On 24 Feb 2005 at 12:24 PST, Paul Kislanko wrote: > > >> -----Original Message----- >> From: [EMAIL PROTECTED] >> [mailto:[EMAIL PROTECTED] >> ] On Behalf Of Ted Stern >> Sent: Thursday, February 24, 2005 1:05 PM >> To: [EMAIL PROTECTED] >> Subject: [EM] Re: Condorcet package >> I used 'relative margins' when what I meant to say was 'margins'. > > Well, thanks for clearing THAT up. Neither is well-defined.
Context: We're discussing how to use the pairwise matrix, "A", to determine the winner in a Condorcet completion scheme when there is no Condorcet winner (CW). In the pairwise matrix, the location A_{i,j} indicates the number of votes for the i-th candidate [C_i] against the j-th candidate [C_j]. In terms of the pairwise matrix, a candidate C_k is the Condorcet Winner when A_{k,j} is greater than A_{j,k} for each j not equal to k. Since there is no such k, most robust completion schemes under discussion rank the defeats C_i > C_j. Here's how winning votes and margins rank them: Winning votes: A_{i,j} Margins: A_{i,j} - A_{j,i} I'm not entirely sure what Relative Margins are relative to, but this is my current understanding: Relative Margins: (A_{i,j} - A_{j,i}) / (A_{i,j} + A_{j,i}) If you're still unclear on these concepts, please search the list archives or start delving (and contributing) on the Election Methods Wiki: http://wiki.electorama.com/wiki/Main_Page I notice that the Ranked Pairs page on this site (copied from Wikipedia) is Tideman's original version, which uses Margins. Steve Eppley's MAM version uses winning votes. And no, there is no definition of winning votes or margins there. Ted -- Send real replies to ted stern at u dot washington dot edu Frango ut patefaciam -- I break so that I may reveal ---- Election-methods mailing list - see http://electorama.com/em for list info