Yesterday I said, in answer to your question, that I didn't know whether or not Tideman(m) is better than Plurality, because I haven't dealt with minutiae like the possible merit difference between methods like that. Of course I never said there _wasn't_ a merit difference. Actually, maybe Tideman(m) is marginally better than Plurality, but not enough to make it an adequate method. I say that because the Condorcet Criterion, in a distant, hypothetical, "what if" sort of a way, does relate to voters' strategy situation. The obvious way in which it has to do with that is that if no one uses strategy, then no one has legitimate reason to regret using strategy. Also, if everyone has complete information about eachother's preferences, and so everyone knows what to do, then the sincere CW wins, no matter what voting system is used (except that I don't want to guarantee that for Borda), when people use the strategy that they need to get their best ourcome for that election. Riker demonstrated that sometime before 1977. It's mentioned in the _Scientific American_ article that he wrote with Niemi in '76 or '77, on voting systems. So, if everyone uses completely well-informed strategy, the sincere CW (SCW) wins. Since the SCW is what people would get if they all knew the situation, the victory of the SCW has a certain rightness. So there's also something right when it can be guaranteed that the SCW will win if everyone votes sincerely. In rank methods that means a guarantee that the SCW wins if everyone sincerely expresses all of their preferences. For the purpose of applying the Condorcet Criterion to rank methods only, it could be defined with reference to nothing about voters except for their votes, as Markus would like: A candidate who pairwise-beats each of the others must win. That too sounds like a good thing to guarantee. So I'm not saying that the Condorcet Criterion doesn't mean anything, and when we're examining the bottom-end methods, something like the Condorcet Criterion can be used to establish a merit difference between bad and worse. But the operative expression above was "what-if". Truncation will always be common, and everyone sincerely expressing every preference is a fiction. That's why I question the value of Condorcet's Criterion for anything other than establishing superiority to Plurality. The defensive strategy criteria are down-to-earth, materially, strategically practical criteria. So I claim that any one of the defensive strategy criteria is worth more than the Condorcet Criterion. For instance, there's an IRV mitigation that meets WDSC, and maybe that's all it meets. Voters are allowed to split their one vote by dividing it between more than 1 candidate, by ranking more than 1 candidate at a rank position, any rank positionn(s). Though, unlike Approval & Condorcet, that IRV mitigation likely meets nothing but WDSC, that's enough to make it better than Tideman(m), Dodgson, or any other rank method other than Condorcet or Simpson-Kramer(wv). (Where Condorcet includes Tideman(wv), SSD, etc.) Why don't we mention Condorcet's Criterion at the website? Anything that meets the 4 majority defensive strategy criteria also meets Condorcet's Criterion. I don't have a proof for that, so if you can cite an exception, feel free to do so. The reverse isn't true: Meeting Condorcet Criterion doesn't mean meeting even one of the majority defensive strategy criteria, or other defensive strategy criteria. So then, why should we mention Condorcet's Criterion? It's covered by the more valuable & stronger criteria that we use. Why bother readers with an additional criterion that is relatively worthless compared to the criteria that we're already using, and whose compliance is guaranteed by compliance with some of the criteria that we're using? Why do I say that Condorcet's Criterion is relatively worthless? Many agree with me that the lesser-of-2-evils problem is a real problem. Either we get rid of that problem to the extent possible, or we don't. Condorcet's Criterion doesn't. So the fact that Condorcet's Criterion can be used to compare bottom-end methods doesn't make it valuable. As I said, either we do or we don't, and Condorcet's Criterion doesn't. It isn't even part of the array of criteria that measure that. Again, you might say I expect too much from a voting system, but there are a number of voting systems that meet some of the defensive strategy criteria, including the simple & modest Approval. So I don't think I'm asking too much from a voting system. Mike Ossipoff _________________________________________________________________________ Get Your Private, Free E-mail from MSN Hotmail at http://www.hotmail.com. Share information about yourself, create your own public profile at http://profiles.msn.com.
