1. condorcet.org definitions page: "Name: Condorcet Criterion Application: Ranked Ballots Definition: If an alternative pairwise beats every other alternative, this alternative must win the election. Pass: Black, Borda-Elimination, Dodgson, Kemeny-Young, Minmax, Nanson (original), Pairwise-Elimination , Ranked Pairs, Schulze, Smith//Minmax, Sum of Defeats Fail: Borda, Bucklin, Coombs, IRV"
2. wikipedia: "The Condorcet candidate or Condorcet winner of an election is the candidate who, when compared in turn with each of the other candidates, is preferred over the other candidate." 3. http://accuratedemocracy.com/z_words.htm: "The Condorcet candidate in a multi-candidate elections that candidate, if one exists, who could beat each of the others in separate pairwise contests,i.e., is preferred to each of the others candidates by a majority." * according to def1, range voting either is or is not a condorcet method depending on the meaning of "pairwise beats." Condorcet.org has a hyperlink on "pairwise beats" (that does not show up in this plaintext snarf) that says they mean majority vote based on the stated rankings <,> relations in the ballots. However, they could have left it with no hyperlink and just based it on whatever voting method was under test, in which case their definition would have been unchanged as far as every single method they ever tested it on (those they mentioned under pass/fail), or Condorcet himself ever tested it on, or (as far as I can tell) the entire polysci literature has ever tested it on, would have been concerned. (Note that, revealingly, they do not consider range voting or plurality voting to either pass or fail.) This no-hyperlink choice is in fact a plausible way to go because then the condorcet criterion is about the logical self-consistency of a method, as opposed to the consistency of method A as judged using method B, which is kind of an unfair pre-biased way to judge A. * According to def2, range voting either is or is not a condorcet method depending on the meaning of "is preferred". * As far as I can tell, the EM people arguing with me prefer def1 (and with hyperlink used). * def3 and arguably def2 in fact DISAGREE with def1. That is because as I remarked in an earlier post, voters who in an N-candidate election ranked A>B in their vote, do not necessarily actully prefer A over B, and may prefer B over A. >tarr: >As a math major, you surely understand that without agreed-upon >definitions, we may as well be arguing in different languages. Define >your criteria. Call it whatever you like. But it is not the >Condorcet criteria, which is already well-defined and cannot be >changed on your whim. --Actually, as a math PhD, what I understand is that the Condorcet criterion is NOT "already well-defined" as I have just proven by exhibiting conflicting incompatible definitions, as well as ambiguous definitions, as well as subtleties the previous definers obviously did not even recognize existed (and the entire polysci literature as far as I know did not recognize existed, far as I can tell by reading re this). I also understand that when one encounters such a situation, it is one's duty to clear up the ambiguity and do better. I have done so. Tarr however has not done so and instead has denied this reality. I suggest to you that that my approach in this case, is superior. The situation is mildly analogous to sqrt(x) which "does not exist" if x<0. Later it was realized the reals are a subfield of the complex numbers and sqrt(x) can and should be defined more generally. There were indeed people who tried to say things like "you are not allowed to on whim do this". They are in the dustbin of history. Now analogously, here we have a definition (Condorcet) defined for ranked ballot voting methods by people who had never conceived of more general kinds of numbers than reals, oh sorry, I mean more general kinds of voting methods. We now generalize our purview to allow complex numbers not just real numbers, oh sorry, I mean more general voting methods than ranked ballot methods. In that case, we have to ask how best to try to generalize the definition of "condorcet." I have shown there are two ways to do so, both of which coincide with the old definition whenever x is real, oops, I mean, which coincide with the old def whenever X is a ranked-ballot mehtod, but which do not coincide when X is range voting. That is the situation. It is no whim. wds ---- Election-methods mailing list - see http://electorama.com/em for list info