On the mathematical-exploration side of things:<br><br><div class="gmail_quote">2011/5/26 <span dir="ltr"><<a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a>></span><br><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex;">
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<br>
> From: Kevin Venzke<br>
> To: <a href="mailto:election-methods@electorama.com">election-methods@electorama.com</a><br>
> Subject: Re: [EM] remember Toby Nixon? FS<br>
> Message-ID: <<a href="mailto:404845.50771.qm@web29613.mail.ird.yahoo.com">404845.50771.qm@web29613.mail.ird.yahoo.com</a>><br>
> Content-Type: text/plain; charset=iso-8859-1<br>
><br>
> Hi Forest,<br>
><br>
> --- En date de?: Mer 25.5.11, <a href="mailto:fsimmons@pcc.edu">fsimmons@pcc.edu</a><br>
> a ?crit?:<br>
> > The main problem is determining (through the disinformation<br>
> > noise) who the front runners really are.<br>
> > Suppose the zero-information front runners to be candidates<br>
> > A and B, but that the media created front<br>
> > runners are C and D.? If everybody votes for one of<br>
> > these two falsely advertised front runners, then they<br>
> > become the front runners, but only through self fulfilling<br>
> > prophecy.<br>
><br>
> The difference between Approval and Plurality here is that in<br>
> Pluralitywhen the frontrunners are A and B, generally only A and<br>
> B can win. Under<br>
> Approval it is not guaranteed that the winner will be one of these<br>
> candidates, as long as C or D haven't dropped out of the race.<br>
> If the perceived frontrunners are actually the worst candidates, any<br>
> better candidates should receive a vast number of votes.<br>
><br>
> If C or D are clones of A/B then I think they probably would<br>
> drop out<br>
> of the race. But if we are simply electing the wrong clone, that<br>
> doesn'tseem like an enormous problem.<br>
><br>
<br>
Yes, Approval is much better than Plurality and quickly homes in on the CW if there is one. But this<br>
homing in typically takes a couple iterations, which doesn't help when the candidates change every four<br>
years.<br>
----<br>
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</blockquote></div><br><div>I suspect that Approval, with even a modicum of openly-reported polling, would mostly get the CW (pairwise champion) on the first try... and that, given (real-world, perhaps-misguided, attempts at) strategy, actual Condorcet methods would not do measurably better at this.</div>
<div><br></div><div>The one case where approval could fail to find the CW, even after a number of iterations, is when there are two near-clones splitting/sharing a majority (call them A1 and A2, and their strongest opponent B), and a "game of chicken" between the supporters of those two. If A1 and A2 have similar levels of support, the winner between those two will not be the CW, but rather whichever of the two has more-strategic supporters. But if there are too many such strategists, B will win. There is no dominant equilibrium to this game.</div>
<div><br></div><div>DYN helps to resolve this somewhat, because it shifts the game of chicken from an impossible-to-coordinate mass, secret-ballot election to the two individual candidates themselves. This makes it much less likely that B will win by mistake; but it does not ensure that the winner between A1 and A2 will be the CW.</div>
<div><br></div><div>It is possible to patch this problem with DYN by using some measure of candidate quality from the first, and only allowing candidates to "approve" of other candidates of higher quality. This is in the spirit of IRV's elimination-and-transfer, and like that process, it is theoretically vulnerable to center squeeze. However, I think that it would be possible to use a measure of candidate quality such that the overwhelming probability would be that the highest-quality candidate by that measure would be the CW, and that exceptions would be minor and/or manageable through simple strategies by the candidates. The measure I'd pick would be the range score of the candidate, measuring preference (circled), approved, and [unmarked or unapproved], as 2, 1, 0 respectively. (I'm grouping unmarked and unapproved so that there is no strategic motivation to explicitly unapprove a near-clone of your favorite candidate. Note that this 2,1,0 range score, unlike any more-finely-chopped range score, has the property that the actual CW is guaranteed to have a range score as high or higher than the highest approval score.)</div>
<div><br></div><div>So, translated into ordinary language:</div><div><br></div><div>"You circle your favorite candidate, and approve or disapprove of as many other candidates as you want. Your favorite candidate is automatically counted as both favorite and approved. After these results are published, your favorite candidate may 'fill in your ballot' by approving of any other candidate who has more favorites plus approvals than themself. If you had left any such candidates unmarked, they then get a vote for you. The candidate with the most approvals wins."</div>