Arrow and Gibbard-Satterthwaite
schulze at sol.physik.tu-berlin.de
Thu Sep 25 07:01:34 PDT 1997
Mike Ossipoff wrote (20 Sep 97):
>I also don't consider the Pareto Criterion important, because
>what difference does it make whether all, or all but one, of the
>voters prefer A to B, when there are, say, a million voters?
>And for that reason, as Markus suggested, I also don't consider
>Arrow's theorem important, if all it's basically saying is that
>we can't have both Pareto & IIAC.
>So, though I intuitively felt that IIAC might be more unattainable
>than Arrow suggested, I also felt that, for all I know, IIAC
>might be attainable without undue cost. But when Markus pointed
>out that anything meeting the Majority Criterion meets PMC, &
>and that anything meeting PMC fails IIAC, that settles that question.
>So much for the ambition of getting IIAC for a reasonable price.
>Of course I agree that the majority criterion is too much to give
>I have to admit that it hadn't occurred to me, about
>Smith//Condorcet(EM), with the subcycle rule, failing Pareto.
>Though I don't consider Pareto important, the academics seem
>to like it a lot, and so (though the criticism wouldn't be
>valid, in my opinion), failure of the Pareto criterion would
>draw academic criticism. As with some other academic criteria,
>criticisms involving Pareto can be answered, if reform proponents
>had as much airtime as would the opponents--but they won't. Also,
>when the critics are academics, professors appearing on TV,
>that's a publicity problem to be avoided. For that reason
>I consider Smith//Condorcet(EM), without the subcycle rule,
>to be the most winnable, because it's un-criticizable in terms
>of existing popular academic criteria. As I always say, it can
>be said that Smith//Condorcet(EM) meets all the criteria that
>the academics write about, and some important majority
>rule criteria that no widely-proposed method meets. It's helpful
>to be able to say that, to be able to say that, criterion-wise,
>Smith//Condorcet(EM) dominates all of the widely-proposed methods.
Mike Ossipoff wrote (21 Sep 97):
>I want to emphasize that I realize that the fratricide proplem
>that Smith//Condorcet with the subcycle rule seeks to avoid is
>more important than the Pareto Criterion. No question about it.
>What I was saying in my recent message, then, was only about
>campaign strategy, rather than method-merit. Certainly the
>subcycle rule improves Smith//Condorcet, especially when a provision
>is added so that it will be used for a subcycle only when
>nothing in that subcycle would win otherwise (the wording
>probably needs improvement). So, if we're talking about actual
>merit, then I agree that Smith//Condorcet(EM) is better
>with the subcycle rule, with the necessary added provision
>about when to use it.
>And of course I should also emphasize that anything I said
>about what is more winnable is pure speculation & guesswork.
>Predicting what would happen in a reform campaign is guesswork.
>So nothing I said should be construed as advocating against
>measures to avoid the fratricide problem that you described,
>and which I agree is a problem. As you said, when that problem
>can happen, that creates a need for a form of defensive
>strategic voting, and I agree that that's always undesirable.
Markus Schulze (schulze at sol.physik.tu-berlin.de)
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