Relative margins were an attempt to obtain a behaviour between margins and winning votes ( relative margins are thus relative to the number of expressed ballots).
As the result was not the one expected, maybe weighted margins would lead to some truncation resistance using a margin-based criteria. Although I would fid it harder to justify such a criteria. At least relative margins corresponded to the case "unexpressed preferences are interpreted like disinterested voters trusting other voters who took the time to express a preference". Margin is equivalent to a 50/50 split of unexpressed preference, and winning votes simply discards unexpressed preferences as if the elector did not vote. I have no idea how to interpret weighted margins... Relative Margins: (A_{i,j} - A_{j,i}) / (A_{i,j} + A_{j,i}) Weighted Margins: (A_{i,j} - A_{j,i}) * (A_{i,j} + A_{j,i}) Steph Ted Stern a écrit : > 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 ---- Election-methods mailing list - see http://electorama.com/em for list info