Hi Chris, You discuss Winning Votes vs. Margins below.
What do you think about using the Cardinal-Weighted Pairwise array in conjunction with the traditional Condorcet array? In other words, either WV or Margins is used to decide whether there is a defeat, but the CWP array is used to determine the defeat strength, in either Ranked Pairs or Schulze. To recap for those not familiar with the technique (due to James Green-Armytage in 2004), a ratings ballot is used: give a score of a_i to candidate i. Ranks are inferred: candidate i receives one Condorcet vote over candidate j if a_i > a_j. Whenever that Condorcet vote is recorded into the standard A_ij array, you also tally the difference (a_i - a_j) into the corresponding CWP_ij location. Ted On 08 Nov 2012 08:55:24 -0800, Chris Benham wrote: > > Robert Bristow-Johnson wrote (1 Oct 2012): > > "my spin is similar. Ranked Pairs simply says that some "elections" (or > "runoffs") speak more loudly than others. those with higher margins are > more definitive in expressing the will of the electorate than elections > with small margins. of course, a margin of zero is a tie and this says > *nothing* regarding the will of the electorate, since it can go either way. > > the reason i like margins over winning votes is that the margin, in vote > count, is the product of the margin as a percent (that would be a > measure of the decisiveness of the electorate) times the total number of > votes (which is a measure of how important the election is). so the > margin in votes is the product of salience of the race times how > decisive the decision is." > Say there are 3 candidates and the voters have the option to fully rank them, > but instead they all just choose to vote FPP-style thus: > > 49: A > 48: B > 03: C > > Of course the only possible winner is A. Now say the election is held again > (with > the same voters and candidates), and the B voters change to B>C giving: > > 49: A > 48: B>C > 03: C > > Now to my mind this change adds strength to no candidate other than C, so the > winner > should either stay the same or change to C. Does anyone disagree? > > So how do you (Robert or whoever the cap fits) justify to the A voters (and > any > fair-minded > person not infatuated with the Margins pairwise algorithm) that the new > Margins > winner is B?? > > The pairwise comparisons: B>C 48-3, C>A 51-49, A>B 49-48. > Ranked Pairs(Margins) gives the order B>C>A. > > I am happy with either A or C winning, but a win for C might look odd to > people > accustomed > to FPP and/or IRV. > > *If* we insist on a Condorcet method that uses only information contained in > the pairwise > matrix (and so ignoring all positional or "approval" information) then *maybe* > "Losing Votes" > is the best way to weigh the pairwise results. (So the strongest pairwise > results are those where > the loser has the fewest votes and, put the other way, the weakest results are > those where the > loser gets the most votes). > > In the example Losing Votes elects A. Winning Votes elects C which I'm fine > with, but I don't > like Winning Votes for other reasons. > > Chris Benham > > > ---- > Election-Methods mailing list - see http://electorama.com/em for list info -- PO Box 3707 MC 0R-JF (Google Voice) 206-552-9611 Seattle, WA 98124-2207 (Fax) 425-717-3652 http://directorysearch.web.boeing.com/bps/details.asp?bemsid=1660261 ----------- Frango ut patefaciam -- I break so that I may reveal ----------- -- araucaria dot araucana at gmail dot com ---- Election-Methods mailing list - see http://electorama.com/em for list info
