AV vs FPTP — a supplementary post

In this post (the first past the previous one) I want to consider some further arguments, most of which have arisen from the interesting comments I have received. You’ll have to be pretty interested in voting theory to have waded through my earlier post and still want more, but NO2AVers who are looking for ammunition may find some here (as long as they are selective about which arguments they go for).

I have also written a shorter post on AV versus FPTP. I plan to post it at the weekend (when people are less distracted by the Royal Wedding, though perhaps the audience for that is rather different from the audience for this).

Tactical voting and gestural voting.

My wife pointed out to me that it is quite easy to imagine circumstances under which a voter in an AV election might decide not to put the parties in their true order of preference.

Take, for instance, a disgruntled Labour supporter at the last election who felt that immigration was one of the most important issues and that it was not getting enough attention. Under AV, such a voter might decide to put BNP first and Labour second, even though they would be horrified if the BNP actually won the seat and definitely preferred Labour. Why would they do this? They might want to make a point by inflating the support for the BNP in full knowledge that the BNP had no chance; in practice their vote would be for Labour (once the BNP was eliminated). This kind of use of a vote is possible under FPTP too. For instance, if that same disgruntled Labour supporter is in a safe Labour seat (or indeed, a safe seat of any kind) then they would be able to vote BNP in full confidence of not affecting the outcome. But AV makes it less risky in more marginal constituencies (the risk being that the party you actually support might not make it without your help).

So does that mean that AV encourages tactical voting after all? To give a coherent answer to this question it is necessary to distinguish between two kinds of voting that might deserve the name “tactical”. One, the kind you get under FPTP, is where you vote for a party that is not your favourite because you judge that your favourite party has no chance. In this case, you vote tactically in order to affect the outcome. The other, which you get under both systems, is what I would prefer to call “gestural voting”, where your reason for not voting according to your true preferences is not that you want to affect the outcome of the election but just that you want to send a message. It seems to me that gestural voting is less of a problem, partly because it exists in both systems and partly because the voter who decides to vote gesturally is doing what he or she wants. A Tory supporter who votes UKIP to send a message about the EU comes away satisfied from the polling booth. A Lib Dem or Green supporter who reluctantly votes Labour because the Lib Dems and Greens have no chance in that particular constituency comes away feeling significantly disenfranchised.

Another kind of gestural voting is to put your favourite party first even when you know perfectly well that they have no chance of even being second because you hope that if their share of the vote is high enough then in subsequent elections more people may consider voting for them. Under FPTP the price you pay for doing this is having no influence on the outcome of this election. Under AV you can make that gesture without wasting your vote, though in theory the gesture shouldn’t make much difference because it is no longer necessary for voters to worry about how other people will vote when they are deciding how to cast theirs.

More about tactical voting.

It was pointed out to me in this comment of Gil Kalai on my previous post (and also another comment that I can no longer find) that there was another situation under AV where tactical voting would make sense.

As with the first situation it involves the top party (in terms of first preferences) not having an absolute majority and the next two parties being close. For the sake of example, and because this is a realistic example, let’s suppose that opinion polls suggest that the situation in the given constituency is this.

Labour 40%
Conservative 28%
Lib Dems 28%
Others 4%

Suppose also that further polling has revealed that Lib Dems mostly prefer Labour to the Conservatives and that Conservatives overwhelmingly prefer Lib Dems to Labour.

Suppose now that you support the Conservatives. What should you do? If the Conservatives beat the Lib Dems in the first round, then the Lib Dem second preferences will come into play and hand the victory to Labour. If the Lib Dems beat the Conservatives in the first round then the Conservatives will be eliminated and their second preferences will hand victory to the Lib Dems. So one thing you can be sure of is that the Conservatives are not going to win the seat. But if that is the case, then you should vote tactically: if you prefer Labour to the Lib Dems then you should vote Conservative, and if you prefer the Lib Dems to Labour then you should vote Lib Dem. Note that in the second case something similar (but not quite identical) to a wasted-vote argument applies: if you are a Conservative supporter then your party has no chance, so if you prefer Lib Dems to Labour then you should put the Lib Dems as your first preference even though they are actually your second preference.

This, it strikes me, is a serious problem with AV if it is used for the election of just one person who will take power. For example, suppose it were discovered after a London mayoral election that if the Conservatives had done slightly less well at attracting votes from the Lib Dems then they would have won. The result of the election would seem pretty arbitrary, and the Conservatives might well be very cross about it. It’s just about possible to argue that the situations where this kind of thing can happen are situations where, taking account of all the preferences of the voters, it is not actually clear who should win, so the apparent injustice is not such a big problem. But many would not see it that way, and the perception of fairness is pretty important.

However, a general election is not the election of just one person. It is 650 separate elections to elect 650 people (soon to be reduced to 600). Moreover, although local MPs and candidates campaign in their constituencies, these campaigns are far less influential than the national campaigns, with their TV ads, billboards, debates between party leaders, newspaper columns, etc. The peculiarities of a few constituencies are not going to result in its being better to campaign less vigorously at a national level. Moreover, if we think of them as a random effect (which is not unreasonable because they tend to happen when the second and third parties in a constituency are neck and neck) then this will probably balance itself out. (I haven’t checked that statement, so cannot rule out that it might favour some kinds of parties, but even if it does, I would expect the effect to be very small.)

Some more serious arguments against AV

The arguments of the no campaign have been terrible. (I’m not saying that the arguments of the yes campaign have been all that great, but there seems to be an important difference: the false statements of the yes campaign tend to be approximations of true statements, whereas the false statements of the no campaign tend to be straightforwardly false.) However, there are better arguments out there and in the interests of balance I’d like to say where they can be found.

First up is Charles Roddie, a Postdoctoral fellow at Nuffield College, Oxford. His basic reasons for voting no are that he doesn’t like hung parliaments and that he thinks that the left is wrong about economics (and that AV would favour the left). Of course, many will disagree with the second statement, but at least it’s an actual argument and is presented in an honest way.

A considerably better than average presentation of the NO2AV case can be found in the following series of posts by Robert Colvile [apologies for previously misspelling this] of the Daily Telegraph. It’s clear that his mind is made up and that he is not interested in good arguments for AV, despite his plea for a grown-up debate. Most of his arguments are fairly weak, or attack weak arguments from the yes campaign, or are arguments that I have dealt with already. But one of his points was quite interesting and deserves some attention. If you look at his reason number 5 to vote against AV, it is that AV is not in fact fairer (by which he means more proportional) than FPTP.

His arguments are these. First, AV makes things harder for small parties to get a foothold, because you need to win the final round, whereas under FPTP the occasional fluke (such as the almost four-way marginal in Brighton that let in Caroline Lucas for the Greens — she got 16,238 votes, Labour 14,986, the Tories 12,275 and the Lib Dems 7,159, which meant that her share of the vote as 31.3%) can let them win the occasional seat. My feeling is that it is so hard for small parties like the Greens or UKIP under FPTP that if it is even harder under AV that will in practice make hardly any difference at all.

His second argument was more serious. He concedes (as he could hardly fail to do) that AV would be fairer to the Lib Dems. But he points to some of the large victories of Thatcher and Blair, and claims that their majorities would have been even larger under AV. I’ll discuss just his main example, the election of Blair in 1997. Because by that time everyone was thoroughly sick of John Major’s government, it seems likely that almost everyone who put Labour or Lib Dem first would have put the other second. If we make that assumption, and if we also assume that people’s first preferences would have been the same under AV, then apparently Labour would have won an even larger majority, with 445 seats, the Lib Dems would have come second with 115 seats, and the Conservatives would have been left with just 70 seats. Since the Conservatives came second in the popular vote with 31% and the Lib Dems got a little over half that, this would have been even more unfair than FPTP has been for the Lib Dems. Incidentally, the source for these interesting figures is this page from the BBC website.

While there is undoubtedly a case to answer here, there are also some further considerations to make that Robert Colvile doesn’t mention. First, there is the assumption that people’s first preferences under AV would have been the same as they were under FPTP. Since the whole point of AV is to allow people to express their true first preference and not worry about the wasted-votes argument, this is a questionable assumption, to say the least. It is likely that under AV the Lib Dems would have received more first-preference votes, so the relative unfairness between them and the Tories would not have been as bad.

But the unfairness could well have existed, which brings me to my second point, which has only recently occurred to me. I had always thought (without ever really thinking about it seriously) that PR was obviously fair, and that its main drawback was the loss of a simple constituency system. But it now occurs to me that this can be questioned. Suppose there were a PR election in which the Conservatives, Labour and the Lib Dems all got roughly a third of the votes. It sounds obvious that they should all get roughly a third of the seats. But what if all Lib Dem voters preferred Labour to the Conservatives, and all Labour voters preferred the Lib Dems to the Conservatives? (Suppose also that the Conservatives were fairly indifferent between Labour and the Lib Dems.) There would be a clear sense in which the Conservatives were less popular than the other two parties, and this would not be reflected in the outcome.

In one sense it probably would be reflected in the outcome, since probably Labour and the Lib Dems would probably end up forming a coalition, but the point I’m making is that the seat count under PR takes no account of people’s second preferences (because they don’t express their second preferences). So the fact that an AV outcome is even less close to a PR outcome than an FPTP outcome is not quite the knock-down argument that it seems. Going back to the 1997 case, one could argue that the Lib Dems doing well is a result of their being the second choice of several voters, whereas the Conservatives are the second choice of very few voters. And perhaps that is not wholly wrong.

I’m not giving these counterarguments as a way of saying that Robert Colvile’s point is worthless: it’s just worth less than he thinks. One final remark: in all the other elections discussed on that page from the BBC website, the differences between the actual results and the hypothetical results under AV are much smaller.

I’d also like to make the general comment that in the previous post I speculated about what the results of certain general elections might have been like under AV. While I am somewhat sceptical of any attempt to guess this, after reading what others have written about it I am also pretty sceptical of my own hunches and I think some of them were wrong.

Perhaps the strongest attack on AV that has come my way since I wrote on the topic has come from Warren B. Smith. Rather than discuss his arguments and my response to them, I refer you to his long comment, which has many links. (He uses the American name IRV for AV. It stands for instant-runoff voting.) He has an agenda: he campaigns for range voting (where you give each candidate a score out of, say, 10). I don’t agree with everything he says, as my response makes clear, but neither am I sure I’m right, and he is certainly making proper arguments (much better than Robert Colville’s, for instance). The most disturbing of these is his assertion that in the long run AV leads to a two-party system. If that’s the case, then rather surprisingly almost everyone should switch sides: if you don’t like coalitions, you should go for AV, whereas if you want to help the Lib Dems and other smaller parties, you should vote to retain FPTP. I’m not convinced by this conclusion of his, but I’m interested that someone who has clearly done a lot of research into voting systems could think it.

Incidentally, if you are a no person and are looking for support from Warren Smith, you may be able to cherry pick some of his arguments, but you should know that he thinks that AV is slightly better than FPTP. His hostility to AV comes from the fact that he thinks range voting is much better than both of them. And in this he may be right.

Chris P’s reversal of perspective.

I picked up an idea I rather like from a comment by ChrisP.

Consider the following multiround system, where the object is to eliminate all but one candidate. To vote, you choose the candidate you like best and put crosses by all the others. In each round, you see who has the most votes (votes being bad for the candidate) and eliminate them. However, unlike with AV, you also remove all ballot papers of people who disagreed with that elimination (that is, people who did not put a cross by the candidate who has just been eliminated). This process continues until there is just one candidate left, and that candidate is declared the winner.

Under this system, you get a vote in each round up to the point where the candidate you favour is eliminated. So the more popular your candidate, the more “bites of the cherry” you get. One might even say that you get more votes if you vote for a popular candidate.

But this system is just FPTP in disguise! If you reverse everything and put a cross by the candidate that you didn’t put a cross by in the above system, then at each stage you eliminate the candidate with the fewest votes, and the supporters of that candidate have no more say in the contest. So obviously the candidate with the most votes wins.

The point is subtle enough that I expect it to be misunderstood, so let me try to spell it out. The NO2AV campaigners often say that it is unfair for some people to get more bites of the cherry than others. (Sometimes, they even say that some people get more votes than others.) But if you change your perspective slightly and think of FPTP as a mechanism for eliminating candidates, then under that system it is voters for the more popular parties who get more bites of the cherry.

I’m not saying that FPTP really is unfair for this reason. I’m just saying that the whole bites-of-cherry criticism is suspect, whether it is applied to AV or to FPTP: under either system, all voters play by the same rules, and voters for more popular parties are more likely to end up with results that they like.

Do you need 50% under AV?

This is something the no people get very steamed up about. So let me steam them up a bit more. Actually, under AV, a candidate needs the unanimous support of the electorate.

How can that be true, you ask. Well, let me explain once again how AV works.

Each voter puts the candidates in order of preference (until they no longer wish to express a preference). In each round, the candidate with fewest votes is eliminated. In each round, your vote goes to the candidate still in play that you have ranked highest. This continues until one candidate has all the votes.

Well, that’s not the normal explanation of AV, but if you think about it you’ll see that it gives precisely the same result. It’s just that when you get down to two candidates, you eliminate one and then do an unnecessary further round with just that one candidate. The point is that this is another change of perspective, and it shows just how wary one should be of drawing conclusions that depend on a particular description of a system rather than on the system itself.

Now if you agree that it’s ridiculous to say that AV leads to candidates with the unanimous backing of the electorate, you’ll have to agree that it is not right to say that AV leads to candidates with the backing of 50% of the electorate. True, you have to get is 50% in some round, but that means 50% out of those who can still be bothered to express a preference. But what is really going on is that you stop the contest when one candidate provably cannot be overtaken.

So is this objection of the no campaign correct? Well, part of it is a piece of hair-splitting. In practice, most voters will express preferences between the two front-running candidates. (If they don’t, then they are wasting their vote.) So in practice, most successful candidates will get over 50% of the vote, just as the yes campaign claim. And even if they don’t, they’ll probably get pretty close.

But there is another objection to this claim, which is that much of that 50% may be made up of second and third preference votes. A successful candidate who squeezes in after four rounds cannot reasonably claim to have the full support of 50% of the electorate. Grudging support might be a more accurate description of it.

Nevertheless, however you look at it, under AV more candidates would have to pay more attention to voters from other parties. This is the main point; the 50% issue is not the main point.

And finally.

If you want to know what voting experts think, have a look at this. (Thanks to Gil Kalai for drawing my attention to this.)

10 Responses to “AV vs FPTP — a supplementary post”

  1. Porphyry Says:

    A very interesting couple of posts on this vexed topic – great public service and much food for thought! Although I’m finding David Deutsch’s arguments pretty persuasive at the moment: http://www.youtube.com/watch?v=c0pZ9LTZW1g
    That said, if Smith’s arguments – that AV tends towards a strong two party system – are applicable to the British political landscape and will lead, inevitably, to the same effects, then, as you say, almost everyone – Deutsch included – will need to swop sides.

    On the issue of gestural voting and AV, one problematic consequence of the increase of such voting under AV for voters would emerge (or, rather, emerge on a much larger scale) from the state funding of political parties. If we maintain the system of Shore money, then grim extremists like the BNP might benefit from the gestural voting of your hypothetical Labour voter in a way that could horrify said voter – turning a gestural vote into an active building block for further BNP campaigns. That ‘symbolic’ first preference would translate into a cash transfer to the party. Shore money may be tied to requirements, as now, that a party receive at least 150000 votes and/or have two MPs elected, but it would certainly not be impossible for extremists of this sort to reach those requirements under AV (e.g. Pauline Hanson). It seems unlikely, at any rate, that we would abandon Shore money. Incidentally, whether such funding is extended or not to encompass all preferences expressed by every voter is intriguing: should all lower preferences also bring with them funding to their respective preferred parties, as well as the first preference? If, under AV, the value of a vote for electoral purposes is not diminished by repeated elimination of higher preferences and the expression of a lower preference in the final, decisive round, then one might make, analogously, a case that all preferences expressed are to be treated as being of equal worth with regards to party funding (although that would be a very difficult case to make in these times of austerity).

  2. Gil Says:

    Suppose that you have a constituency with a firm control of conservatives over many elections. Roughly, the support in this consituency is 60% conservatives 40% labour. A new liberal democrate candidate run and promise to finally make a difference and get 30%. This does not mean that in an election based on popular support 30% of this constituency voters will vote for LD. The 30% support reflects the specific political situation in this constituency.

    It is true that the current system gives much less parliament representation to the third largest party compared to an election based on popular support. But there are also several factors in the current system that inflate the third-largest-party’s popular support as seen from the election’s outcome compared to the popular support it would get in an election which is based on popular supprt to start with.

  3. Colin Says:

    “Do you need 50% under AV?” Yours is propbably the best eplainaition I have seen concerning this misleading statement by proponenets and reporters alike. “Majority Winners!” they exclaim. But ask anyone on the street what a majorty winner is and the beleive its >50% support of those that sjhowed up at the polls, which is correct. Majoroty winners is not “a majority of those ballots that have continued to the last round” And as you point out, using AV’s logic, you could go further and have unanimous winners using the same system.definition.

    This is think is the most egregious ply on AV’s part (and reporters) either by naiveté, or outright misleading the public.

    You see, al around the world, AV has typically replaced a Majority system like top-two-runoffs rather than a plurality system like the UK.

    Examples in the US are ripe with instances where candidates get 25-45% support, though AV supports claimed AV would provide majority winners!

    AV is just plurality with lipstick.

    Here’s results from many AV elections (called IRV in the US)

    • Tom Says:

      This all depends on whether you consider “don’t care” a valid response. If you do, then people who didn’t fill their ballot card to the maximum level (or at all) are still having their voice heard; they are just saying “I no longer wish to influence the outcome”.

      If you don’t, then you have to start worrying about voter turnout…perhaps that’s why Australia enforces both voting and the listing of every candidate.

  4. polleetickle Says:

    [Under AV … you stop the contest when one candidate provably cannot be overtaken.]

    If a voting system proposed to replace an existing system regarded by some as ‘less than perfect’, is found to be less than perfet itself, then British Electoral Academics and Pro-AV contributors need their collective rainbow coloured heads banging together!

    Instead of change for the sake of it, UK must look toward *evolving* a democratically proven system and instead invest in Democracy Version 2.0 – how about Multi-FPTP?

    • gowers Says:

      It wasn’t British Electoral Academics who decided that the referendum would be between FPTP and AV.

      But if you can somehow get multi-FPTP on to the ballot paper then let me know — then I’d look into it. I don’t know what it is, but it has to be an improvement on FPTP.

  5. 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) […]

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

    […] has a very good essay, taking a slightly mathematically-oriented look at AV vs. FPTP. His supplementary post deals with a few more […]

  7. RodCrosby Says:

    Tactical voting and gestural voting.
    Tactical voting is defined as “misrepresenting one’s preference(s) to achieve a better outcome. So gestural voting is not tactical voting.

    More about tactical voting.
    Taken to its logical conclusion, both Labour and Tory candidates and their voters should “aim to come third”, which is just ludicrous. No opinion poll in the situation you describe will have the accuracy to enable voters [if they so wished] to employ this Pythonesque form of tactical voting. In your example, the true position could easily be Lab 37, Con 31, LD 25. The more rational behaviour for a Con candidate in those circumstances would be to to continue to fish for as many first and second preferences as possible, surely, rather than “aim to come third.” Con voters reversing their preferences and putting the LibDem first, in an election the Con might have otherwise won, isn’t tactical voting – it’s kamikaze voting!

    Some more serious arguments against AV
    I’m glad someone else has noted the potential “paradox” inherent in this referendum, whatever the outcome. I wrote an article on politicalbetting recently, going into it more fully.
    [the reactionary trolls there are so amusing, arent they?]

    Chris P’s reversal of perspective.
    sounds like the [multiple round verson of the] Coombs method, which although superficially similar to AV, is a bit inferior, imho. Don’t get the “eliminate the ballots of those who disagree” bit though. Are sure sure there would be any ballots left to count? [!] What’s the point if it’s done in multiple rounds and everyone, presumably, gets the chance to vote again?

    Do you need 50% under AV?
    Yes, most certainly, whichever way you look at it. Either one candidate gets 50%+ of the countable votes [is there any other kind of “vote”?] in the decisive round, or those who have neglected to preference either of the final two candidates can still have their preferences implied, and added to the totals. [this is a preferential electoral system, and a blank preference is still a statement by the elector, unlike an unrecorded preference under FPTP]

  8. Zaid Siddiqui Says:

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