On Mon, Jul 30, 2012 at 1:45 PM, Jameson Quinn <[email protected]> wrote:
> As far as I can tell, you are arguing that ICT meets the majority Condorcet > criterion No, I'm arguing that ICT meets Condorcet's Criterion, if Condorcet's Criterion is about electing the candidate who beats each one of the others, or who is the only unbeaten candidate. ICT does that, you know. Yes, it defines "beat" differently, but I claim that unimproved Condorcet's definition of "beat" is no more valid than that of ICT. Less valild, if judged by the intent and wishes of the equal-top-ranking voters. But yes, it meet the Majority Condorcet Criterion too (I capitalize names of methods and criteria for clarity). You said: (does it? [endquote] Yes. Every method that meets CC, when ICT's "beat" definition is used, also meets MCC. But the reverse is not true. You continued: it seems to...) and that the MCC is more important than > the CC. [endquote] It certainly could be said that MCC is more important than CC in the sense that failing a more lenient criterion is worse. But, on the other hand, meeting a stronger criterion counts for more than meeting a weaker one. So then, who can say which is more important. But I was talking about CC, not MCC. You said: Do I read you correctly? [endquote] I'm claiming more than you thought that I was. I'm saying that ICT meets Condorcet's Criterion. That sounds like a preposterous thing to say, if you regard the definition of "beat" to be part of CC's definition, and if you take, as "beat" 's definition, the "beat" definition used in traditional unimproved Condorcet. But "beat" could be regarded as a word defined external to CC's definition. And I've told why unimproved Condorcet's beat definition is no more valid or legitimate than that of ICT. Looked at in regards to the wishes and intent of the equal-top-ranking voters, the ICT beat definition is the more justifiable one. The two beat definitions: First I'll repeat some terms: (X>Y) is the number of ballots ranking X over Y. (Y>X) is the number of ballots ranking Y over X. (X=Y)T is the number of ballots ranking X and Y at top. (X=Y)B is the number of ballots ranking X and Y at bottom. Unimproved Condorcet's "beat" definition: X beats Y iff (X>Y) > (Y>X) Improved Condorcet's "beat" definition: X beats Y iff (X>Y) > (Y<X) + (X=Y)T Double-Ended Improved Condorcet's "beat" definition: X beats Y iff (X>Y) + (X=Y)B > (Y>X) + (X=Y)T Which method meets CC depends on which "beat" definition you use with CC. You could say that you consider unimproved Condorcet's "beat" definition to be part of CC's definition. Or you could say that the meaning of "beat" is external to CC's definition. I suggest that the only justification of insisting on the former is if you think that the traditional "beat" definition, that of unimproved Condorcet is actually better, more justified. Otherwise, you're just clinging to tradition. I've compared the justification of those two "beat" definitions. ICT meets CC at least as validly, and arguably more validly, than traditional unimproved Condorcet. Mike Ossipoff ---- Election-Methods mailing list - see http://electorama.com/em for list info
