The equal-top-ranking voters are not the ones who have a right to complain about a CC violation. The ones who vote for the CW over the winner are. You claim, they are not a majority, so the majority who top-ranked or voted for the winner should be more important. So essentially, you are arguing that the majority CC is the "meaningful" CC. Which is a perfectly valid position, and one I largely agree with. And in my opinion, saying it that way is more convincing than the seemingly circular argument that ICT is a good system because ICT's definition of "beats" is a good definition.
Jameson 2012/7/30 Michael Ossipoff <[email protected]> > 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 >
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