On Apr 13, 2005, at 21:33, Jobst Heitzig wrote:
Ok. You refer to practical voting methods here. Using random selection could be possible is SVMs too, but that would mean that there is no "complete SVM" (= method that would be able to always pick the winner) behind but only a set of sincere criteria that leave some space for picking any of the "good enough" candidates as the winner.
I don't understand this. DFC is a method that is always able to pick the
winner. It is based on the natural measures of approval and pairwise
defeats and on the principles of fair chances for all voters and
proportional representation in the long run. This makes it a perfectly
sincere method, even when you don't agree on the importance of these
measures and principles.
Ok. Maybe I should take one step back and agree that the concept of SVM could be extended to cover also these cases, and random selection could be seen as one possible sincere target. In this case one however gives up the idea of seeking and naming the (one and only) best candidate. The difference is thus "method that produces the wanted ideal results with the sincere votes" vs. "method that elects the best candidate based on the sincere votes".
One SVM candidate with the extended definition is letting a random ballot to decide who wins. In this case one probably thinks that it is a good thing to have various more _and_less_good_ people elected in a balanced way.
((Naming of these categories could be something like SSVM (Sincere Statistical Voting Method) (= extended SVM) and SEVM (Sincere Exact Voting Method) (= old SVM) or something similar.))
In my opinion, clone independence (aka component consistence) is a
sincere criterion since it can be interpreted like this: When a group of
candidates appears lumped together in all individual rankings, the
result should be the same as when first treating these "cloned"
candidates like one candidate and then, if that candidate wins, applying
the method again to the set of these cloned candidates.
Ok. I understand that clone independence is a sincere criterion for many. Looks like a positive target to me too. But just like I have my doubts about the Smith set, I'm also not yet quite certain that the "clone set" should always be respected and that what appears to be a clone set (=lumped in all votes) really always is a group of homogeneous (= one party) candidates.
My problem with clones is that I'm not 100% sure that we should always respect that criterion. I think Smith set is a criterion that should apply in 99% of the cases but not in 100%. The same might apply to clones. I can't say yet.
(My reference to strategic use of clone independence referred to ability to manipulate the election outcome by e.g. intentionally voting a loop between candidates of a competing party, and picking a suitable voting method to defend against that threat.)
Pointers to classical examples where e.g. minmax has problems with clones would be appreciated.
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