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Musing on Ben Parker's blog post, I came up with an interesting… - Sally's Journal
April 27th, 2011
04:55 pm

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Musing on Ben Parker's blog post, I came up with an interesting thought experiment about the AV/FPTP debate.

Parallel run the next set of elections, letting people vote twice, once under AV and once under FPTP. Announce the results under AV, and the results under FPTP. Then in every constituency where the outcome was different, let everyone vote for whether or not they wanted the candidate elected under FPTP, or the candidate elected under AV, in a straight fight between the two candidates.

I think, trivially,[1] that the majority would vote for the candidate elected under AV over the candidate elected under FPTP when these were different, because that's what AV does better at finding. Which suggests to me AV is a better system for finding the people we want to represent us.

[Not to mention that it's better for increasing information on voter preferences, avoiding tactical voting, etc etc etc. Let me encourage you all once again to read Prof Gowers' fabulous article on AV]

[1] assuming conservation of voters - if you suddenly got lots of people turning up to vote the second time who were too apathetic to vote the first time then things might jump around a bit.

(36 comments | Leave a comment)

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From:arnhem
Date:April 27th, 2011 04:02 pm (UTC)
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Except that FPTP supporters might vote for the FPTP winner even if it weren't otherwise their preferred choice, on the basis that otherwise the result would be used as evidence for the case for AV. 8-)
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From:atreic
Date:April 27th, 2011 04:03 pm (UTC)
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Thus adding weight to the argument that tactical voting is bad, mmmkay, so AV is better than FPTP ;-)
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From:arnhem
Date:April 27th, 2011 04:04 pm (UTC)
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No, it just suggests that tactical behaviour is very difficult to get away from.
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From:atreic
Date:April 27th, 2011 04:06 pm (UTC)
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You cynic :-p

It's impossible to stop people doing lots of things, but that doesn't mean we don't as a society strive to reduce bad things where possible.

*hugs*
From:yrieithydd
Date:April 27th, 2011 05:24 pm (UTC)
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Indeed. But at least AV enables one to express one's preferences rather than having to choose to vote for the person one likes or the person of the two (or possibly three) likely winners you'd rather have.

AV tactical voting is a lot more complicated!
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From:arnhem
Date:April 27th, 2011 06:34 pm (UTC)
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But AV tactical fielding-candidates is quite straightforward, and (once the big players with the resources to do it work it out) won't make the future nearly as glorious as appears to be fondly hoped.

Where we currently have the big parties acting locally to try to focus as much effort into a single candidate as possible, under AV, they'll just have to spend a bit more in fees.

The obvious tactic lies in creating a cluster of candidates who are all loosely affiliated to your colour (let's say "blue-ish" and "red-ish").

One of these candidates is your all-purpose blue-ish/red-ish candidate, as now. The others each identify themselves strongly and unconditionally with a particular single issue, but also make clear that they affiliate with the all-purpose candidate.

The single-issue candidates campaign within their particular interest group, but encourage "their" voters to put them first and their affiliated all-purpose candidate second.

The party with the money to field the largest number of supportive single-issue candidates in their camp will probably win.

I think I prefer it where the tactics lie with the individual more than with the big parties.
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From:arnhem
Date:April 27th, 2011 06:41 pm (UTC)
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And to deal with a specific obvious objection (that an unaffiliated single-issue candidate will do better than an affiliated one).

The ones-with-affiliation will be able to claim that they have influence where it matters ...
From:yrieithydd
Date:April 27th, 2011 09:41 pm (UTC)
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This has not occurred in Australia as far as I know. Interesting you say 'fees' when they are in fact deposists (i.e. you get it back if you win enough votes).
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From:neoanjou
Date:April 27th, 2011 04:37 pm (UTC)
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re: [1] - I think it's more likely that you would get less voters for the second election.

Imagine that I'm a labour voter in a rural constituency. FPTP has chosen a Tory, and AV a Liberal Democrat. In the second election, not only do I need to prefer the LD over the Tory (or vice-versa), but it also needs to be a sufficient degree such that I can be bothered to get out and vote.

And AV only really discourages tactical voting by making it less relevant (and harder to work out how to vote tactically). Apparently in Australia you tend to find that tactical voting has been outsourced to some degree with parties handing out papers saying 'the XXX party recommends you rank your candidates in *this* order...'.

However, AV is still IMHO a better system than FPTP.
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From:woodpijn
Date:April 27th, 2011 04:44 pm (UTC)
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Very interesting thought experiment :)

To avoid the problem arnhem suggests, maybe on election day they should also have everybody pick a preference between each possible pair of candidates (assuming there are few enough that this won't take forever), and then use the presumably-truthful result for the pair which later turns out to be relevant.
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From:andrewducker
Date:April 27th, 2011 05:27 pm (UTC)
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A preference between each pair of candidates can be easily simulated using a preference list - i.e. the way that AV already works :->
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From:woodpijn
Date:April 27th, 2011 05:38 pm (UTC)
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I know - as an AV supporter I agree that Sally's experiment will trivially prove AV is better.
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From:andrewducker
Date:April 27th, 2011 07:12 pm (UTC)
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Sorry, didn't mean to come off as patronising there.
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From:woodpijn
Date:April 27th, 2011 07:27 pm (UTC)
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No problem, I didn't think you were.
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From:woodpijn
Date:April 28th, 2011 08:32 am (UTC)
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In fact, I'm wondering if Sally's point plus my point constitute some kind of proof that AV is better, or if I'm missing something.
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From:andrewducker
Date:April 28th, 2011 08:46 am (UTC)
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I rather think it does :->
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From:cartesiandaemon
Date:April 27th, 2011 05:40 pm (UTC)
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Although, once you _have_ the preferences, I think you can use them to implement one of the systems which is like-AV-but-a-bit-more-theoretically-acceptable-if-harder-to-explain (?) :)
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From:cartesiandaemon
Date:April 27th, 2011 05:34 pm (UTC)
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Hm. You're right. It's a bit too long to fit on a banner, but somehow it sounds appeasing to the (small) FPTP bit of my brain, even though I know it will produce the same result as AV :)
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From:yrieithydd
Date:April 27th, 2011 06:46 pm (UTC)
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Just read the Prof Gowers article. Very good and actually funny in places:

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 love the parenthesis!
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From:robert_jones
Date:April 27th, 2011 11:00 pm (UTC)
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As with most thought experiments, I think you're only driven to believe that it has the outcome you expect because that is what your prior position implies. I can't see it being convincing to people who aren't already supporters of AV.
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From:atreic
Date:April 27th, 2011 11:11 pm (UTC)
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If preferences as expressed when constituents vote under AV were fixed and immutable between the two votes, then the majority of people must prefer the AV candidate over the FPTP candidate in a straight race, by definition.

I find it hard to believe that people might prefer Labour to the Conservatives on Monday, and then on Wednesday go 'oh, actually, we prefer the Tory chap'. (But this referendum is teaching me a lot of rather depressing things about people, so maybe you're right.)

If that wasn't the reason you were alluding to, I honestly can't think why it wouldn't have the outcome I expect.
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From:robert_jones
Date:April 28th, 2011 05:43 pm (UTC)
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According to that paper Matthew linked to a while ago, something approaching half the voters under AV only express a first preference (unless compelled to do otherwise). Nevertheless, I imagine if faced with a choice between two specific other candidates, these people would in fact have a preference. Also I doubt that even people who do express third and fourth preferences will give much thought to which order they come in, whereas faced with an actual choice between those candidates they would weigh the decision rather more carefully and might well reach a different concluion.

Moreover, some voters certainly are finely balanced in deciding which of two candidates they prefer, and the actual decision they reach could well be different on Monday and on Wednesday.

Also, as we've already observed, turnout would probably be different in the two elections.

I just don't believe that AV will produce equivalent results to actually conducting a run-off election.
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From:benparker
Date:April 28th, 2011 11:03 am (UTC)
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It was convincing to me with no particular prior beliefs; do you really believe that A should be elected rather than B if more people prefer B to A?
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From:robert_jones
Date:April 28th, 2011 05:47 pm (UTC)
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In an election with two candidates, I think it's obvious that the candidate with the most votes should win. It gets more complicated in elections with three candidates. There's a well-known problem that the electorate may prefer A to B, B to C and C to A, but apart from that, why should we care about what the pairwise results would be in an election which is in fact between three candidates?

(But also as I say in my comment to Sally, I doubt that the AV results would allow one to predict the results of pairwise elections: that would require the electors to be far more mechanical than they are.)
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From:jamesofengland
Date:May 6th, 2011 03:12 pm (UTC)
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I think that Sally's right, not because voters are mechanical, but because AV results would correlate, weakly at the very least, with the runoff results and I think some people would be persuaded by that. I remain very relieved by what appears to be the preservation of democracy of the issues, rather than democracy of the candidates, but this strikes me as a way of highlighting the best features of AV.

I think that you would be more right if there was a useful gap between the initial vote and the second vote, as in, eg. France. Increasing media scrutiny of candidates would mean a more democratic vote and decrease the difference between AV and FPTP as a prediction of the second result. Run election 2 a couple of days after election 1, though, and you're likely to see the tautology of "people whose 3rd prefence was x and whose preference for y ranked >3rd prefer x to y" voting in a classic, simple, voting system and demonstrating that AV is "fair". Indeed, you might even find the word "proof" being thrown around, a la woodpijn.
From:emarkienna
Date:April 27th, 2011 11:18 pm (UTC)
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I like this idea :) I guess one problem is that ultimately it's still another voting system, and FPTP supporters would still campaign against it by whatever means and argument possible, even if it seems like it ought to be fairer than both FPTP and AV. But still - it's an interesting thought experiment to get people to think about which is the better system.

I note that one advantage this has over other two-round runoff systems is that in most cases, you'll only have to have one round. I'm curious what voting criteria it would have - I guess it would still fail the monotonicity criterion, but pass the same criteria that AV has(?)

I think, trivially,[1] that the majority would vote for the candidate elected under AV over the candidate elected under FPTP when these were different, because that's what AV does better at finding. Which suggests to me AV is a better system for finding the people we want to represent us.

I agree - though to play devil's advocate, there are some cases where even though the AV candidate would still be elected under this FPTP vs AV system, one could still argue that the FPTP winner was the best solution.

The obvious cases to look at would be look at are monotonicity examples - consider the example at http://en.wikipedia.org/wiki/Monotonicity_criterion , with the addition that FPTP votes equal the 1st preferences:

In the second election, Cynthia wins under AV, where as Andrea wins under FPTP. Then in an election between the two, Cynthia would still win.

But the catch is that although C beats A in an election with only those two, we also have: A beats B; and B beats C. So the counter argument would be that there's nothing special about looking at who wins in the FPTP vs AV outcome, when there's a cyclic set of preferences. And although it's somewhat a matter of opinion, it's not unreasonable to argue that A should be the actual winner with those votes (not just that A wins FPTP; I believe A would also be selected by methods such as Borda Count and Minimax).

I hope I'm not dissuading any potential Yes voters! My view is that such cyclic cases seem rare, and would still be far outnumbered by the cases where AV gives a better choice than FPTP (the same reason why I don't think the monotonicity criterion makes FPTP better than AV).

Plus, as I say, I still think this is a useful thought experiment - I'm not convinced that most people thinking of voting No seem to be concerned or even aware of the monotonicity criterion.
From:writinghawk
Date:April 27th, 2011 11:40 pm (UTC)
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I think this is a rather brilliant thought experiment. I strongly encourage you to add a comment to Tim Gowers' post mentioning it!
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From:keirf
Date:April 28th, 2011 07:11 am (UTC)
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What you have effectively proposed is "Run two elections - one FPTP and one AV. If the outcomes differ, rerun the election wtih what would have been the last stage of AV, and see which result you get."

Unsurprisingly, the result will support AV unless [1] applies.
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From:atreic
Date:April 28th, 2011 08:15 am (UTC)
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Yes, I know that, which is why I wrote 'trivially'.

But surely the question of 'do you want the person FPTP would elect, or the person AV would elect' is a useful rephrasing of 'which voting system would you prefer'?
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From:ilanin
Date:April 28th, 2011 11:28 am (UTC)
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No. Or at least, it should not be. Confusing process and product is common, but that doesn't make it right.

Fortunately your thought experiment doesn't actually ask this question on a personal scale, so it's mostly fine.

It is, of course, still possible to believe that AV will produce a House of Commons which may be more representative of people's votes and less representative of the country. Everyone predicts that the effect of chasing second-preference votes will drive parties towards the political centre - and of course relatively few people are natural centrists.
From:emarkienna
Date:April 28th, 2011 11:43 am (UTC)
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I'm not sure it's true that relatively very few people are natural centrists. And if that was true, it's not clear to me that a party or candidate would gain under AV by being in that centre - you still have to get enough preferences to not be knocked out, so anyone in representing a position that few people actually want wouldn't get in under AV either. (E.g., if we have the left wing party, the right wing party, the centre party, and most people have left or right as first choice, then the centre party gets knocked out. The point about AV is that the centrists are still allowed a say, on whether they prefer left over right, without having to resort to tactical voting.)

We also see this affect of parties tending towards each other under FPTP anyway, e.g., Labour moving from left to the centre; or places like the US where you tend towards a two party system where both parties aren't hugely different from each other. (Well okay, there are some areas where I think Republicans are far worse, but economically they both seem rather right wing by world standards.)
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From:atreic
Date:April 28th, 2011 12:05 pm (UTC)
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I agree with emarkienna that lots of people are centrists. Also, while compromise is an ikky word in politics, it strikes me as fairly sensible that (for example) if half the country wants taxes to rise and half want taxes to fall, a centrist position where they stay the same isn't a bad approach to making everyone only slightly unhappy...
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From:keirf
Date:April 28th, 2011 01:49 pm (UTC)
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Unless the total happiness of the country is the sum of the square of the happiness of each person. Then you are better off having half the population very happy and half very unhappy, than everyone only slightly unhappy.
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From:benparker
Date:April 28th, 2011 11:01 am (UTC)

Brilliant

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I've not seen this idea before, but this is a very convincing mathematical argument.

(I'm not sure the proof is trivial, but I think I have a fairly simple one that works.)

I like the condorcet axiom that A should be elected rather than B if more people prefer A to B. I don't think it shows that more people wouldn't prefer C, in either system, so AV and FPTP might both be rubbish, but if we're going to choose one of the two, it looks like AV is mathematically better. I think my other arguments against AV (http://www.ben-parker.co.uk/?p=251) still apply.
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From:ilanin
Date:April 28th, 2011 11:47 am (UTC)
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You never actually get conservation of voters in runoff elections, btw. The best example for runoffs doing weird things is the French presidential election of 2002, where an extra 2,564,518 people showed up at the polls to vote against the National Front in the second round. Normally though runoffs have a slightly lower turn-out than first round elections.

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