support the Conservatives, then probably you should vote no. It was the FPTP system that allowed Mrs Thatcher to rule for eleven years with large majorities and well under half the votes. It is possible that the Liberal Democrats are so damaged by the current coalition that we will see a return to straight two-party politics for a while (in which case whether we have FPTP or AV will not make much difference to the outcomes of elections). But unless the political landscape really has permanently changed, FPTP gives the Conservatives the best chance of exploiting the split on the left, whereas AV allows those of a broadly left-wing persuasion to vote in an anything-but-Tory way.

If you support the Liberal Democrats then it’s a no-brainer.

If you support Labour, then it is less clear what you should do. Perhaps you will look back at the three elections won by Tony Blair, and at the current unpopularity of the coalition, and think that you don’t need the help of AV. But if that is your view, then I suggest you look back further to the dark days of the 1980s. Under AV there is a real chance that Labour would have won the 1983 election, or at least been able to form a grand coalition with the Alliance, and the same goes for the subsequent elections: it is unlikely that John Major would have had his shock victory in 1992, for instance. And AV would not have stopped Blair from winning his resounding victories. Probably in 2005 it would have left Blair a little more punished for the Iraq war, but probably you wouldn’t regard that as a defect of AV. And as for the future, when the Conservatives reduce the number of seats you will have a lot of electoral ground to make up. If the Lib Dem vote collapses then AV won’t harm you, and if it doesn’t collapse then AV will make it much more likely that you will be in a position to defeat the Tories.

To put it in slogan form again,

A LABOUR SUPPORTER VOTING FOR FPTP IS A TURKEY VOTING FOR CHRISTMAS.

Or to be more visual about it,

As I’ve said above, it’s a little more complicated than that, but the whole point of slogans is to ignore all those little qualifications.

Some claims by the NO2AV campaign.

I would like to assess some of the claims about AV that have been made by those campaigning against it.

1. Under AV the person who comes second or third can win.

I find this argument laughable. The truth that the above sentence expresses is that under AV the person who would have come first under FPTP will not always win. Well I’ll be: it turns out that AV and FPTP do not lead to identical results. So that is why we are having a referendum. Duh.

This objection to AV is so blatantly question-begging that it is quite extraordinary that anyone can seriously advance it as an argument. The NO2AV campaign has a TV advertisement involving a horse race. At the end of the race, to everyone’s bemusement, the horse that comes in third is deemed to have won. This is supposed to be an argument against AV.

If I had the resources, I would make a counter-advertisement. It would go something like this. There is a mile-long horse race. As the horses approach 4/5 of a mile, Tory Boy is in the lead, but Labour Lad is storming up from behind and clearly about to overtake. Meanwhile Demon Libby is flagging badly and may not finish.

Suddenly the race stewards run on to the track and stop the race. To general bemusement, Tory Boy is declared the winner, despite the fact that the race was not yet over and Labour Lad clearly had more in the tank for the vital closing stages.

Final slogan: UNDER FIRST PAST THE POST, YOU DON’T HAVE TO BE FIRST PAST THE POST!

2. AV is unfair/undemocratic.

I don’t actually know what the NO2AV campaigners mean here. But I think they again mean that AV yields results that are different from the results of FPTP. The extreme unfairness of relatively large third parties getting a negligible share of the seats under FPTP does not figure in their calculations.

The idea that AV is less democratic than FPTP makes even less sense to me. AV allows people to express their actual political preferences rather than being forced (if they don’t want to waste their vote) to vote tactically.

I suspect that the NO2AV campaigners would rather not specify what they mean by calling AV unfair and undemocratic, since that way their arguments cannot be properly scrutinized. However, it may be that in the back of their minds is another objection that has been made several times, which is the following.

3. Under AV, some people get more votes than others.

The beauty of this objection (from the point of view of its political effectiveness, by which I mean its ability to persuade people who don’t feel like thinking critically) is that it cleverly confuses a true statement with a false statement. It would be ludicrously unfair if some people were given more ballot papers to fill in than others. But that, it hardly needs pointing out, is not what happens. What does happen is that some people’s second (or lower) preferences are taken into account and other people’s are not.

This is presented as an unfair advantage to those whose lower preferences are taken into account. A hypothetical example sometimes given by the NO2AV campaign is of a BNP supporter getting five bites of the cherry whereas decent Conservative and Labour supporters get only one. (The British National Party is our lunatic far-right party. A typical quote from its manifesto: “At current immigration and birth rates, indigenous British people are set to become a minority well within 50 years. This will result in the extinction of the British people, culture, heritage and identity.”)

Is there any significant sense in which AV gives more votes to the BNP? There are various ways of thinking about this question, and none of them is of much comfort to BNP supporters.

Consider first what it means if you get five bites of the cherry. It means that your first-choice party is eliminated, and your second-choice party, and your third-choice party, and your fourth-choice party. Compare that with the poor old voter who gets just one bite of the cherry. Their party is either the party that wins or the party that comes second. In the first case, they obviously do better by far. In the second case, it is not clear: if you vote Labour and Labour come second to the Conservatives, then you might well have preferred the Liberal Democrats or the Greens. But (i) they were behind Labour and (ii) right until the final round your vote was counting for your favourite party rather than for lower and lower choices.

A quick slogan:

GETTING MORE BITES OF THE CHERRY IS A DISADVANTAGE STUPID!

The idea that it is unfair for some people to have their vote counted more often than others is — in so far as it means anything at all — just plain wrong. The NO2AV campaigners are saying that supporters of unpopular parties get more votes. What they actually get is more opportunities to change their vote. Since each change is from a higher preference to a lower preference, changing one’s vote is not something one wants to do. Simple isn’t it?

Here is another way of thinking about this bizarre objection to AV. Let us contrast it with a different system that is manifestly fair. I’ll call it MR for Multiple Rounds. Under this system, everybody votes for just one candidate. If no candidate gets over 50%, then the least popular candidate is eliminated and there is a new round. Again, if no candidate gets over 50%, then the least popular candidate is eliminated and there is a new round. This process continues until a candidate does get over 50%.

This time, everybody gets one vote per round. How does that differ from AV? The answer is that under MR you have more flexibility in how you vote, for two reasons. The first reason is that if you put a party as your first choice in one round, you can put a different party as your first choice in a later round, even if the first party is still in the running. Secondly, you can allow your votes in later rounds to depend on the results of earlier rounds, which increases the opportunities to vote tactically.

Why might you want to change your first preference if the party you voted for is still in the running? I can think of a few reasons. One is that you might want to vote tactically because of something like the scenario I outlined earlier that can occur under AV: you want to eliminate a party so that the party you actually like can pick up votes from the supporters of that party. Another is that you like backing a winner, and you sense that a candidate has “momentum”. The first reason is a legitimate one but an undesirable feature of MR (so it is good that AV lacks it). The second is not, I think, rational in a vote for an MP, though it might be rational if you are voting for a party leader and want a display of unity.

So AV is effectively MR under two restrictions: you are not allowed to change your vote from round to round unless the party you are currently supporting is eliminated; and you are not allowed to know anything about the votes cast in previous rounds except which parties have been eliminated. Given those restrictions, you might as well just list your preferences in advance, and if you do then you’ve got AV.

A quick slogan:

AV IS MULTIPLE-ROUND VOTING MINUS TACTICAL GAME PLAYING.

If you think about AV that way, then you can see easily that no voter has an unfair advantage over any other voter — and supporters of unpopular parties are the worst off.

4. AV is unfair because the least popular party gets its second-choice votes counted first.

Oh dear. There was even an article published in the Guardian that made this completely wrong point. If you buy the equivalence of AV and MR with restrictions, then you have an instant proof that the objection is wrong: under MR with restrictions, the least popular party does not get its second-choice votes counted first and yet the result is precisely the same.

Here is a different argument. Suppose there is a constituency with four candidates, representing Labour, the Conservatives, the Liberal Democrats, and the British National Party. The first preferences are

Labour, A
Conservative, B
Lib Dems, C
BNP, D

where and (let us suppose)

Those lucky BNP supporters now get their second-choice votes counted. Let’s suppose that and that and are the percentages of votes transferred to Labour, the Conservatives and the Lib Dems, respectively. So after the first elimination the position is

Labour, A+E
Conservatives, B+F
Lib Dems, C+G

Suppose now that the Lib Dems are third. Now we have and and the standings are

Labour A+E+H+K
Conservatives B+F+J+L

Let us think carefully what and stand for. is the number (expressed as a percentage of the total number of voters) of Lib Dem voters who transfer to Labour, which means Lib Dems who either put Labour as their second choice or put the BNP as their second choice and Labour as their third choice. is the same thing but with “the Conservatives” replacing “Labour”. is the number of BNP supporters who put the Lib Dems second and Labour third, and is the number of BNP supporters who put the Lib Dems second and the Conservatives third.

To see that this is exactly symmetrical between the BNP and the Lib Dems, let us see how the Conservative vote now breaks down. The votes they have are from

(i) people who put the Conservatives as their first choice,
(ii) people who put the BNP as their first choice and the Conservatives as their second choice,
(iii) people who put the BNP as their first choice, the Lib Dems as their second choice and the Conservatives as their third choice,
(iv) people who put the Lib Dems as their first choice and the Conservatives as their second choice,
(v) people who put the Lib Dems as their first choice, the BNP as their second choice and the Conservatives as their third choice.

Notice that the situation is entirely symmetrical between the BNP and the Lib Dems. The fact that the BNP second preferences are counted first is just a procedural convenience that does not affect the outcome. It does not give the BNP more power than the Lib Dems.

Here is a third, more concise, way of making the point. In the rounds where the BNP supposedly has an advantage over the Liberal Democrats, the BNP has been eliminated. So the BNP has lost and they have to make do with their second choices, while the Lib Dems are still in with a chance and can still have their first choices counted. In which position would you rather be?

5. AV helps the BNP.

If that is the case, then it is odd that the BNP is against AV. But it is also odd that about half the Labour party is against AV, so perhaps the BNP is just being stupid (a possibility that, in the light of other evidence, cannot be discounted).

I have just explained why being eliminated first does not give you any advantage under AV, even over the party that is eliminated second. But perhaps it is nevertheless the case that your average BNP supporter is better off under AV, merely by virtue of being able to express a second preference at all. Under the current system, a BNP supporter has two options that are not completely daft. The first is the obvious one of voting BNP. (When I say that that is not completely daft, I mean that it is not daft if one’s object is to help the BNP. That object itself is of course completely daft.) The second is to buy the wasted-votes argument and choose the most racist party one can find that has a decent chance of being elected. The Conservatives tend to be tougher on immigration than Labour or the Lib Dems, so they will probably be the one to choose.

Under AV, this BNP supporter will no longer have a dilemma: it will be possible to vote BNP first, then UKIP (probably number two in the racism stakes), then Conservative, then Labour, and finally the Lib Dems.

This sounds like a big disadvantage of AV: it gives people a chance to vote BNP without wasting their vote.

Here are two counterarguments. The first is that it is not just BNP supporters who benefit in this way: all voters are freed from the shackles of the wasted-votes argument. If you are a Conservative supporter in a constituency where the Conservatives came third last time, you don’t have to agonize about whether to vote Conservative and risk letting in Labour: you can vote Conservative first and Lib Dem second, for instance. And the vast majority of the country who detest the BNP can express their dislike more forcefully by showing not just that the BNP is not their favourite party but that it is their least favourite party. To argue for FPTP on the grounds that AV helps the BNP by letting them express their preference for the Conservatives over Labour is to suggest that all voters should be punished for the sins of a tiny minority.

Slogan time.

WE SHOULD NOT LET THE BNP DICTATE HOW WE RUN OUR POLITICS.

A related point is this. Under AV the larger parties will know that once the BNP is eliminated, the second choices of BNP voters will count every bit as much as the first preferences of other voters. Since the BNP will, with probability 1, be eliminated, it would appear that there is now more reason to court the BNP vote than there was under FPTP. So AV could lead to parties adopting more unpleasant racist policies than FPTP does.

This argument sounds plausible but doesn’t stand up to scrutiny. First of all, it is simply untrue to say that FPTP gives a party no reason to court the racist vote. After all, under FPTP those racist voters are still out there, and they still might decide not to vote BNP (either because it is a wasted vote, or because they are embarrassed to vote for a party that is explicitly racist rather than dressing up their racism as concern for ordinary hard-working British families). And we do see, at every election under FPTP, parties talking tough on immigration in an unpleasant way — or being punished for not doing so.

One further point is that in most constituencies the BNP are a smaller party than the Lib Dems or the Greens or UKIP. So they will be contributing far fewer of those precious second-choice votes. Therefore, courting the BNP (which in any case is politically hard to do explicitly) is not a sensible strategy, since for each BNP supporter that you attract, there will probably be ten Lib Dems that you alienate.

6. AV is expensive.

Here is how the NO2AV campaign breaks down the cost of AV.

The referendum itself: £91 million.
Electronic vote counting machines: £130 million.
Explaining AV to voters: £26 million.

This adds up to £250 million (or rather, they say it does — actually it adds up to £247 million). We can take that straight down to £156 million with the help of the following simple observation:

THE REFERENDUM IS HAPPENING ANYWAY! DUH.

Just to make that point clear, imagine that a group of friends want to go to the cinema. Some people want to see Avatar, which is the film showing in a single-screen cinema just round the corner. But others are not so sure, so they suggest catching a bus to a large multiplex cinema where there are three films that look promising, one of which is Avatar. This plan is agreed upon, and when they are at the multiplex a discussion ensues about which film to watch. The Avatar supporters argue that the cost of the bus fare is an argument against choosing another film, since it would have been possible to watch Avatar without a bus journey. The rest of the group laugh in their faces.

£156 million is still a lot of money. Luckily we can take it down further: it is a straightforward lie that AV requires electronic vote-counting machines. That gets us down to £26 million.

Does it take that much money to explain AV to voters? If so, could I please please be the one who is paid £26 million to say “Put the candidates in order of preference until you don’t care any more”? Obviously, to explain how these preferences will affect the outcome is more difficult, but it is also not necessary, since following the simple instruction to put the candidates in order of preference is the right and rational thing to do (given that there will tend not to be enough information to make tactical voting a practical possibility).

But for those who think it’s necessary, here’s another slogan.

AV IS EXPLAINED ON THE INTERNET.

7. AV is complicated/obscure/perverse.

I’ve just dealt with this objection. My basic answer to it is, “No it isn’t.”

Let me repeat how to vote under AV:

PUT THE CANDIDATES IN ORDER OF PREFERENCE UNTIL YOU DON’T CARE ANY MORE.

That is not complicated, obscure or perverse.

In case you want to know how your vote will count:

THERE ARE MULTIPLE ROUNDS. AS SOON AS A CANDIDATE HAS AN ABSOLUTE MAJORITY THAT CANDIDATE WINS. AFTER EACH ROUND THE LEAST POPULAR CANDIDATE IS ELIMINATED. IN EACH ROUND YOUR VOTE GOES TO YOUR TOP PREFERENCE AMONGST THE CANDIDATES STILL IN PLAY.

That takes a bit longer to explain, but it is still pretty simple. Simple enough, for example, for leadership elections in the main political parties. And if, despite that, you don’t understand it, it doesn’t matter, since it is still in your interests to put the candidates in order of preference. (An analogy: your computer is very useful to you even if you don’t understand in detail how it works. And if you did understand how it worked, it wouldn’t affect how you surf the internet, send emails, etc.)

8. AV leads to the election of mediocre candidates.

The argument here is that under AV you often end up electing the candidate who is least disliked rather than the candidate who is most liked. This is supposedly a recipe for mediocrity.

Let us set aside the obvious point that mediocre people do not seem to be blocked from the House of Commons by FPTP. It might still be the case that more mediocre people would get in under AV. But would they?

Let us consider a typical case where AV and FPTP lead to different results. Suppose that there is a constituency with a solid 40% support for the Conservatives and a split of the left vote between Labour and the Liberal Democrats (with Labour getting 35% and the Lib Dems 25%, say). If the Lib Dems tend to prefer Labour to the Conservatives, then Labour will probably win this seat under AV, while the Conservatives would win it under FPTP.

The question we are now considering is this: would the Labour candidate be likely to be more mediocre than the Conservative candidate? If you are sufficiently right wing, then perhaps you will think that the answer is yes merely because the Labour candidate is a Labour candidate. But in that case you are not thinking about the merits of AV in the abstract but merely about whether it helps your party. And I’ve already made the point that AV probably wouldn’t help the Conservatives, which is why they are campaigning vigorously against it.

Does it favour mediocre candidates (or parties) if second preferences have a significant effect on the vote? Let us try to imagine how AV would affect an election campaign in the hypothetical constituency just discussed. Under FPTP the Conservatives could afford to reach out to their core support and be pretty confident of winning the seat. But under AV they would know that that was not enough: they would need to attract at least two fifths of the Lib Dem voters. Similarly, Labour would know that they needed to attract at least three fifths of Lib Dem voters.

Since the Lib Dems are somewhere in the centre, it would probably be a bad idea to push for extreme right or extreme left policies. So in this constituency, the need for the two largest parties to attract the second preferences of Lib Dems would act as a curb on extremism. I’m not talking here about BNP-style extremism but just the sort of extremism-lite that you get on the right of the Conservative party and the left of the Labour party. Does that mean that candidates would become bland and mediocre? Well, it’s true that some of our more colourful politicians, people like Enoch Powell, Tony Benn, Dennis Skinner, Norman Tebbit, have been on the extreme wings of their parties. But some pretty notable politicians have come from the centre too, such as Kenneth Clarke, Tony Blair, David Owen, and many more. And AV isn’t going to get rid of those with extreme views since there will still be safe seats where they do not need to attract Lib Dems — it’s just that there won’t be as many of them.

To sum this up in a slogan:

FPTP HELPS EXTREMISTS.

In general, suppose we have a constituency where one candidate is liked by 40% of voters and loathed by 60%, while another candidate is liked by 35% of voters and quite liked by a further 20% of voters. Which candidate best represents the views of the constituents? There is a strong case for saying that it is the second. Certainly, if you were to ask the constituents which they preferred just out of the leading two candidates they would say the second.

In fact, I can feel a slogan coming on.

UNDER FPTP A CANDIDATE IS OFTEN ELECTED EVEN THOUGH MOST PEOPLE PREFER A DIFFERENT CANDIDATE.

9. AV leads to more coalitions and hung parliaments.

In the UK there have been a number of coalitions and hung parliaments under FPTP, as well as periods where one party has been dominant. Would there have been more under AV? The evidence from other countries is inconclusive. I suspect that there might well have been a hung parliament in 1983 under AV, since the split on the left would no longer have given Margaret Thatcher her huge majority. But in general it is far from clear that AV has this effect: indeed, some have argued that AV leads to swings that are even larger than those under FPTP. As an example, consider the 1997 election. There the Conservatives were extremely unpopular but held on to 165 seats with the help of FPTP. I don’t know the figures, but probably they had outright majorities in many of those seats. However, there will also have been several seats where they won with less than 50% of the vote, and it seems likely that in many of those they would have lost out under AV, since Labour and Liberal Democrat voters would have been unlikely to put the Conservatives as their second choice.

There is also the question of whether, if AV leads to more coalitions (which is debatable), one should regard this as an advantage or a disadvantage. Such is the unpopularity of the present coalition that many people have now decided that they don’t like coalitions at all. But the alternative to coalitions is that representatives of a minority of the country have unfettered power to do what they like. It is not obviously better.

10. AV benefits the Lib Dems and nobody else.

This is false. It benefits any party that is small but large enough to have a serious chance of getting seats. (I am not including the Scottish and Welsh Nationalists or the parties in Northern Ireland, because I count those as large parties in the areas that they represent.) The Greens are an example, and perhaps UKIP will be another. The Lib Dems are so unpopular now that at least for the time being it is unlikely that any voting system will help them. And if it ever does, we will be talking about an overhauled and rehabilitated Lib Dem party. And AV would in the past have helped Labour on a number of occasions, because they could have picked up Lib Dem (or Lib, or Alliance) second-choice votes.

11. Voting AV will give a big boost to Nick Clegg.

Yes, if AV wins then it will put a big creepy smile on Nick Clegg’s face. So a slogan is needed again.

THIS REFERENDUM HAS NOTHING TO DO WITH NICK CLEGG!

If you are planning to vote no to spite Nick Clegg, you should bear in mind the following points.

(i) The chance to change the voting system comes around very rarely because under FPTP the parties in power tend to have no interest in changing it, and hung parliaments, which give the Lib Dems a chance to negotiate, come around about once a generation.

(ii) You may hate the Liberal Democrats now, but think back to when you hated other parties. If you vote no to AV, then today’s Liberal Democrats will be very disappointed. But so will the Liberal Democrats of fifteen years time, who will be a completely different bunch of people, chastened by the experience of this coalition and certain to make keeping their pre-election promises their absolute top priority. Or perhaps they will have been annihilated completely and a different party, such as the Greens, will occupy the ground that they have traditionally occupied.

DON’T TAKE A LONG-TERM DECISION FOR SHORT-TERM REASONS!

(iii) Why do you hate Nick Clegg so much? Presumably because you hate the Conservatives, and Nick Clegg has allowed the Conservatives to govern with a minority. So it’s really the Conservatives you don’t want. And who has most to gain from retaining FPTP? The Conservatives.

Let me summarize:

NICK CLEGG IS TOAST ALREADY. VOTE YES TO SPITE DAVID CAMERON AND GEORGE OSBORNE!

Let me summarize again:

DON’T BITE OFF YOUR NOSE TO SPITE YOUR FACE!

12. FPTP makes it easier to get rid of unpopular governments.

This is a clever argument that was put forward a couple of days ago by David Cameron. Once again, I mean clever from the political point of view: it sounds persuasive despite being wrong. In fact, it is better still, since it suggests a general technique that all politicians can use. If your party stands for X and Y is an adverse consequence of X, defend X on the grounds that not-Y is a consequence of X. For example, if, as all economists will tell you, spending cuts lead to increased unemployment, go out and say that you are making spending cuts in order to create jobs in the future.

The idea that FPTP has made it easy to get rid of unpopular governments is one that you can hold only if you wilfully ignore history. Mrs Thatcher’s government was deeply unpopular but proved to be extremely hard to dislodge. Blair was loathed after the Iraq war but went on to win another election, and his successor, Gordon Brown, though defeated in 2010, came close to having enough seats to form a viable coalition with the Liberal Democrats. Under AV it would have been much easier to get rid of Mrs Thatcher, for reasons I have already discussed: she would not have been able to exploit the split on the left. However, it is also worth saying that part of the reason that it was so hard to get rid of Thatcher and later Blair was that Labour in the 1980s and the Conservatives in the 2000s were going through periods of internal conflict and were not obviously electable. If you want to get rid of an unpopular government, it helps to have a viable opposition.

Perhaps it’s worth having a look at the results of another election, the one that took place in 2005, not long after Blair’s decision to invade Iraq. A large number of people were furious with him for misleading them about weapons of mass destruction, with the result that his share of the vote dropped substantially. The results were

Labour, 35.2% of the vote, 355 seats

Conservatives, 32.4% of the vote, 198 seats

Liberal Democrats, 22.0% of the vote, 62 seats.

With barely over a third of the votes, Blair still had a comfortable majority in the House of Commons. It is difficult to reconcile this with the idea that FPTP makes it easy to get rid of unpopular governments. Under AV, the most likely result would (I am guessing) have been a hung parliament with Labour the largest single party. There is no chance that Charles Kennedy would have formed a coalition with the Conservatives, so we would probably not have got rid of Blair. But he would have been properly punished for Iraq by being forced to cooperate with the Lib Dems, who were the one strongly anti-Iraq-war party.

Here’s what I think David Cameron might have meant by his statement. He thinks that AV leads to more coalitions, so he has a picture of an unpopular government managing to survive by forming a coalition with a smaller party. But how much of a danger is that? Nick Clegg was desperate, after the last election, not to be seen to be playing that role for Gordon Brown.

Another slogan:

AV MAKES IT EASIER TO GET RID OF UNPOPULAR GOVERNMENTS!

To explain why in the abstract: if a government is unpopular, under AV you can vote for anything-but-the-status-quo. The party in power cannot rely on its core support. FPTP allows unpopular governments to cling on with the support of a minority of voters.

13. FPTP gives equal votes to everybody.

I have already explained why it is nonsense to suppose that AV gives “more” votes to supporters of unsuccessful parties. In another post I explained in detail why FPTP does not give equal votes to everybody. To put that slightly better, although everyone gets one vote, some votes count far more than others: if you are in a marginal constituency, you have a far bigger chance of influencing the result of the election, and if you are in a safe seat then the politicians can afford to ignore you (whichever side they are on). Under AV this would still be a problem, but there would be fewer safe seats so the problem would be reduced.

If you want this point in slogan form, here it is:

VOTE YES TO AV UNLESS YOU LIVE IN BASILDON!

14. FPTP has served us well for over a century.

There are variants of this, such as that FPTP is a traditionally British institution, part of how we do things here, etc. FPTP has given us long periods of stable Conservative or Labour rule, supported by a minority of voters. It has also given us periods of instability, such as in the 1970s, the mid-1990s, and perhaps — we shall see — the 2010s. It has been manifestly unfair on a number of occasions. It has provided us with a strange cycle where, to oversimplify grotesquely, Labour spends too much of our money, which is lovely for a while but eventually gets the economy into a mess, then the Conservatives promise to sort out the mess but do so in a brutal way without much regard for the social consequences. (Because economic decisions tend to have effects only after quite a long time lag, we also have the phenomenon that a party’s reputation for economic competence depends a lot on the economic consequences of decisions made by its predecessors.)

Is FPTP serving us well? I don’t think so. If there were more of a need to court the centre (as there would be under AV, since Lib Dem second-choice votes would be more important), then perhaps, just perhaps, the boom/bust cycle could be stabilized. I don’t want to say that that would be an inevitable result of AV, since short-termism is always going to be very tempting for politicians, but with FPTP we can be pretty sure of getting more of the same (unless the current economic crisis is so severe that recovering from it takes decades rather than years).

If you are voting no because you regard FPTP as a Great British Tradition, then you might be interested in this article in the Independent.

Conclusion.

I realize that I have largely failed in my aim to adopt a neutral tone. However, that is because most of the arguments put forward by opponents to AV have been clearly wrong, in several cases so wrong that one can actually prove mathematically that they are wrong. I find it very dispiriting to live in a country where it can benefit a politician to use a provably incorrect argument. I have complained about this in other posts on this blog: a short, succinct, punchy statement that is wrong trumps a longer and ever so slightly complicated explanation of why it is wrong. That is why I have interspersed my longer explanations, which, if I were to make them in parliament would probably be met with derisory who-is-this-guy laughter, with shorter slogans. Perhaps you can think of some better ones. In my wildest dreams, I wonder whether some people might consider tweeting them. Could “WTF IS THE POST?” go viral? Well, probably not, but if it did then it would change more minds than dull and not obviously correct pro-AV slogans such as “Make your MP work harder.”

I don’t for a moment suppose that the power of incorrect arguments is a uniquely British phenomenon. I thank my lucky stars that we don’t (yet) have Fox News to contend with and that we don’t have to waste time explaining that Barack Hussein Obama is not a Muslim or that free universal healthcare in Britain doesn’t make us communists. (Unfortunately in Britain we do have to waste time, and probably trillions of pounds of our grandchildren’s money, explaining that there is an overwhelming consensus amongst people who know what they are talking about that man-made global warming is a serious problem. But the opposition to this view is more virulent in the USA.)

OK, rant over. I’ve wasted hours of precious work time on this, but I think it is a lost cause and need to get back to some mathematics.