You wrote:
I'm not sure I've understood your idea, but I'm sure such ideas are worth exploring. The most intuitive change, it seems to me, would be to actually eliminate "eliminated" candidates (not just bar them from victory) and start the process over. Maybe you're saying that. (But I also imagine there must be a cost to altering the method in such ways. I'm eyeing Participation, of course.) CB: Yes, that is what I said. Also I notice in the example you gave, 23 A>C>D>B 29 B>A>D>C 48 D>A>C>B that the method seems to work ok if it is repeatedly used to one-at-a-time eliminate candidates until one is left.(First B(71) is eliminated, then C(77) and then D(52), and so A,the CW wins.)
KV:Another idea I haven't thought through would be to change the way the members of an acquiescing coalition are counted. For instance, in DAC, it bothers me that an A>B>C=D voter contributes to set ABC as surely as A>B>C>D would. CB: This doesn't bother me because I think it is this quality that makes the method resistant to insincere truncation. In his article, Woodall claims that Condorcet is incompatible with Participation, 4 out his 7 different types of Monotonicity, Later-no-harm and Later-no-help. For the Condorcet die-hards, would DAC (either version) be a good Condorcet-completion method? KV:I'm not sure what you're thinking here. Completing with DAC wouldn't permit the method on the whole to meet Participation or later-no-help. DAC's order- reversal incentive would no doubt rub off to some extent, as well. CB: I had in mind Diana Galletly's problem, where it might be decided that Condorcet is more important than Participation. I agree with what you recently wrote about resolving Condorcet cycles by eliminating candidates, so maybe Condorcet completed by reversed DAC elimination (stop eliminating as soon as there is no more cycle). In this paper, Woodall introduces the so-called "plurality criterion": Plurality: If some candidate x has strictly fewer votes in total than some other candidate y has first-preference votes, then x should not have greater probability than y of being elected. "I do like this. It seems to acknowledge meaning in being ranked non-last." CB: While I of course know what "first-preference votes" are, I am not at all clear on exactly what the phrase "strictly fewer votes in total" means (in a ranked-ballot context). What does it mean ? KV:For me, "votes in total" or "non-last votes," or "being voted preferable to at least one candidate," means the number of ballots which acknowledge the candidate, support him, in any way at all. The other ballots, in my view, most likely truncated the candidate. So the criterion means that if X is mentioned on fewer ballots than Y received first-place votes, we can't pick X. It sounds like a good criterion to me, because it seems unlikely that, in this case, we could possibly have a good reason, sufficient information, to think that X is a better pick than Y. But the main reason I noticed this criterion is because I think "number of ballots which acknowledge the candidate in any way" can be useful information. CB: For the time being I am skeptical. I don't see why we need this as well as Monotonicity. This is the first election-methods criterion that I have seen that employs the word/concept "probability". I think that there might be a place for "Weak Monotonicity" as a fundamental standard for those who like to rigorously avoid any reference to sincerity/insincerity in their criteria. Something which just says that a candidate X generally placed higher on the ballots than candidate Y should have a greater probabilty of winning, just to knock on the head any absurd method like "elect the candidate with the greatest number of second preferences". Chris Benham
