Mike Ossipoff wrote: > Sincere preferences:
> 40: ABC > 25: BAC > 35: CBA > B is the CW. > A possible set of sincere Approval ballots: > 40: A > 25: B > 35: C > The premise of our CC is complied with: There's a CW, and everyone is > voting sincerely. But the CW doesn't win. So the requirement isn' t met. You're entirely right. I wasn't thinking clearly about what "preference" meant (I had in mind something more like "voting a preference" or "expressing a preference") and I also misinterpreted this definition: > [ From http://www.electionmethods.org/evaluation.htm ] >>A sincere vote is one with no falsified preferences or preferences >>left unspecified when the election method allows them to be specified >>(in addition to the preferences already specified). For some reason, I thought this meant that either your example Approval ballot wasn't sincere (by the above definition) because there were preferences (in the common-sense meaning) that couldn't be specified -- or that the sincere preferences you gave in your example weren't accurate because only "expressed preferences" mattered. Basically, I started off trying to extend the notion of "voted higher" as applied to Approval (which was detailed in the MC section immediately preceding the CC section on the same page) and then compounded my error by misinterpreting the definition of "sincere vote." > Approval doesn't pass our CC. I completely agree. Sorry for the confusion on my part. > But yes, it would pass Blake's CC if he didn't stipulate that his CC > only applies to rank methods. I'm unfamiliar with Blake's version, and am curious why he would make that stipulation if Approval would pass otherwise. I've tried searching through the archives (actually, on Google) for 'Blake "Condorcet Criterion"' (and found a discussion between you and Blake Cretney that on first glance raises some of the very same issues regarding the meaning of "preference" as we've raised here) -- but nothing that looks like a definition of a CC variant. Would you be so kind as to provide a reference? As Alex Small pointed out, I was basically trying to reproduce the result proven by Brams and Fishburn (though I'm unfamiliar with their results, as well.) Here is what Alex had to say about it: > If all voters only have dichotomous preferences (i.e. each voter's > SINCERE preferences sort the candidates into two groups, and the voter > is indifferent among candidates in the same group) then there is always > a Condorcet Winner, and approval voting always picks that candidate if > all voters vote sincerely. If preferences are restricted to those that can be expressed (as I was unthinkingly assuming) then Approval would indeed meet CC. However, as was explained on the electionmethods.org website, the whole point is that Approval doesn't allow you to fully express your preferences. Restricting the notion of "preference" would just be cheating. -Bill Clark -- Dennis Kucinich for President in 2004 http://kucinich.us/ ---- Election-methods mailing list - see http://electorama.com/em for list info
