On 26.5.2012, at 10.25, Michael Ossipoff wrote: > You said: > > I assume that the definition covers at least the case where we have a top > loop of three candidates, and one of those looped candidates has > the smallest worst loss of all candidates when measured as winning votes, > and that candidate shall win. > > [endquote] > > Yes. I'd say that that, if there are only 3 candidates in the top cycle, > then every Condorcet(wv) version that I'm aware of would elect the top-cycle > candidate with the weakest defeat, as measured by wv. > > But remember, I'm no longer advocating Condorcet, and so it is no longer my > responsibility to define it. Well, yes, I've been saying things about > Condorcet's strategy problems, and so you can use the definition that I gave > above to determine what I mean by "Condorcet".
One way to make the coverage more complete (valid with all possible votes) would be to name some methods that it is supposed to cover always, e.g. wv based minmax, beatpath and ranked pairs. I'm trying to clarify the scope of your claim. If you want to prove that Condorcet methods are vulnerable (or have a strategy that is always useful), maybe you should state which ones have problems, or if all of them have problems. Now the target seems to be to say that at least the most common wv based Condorcet methods are vulnerable (maybe the ones that I listed above) (at least when the top loop has no more than three members, maybe also with more than three members). > But remember that those who say that Condorcet is better than Approval > likewise have a responsibility to define Condorcet, if I do. Yes. Some claims may cover all Condorcet methods, some only the method that this individual Condorcet promoter wants to promote. I guess in this comparison the target is to seek a good deterministic compromise seeking single-winner method for typical large and competitive political elections. I think all the usual Condorcet methods do pretty well in this comparison. > I'd say that surely or almost surely, the Condorcet favorite-burial strategy > that I described is also optimal with any method that fails FBC, provided > that your information about how others will vote isn't better than it is in > our actual elections, and provided that it's all-important to you that you > maximally help the Democrat against the Republican, and provided that you > believe that the Democrat is the only candidate who can beat the Republican. Maybe the strategy is not opimal or recommended for all methods that fail FBC, e.g. for a modified Approval method that occasionally (randomly with probability 0.001) elects the candidate with second highest number of approvals. The "information about how others will vote isn't better than it is in our actual elections" condition describes a typical real life environment. It can usually be taken as an assumption when we discuss practical strategies (of real life elections). The "all-important to you that you maximally help the Democrat against the Republican" condition seems to say that the Democrat is the most liked and the Republican is the least liked candidate, which makes the strategy trivial (= no changes to the sincere vote) if the idea is that the Democrat is the candidate that should be ranked alone at top. Juho ---- Election-Methods mailing list - see http://electorama.com/em for list info
