Mike wrote: I've always said that standards are entirely subjective. Your standards are different from mine, and may your methods have great success with people who share your standards. The only way to be wrong about standards is to say that your standards are best, or that
someone else's standards are wrong, ot that your standards are more objective than someone else's. I reply : Maybe saying you lack some objectivity are not the appropriate terms. It is not exactly what I mean, sorry for my improper english vocabulary. In the same way I apologize for using the term "claim" which was, to my understanding an equivalent to "publicize" or " makes public". I recognize you proved what you "claimed" or simply "informed others". What I mean follows. We agree Condorcet methods using winning votes respect your "defensive strategy" criteria. You seem to accept that Condorcet methods using "relative margins" produce a ranked winners list that minimizes the biggest ranking reversal. All I say is that this second mathematical criteria is the best algebraic definition I am able to fit with the definition of fairness. I would not find fair a method that would output A as a winner if it represents overulling the judgement of 70% of the voters about one pairwise, if there is another solution that would give B as a winner and only overules the judgement of 53% of voters in this other ranked list. You could argue that if my method does not pass your defensive strategy criteria, thus voters do not necessarily vote sincerely so my result is flawed from start. I told you that in a similar way, methods that pass your defensive strategy criteria are flawed in the same way because producing a complete ranking of preference can harm a voters own preference. So even these methods are flawed from the start because we - usually - do not know the outcome of an election at the beginning and there is no garantee voters will vote sincerely. Mike wrote: Yes, truncation can change the outcome with wv. Truncation can also change the outcome with margins methods, relative margins methods, and with any rank balloting method. The difference is that with wv, truncation won't steal the election from a majority-supported CW, as it will with margins and relative margins. I reply: This is where I think we can see the problem. I agree that: (please quote me entirely on this in the future) "With wv, truncation won't steal the election from a majority-supported CW, as it will with margins and relative margins." WHEN YOU CONSIDER THE CW DEFINED WITH WV. (I am not shouting just underlining our difference of opinion). I believe there can be two different CW, one CW(wv) using winning votes and another CW(rm) using relative margins. "So with wv, truncation won't steal the election from a majority-supported CW(wv), as it will with margins and relative margins, but IT WILL STEAL THE ELECTION FROM A MAJORITY-SUPPORTED CW(rm) as it will with margins and relative margins. Now, I do believe the CW(rm) is the "right winner" when both exists and are different for the reasons explained previously. For me sincerity is prevalent to fairness, but you haven't reach that point yet with your proposed winning votes methods and criteria. If you could produce a method that can garantee to voters to protect the CW(rm) and make them vote sincerely, thus I think I would admit the input is not flawed. And I could accept that a sincere result is better than the fairest result obtained from a flawed input... Mike wrote: We've really got to have a FAQ about this. Gibbard & Satterthwaite have shown that, in every nonprobabilistic method, there can be incentive for strategy. No one ever claimed that that doesn't apply to wv methods. But we can choose what kinds of strategy we'll have incentive for, and how badly we'll need them, and under what conditions, and whether or not all the Nash equilibria involve those strategies. I reply: I think too there is no way to remove all strategies. Removing some of them could be usefull I you could attach a low probability for the occurrence of the remaining cases. My engineer macroscopic evaluation tells me your criteria makes the "strategical issue" probality go from very rare to still very rare but obviously I could be wrong. It is however very difficult to evaluate because we would need to approximate the ability of identical voters to regroup and to organize so to exploit this strategical opportunity. I believe less than a handfull of voters with the exact set of preferences would go under such a process and thus this is why I obtained very low probabilities. Sorry Mike for lacking adequate terms, I hope it is clear enough. I do my best. An english version of my best multiple-winners method should be on the Electoral_systems_designers site soon. It is under study by Commissions for Electoral Reforms of Quebec's government and parliament (both entities decided to look at electoral reform in the same time). Steph. ---- For more information about this list (subscribe, unsubscribe, FAQ, etc), please see http://www.eskimo.com/~robla/em
