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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.

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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: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: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 :)
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.
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: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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