<div>First off, I heartily agree that the cooperation/defection problem (aka ABE, aka Chicken Dilemma) is probably the most broadly-applicable, hard-to-solve problem in voting theory. The reason is simple: if there's a majority condorcet winner, it's easy to make a system which has a unique-winner strong Nash equilibrium, but if the CW is non-majority, no majority method can have such. The standard chicken dilemma is the simplest case where there is a CW but no majority CW.</div>
<div><br></div><div>Still, again I have to ask you, Mike: where's SODA? You were right earlier that SODA fails FBC. But there are three mitigating factors.</div><div><br></div><div>1) Failure would be very rare; I hope to be able to be more precise about this in the near future.</div>
<div><br></div><div>2) Even when failure happens, SODA would never fail FBC without at least giving the non-betrayed favorite a chance to restore FBC by giving the win to the should-have-betrayed-for-them lower choice. (This is not mathematically necessary, but to make it untrue, you must divide the candidates in question into several clones, or give them a negligible fraction of their votes in delegated form, either of which makes an already-strained scenario completely implausible.)</div>
<div><br></div><div>3) There is a polytime(?), summable fix for the method, which restores full FBC; though I admit it's an ugly hack. Basically, there's a way to use the co-approval matrix to check if FBC has been violated and make those voters for whom it was violated "virtually" betray their favorite. Since, when that happens, it is the only way to give these voters a winner who they approved, it is not hurting them at all. There's also a slightly less-ugly, but imperfect, fix that merely makes the process in step 2 automatic; this would be good enough in practice.</div>
<div><br></div><div>I believe that with these three factors, and most particularly the first one, SODA's FBC failure is tolerable. For instance, I don't have the numbers yet, but I believe that I will find that in maximum-entropy models, SODA fails FBC less than any Condorcet system.</div>
<div><br></div><div>And as for cooperation/defection: SODA without question solves that problem more completely than any of the alphabet soup you mention. (Though I'd still really appreciate it if you made quick electowiki pages for all of that, because I'd bet that nobody but you actually knows what every one of those means, and it would be considerate of you not to ask us to continually look up all the definitions and redefinitions in the archives).</div>
<div><br></div><div>Jameson</div><div><div><br><div class="gmail_quote">2012/2/28 MIKE OSSIPOFF <span dir="ltr"><<a href="mailto:nkklrp@hotmail.com">nkklrp@hotmail.com</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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C/D:<br><br>It seems to me that the co-operation/defection (C/D) problem is more difficult to truly eliminate<br>than I'd believed. Hugely reducible, but maybe not eliminatable.<br><br>The methods that I've been suggesting, to get rid of the C/D problem--I'll refer to those as <br>
"defection-resistant" methods. They include AOC, MTAOC, MCAOC, AOCBucklin, AC, MTAC,<br>MCAC, ACBudklin, MMT, GMAT, and ICT.<br><br>It seems to me that all of the defection-resistant methods that I know of which meet FBC <br>
still allow another C/D problem, with burial. Of course the mechanism differs with different<br>methods, but they all seem to have that burial C/D problem.<br><br>For example, with the conditional methods, the burial takes the form that Jameson described.<br>
<br>But, for one thing, as I said, the burial can backfire, in the conditional methods, just as it<br>can in the pairwise-count methods. <br><br>Besides, unlike pairwise-count methods, the conditional methods have no such thing as <br>
truncation offensive strategy.<br><br>I don't know, but it may well be that, in principle, strictly-speaking the new C/D problem,<br>with the defection, is the same as the old one. But there's a big and important difference:<br>
<br>It requires the drastic offensive strategy of burial. Burial is much less likely, more culpable, and<br>better-deterred than mere truncation or non-support.<br><br>So I still claim that the defection-resistant methods are a big improvement. I still claim that<br>
they're the only significant improvement over Approval, and that there's no point proposing<br>or using something more complicated than ordinary Approval, unless it's defection-<br>resistant.<br><br>Maybe someone could show that the C/D problem can't be entirely eliminated with a<br>
FBC-complying nonprobalistic ballots-only method. Defection-resistant, yes. Defection-proof,<br>no.<br><br>Another Approval C/D mitigation:<br><br>This isn't anything new, but I just haven't mentioned it before:<br>
<br>Actual elections are different from examples, such as the Approval bad-example (ABE). When there's going to be an actual<br>Approval election (ordinary non-conditional Approval), people will know what the supporters of other<br>
candidates are saying about their candidate. You'll know if they're going to vote for hir. In fact that<br>matter could be made explicit during a campaign. There could be an agreement that the supporters<br>of 2 candidates, or members of 2 factions, will vote for eachothers' candidate. Or it could be declared<br>
that they won't.<br><br>So Approval's C/D problem is exaggerated by the Approval bad-example.<br><br>But I still claim that AOC would be better, and that, in general, the defection-resistant methods would<br>be better.<br>
<br>Still, Approval looks quite adequate and merit-possessing, as a first proposal. I don't think that there's any<br>reason to propose anything other than Approval, as a first proposal. For me, there's no question about what<br>
voting system should be proposed: Approval.<br><br>IRV with sincere voting:<br><br>Though I don't like FairVote's dishonesty, I must agree with something that they've claimed:<br><br>Sincere voting is an ok strategy in IRV. But that doesn't mean that people will vote sincerely.<br>
I hasten to add that we know that voters are overly <br>compromise-prone, and that they _won't_ vote sincerely. We can't not take that into consideration when<br>proposing a voting system. At least if the method is Approval, no one will fail to fully support for their<br>
favorite. I'm not saying that IRV would be as good a proposal as Approval.<br><br>But, for sincere voters, IRV wouldn't be so bad. As you know, it meets the Mutual Majority Criterion (MMC). <br>A mutual majority has nothing to fear when voting sincerely. One of their candidates will win.<br>
<br>Maybe you're not in a mutual majority, and the supporters of your needed compromise will bottom-rank your<br>favorite, and so, when Compromise gets eliminated, due to your not top-ranking hir, Worst will win.<br>
<br>
That's why I earlier suggested, and still suggest for that situation, ranking the _acceptable_ candidates<br>in order of their winnability. The key word is _acceptable_. The problem is that voters who are resigned to<br>
compromise tend to be willing to compromise their hopes away too readily.<br><br>So, in IRV, advise people to rank sincerely, because a mutual majority can't lose that way.<br><br>And advise them that if they're not in a mutual majority, even then, they should reserve their compromise-<br>
high-ranking only for acceptable candidates. And they should be very particular what they deem acceptable.<br>They shouldn't give up their hopes. They should rank the genuinely acceptable candidates over all the others.<br>
...no matter what they think the winnabilities are. Do that, and IRV would be ok.<span class="HOEnZb"><font color="#888888"><br><br>Mike Ossipoff<br><br><br><br> </font></span></div></div>
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