(You sent this personally to me, not to the list.) I still don't understand it. My time is quite limited, so if I can't get it by reading it over, I don't have time to figure out what each clause might possibly mean. That's the kind of analysis it would take. I assume that you *do* mean something, that there is a defined method, but I could not even come close to applying it to a vote. I don't understand *at all* how you derived the winner from the votes.
But this stares me in the face. From the presented vote data, B should *clearly win,* though this violates the Majority Criterion. Your method, apparently, selects A. I'm not highly motivated to figure out how a complicated method that seems to pick the wrong winner works! At 04:37 PM 10/26/2006, Juho wrote: >As promised in my previous mail here are some example calculations to >demonstrate how the Ranked Preferences work. Plus some additional >notes at the end. > >- I use * to mark numbers that are based on the tied at top/bottom >rules. >- I use "A-B" as a shorthand for "A compared to B" >- I use "[ ]" to mark changes in the preference matrix calculations > > >Example 1. > >55: A>B>>C >45: B>>A>C > >A-B = +55* -45 = +10 >A-C = +55 -45* = +10 >B-A = +55* +45 = +100 >B-C = +55 +45 = +100 >C-A = -55 -45* = -100 >C-B = -55 -45 = -100 > >C will be eliminated. Top strength of the 55 first votes is now ">". > >A-B = [+55] -45 = +10 >A-C = +55 -45* = +10 >B-A = [-55] +45 = [-10] >B-C = +55 +45 =+100 > >B will be eliminated. A wins. > >Having majority of the voters on A side made her the winner. > > >Example 2. > >40: A>>C>B, 40: B>>C>A, 20: C > >A-B = +40 -40 -20* = -20 >A-C = +40 -40* -20 = -20 >B-A = -40 +40 -20* = -20 >B-C = -40* +40 -20 = -20 >C-A = -40 -40* +20 = -60 >C-B = -40* -40 +20 = -60 > >C will be eliminated. Top strength of the last 20 votes is still >">" (the minimum level). > >The matrix values will be the same. > >A-B = +40 -40 -20* = -20 >A-C = +40 -40* -20 = -20 >B-A = -40 +40 -20* = -20 >B-C = -40* +40 -20 = -20 > >Either A or B is eliminated and the other one will be the winner. > >Flat preferences Condrcet winner was eliminated since she was >disliked by 80% of the voters. > > >Here are some more comments on the method that I missed in my first >description of it. > >I should have included this rule (maybe obvious but maybe better to >explain still). >- The strength of preference when comparing two candidates on a >ballot is the strongest preference relation between these two candidates > >I should have defined as well: >- The top strength of a ballot is always ">" or higher > >One possible maybe interesting option that I didn't mention is not to >use the tied at top or tied at bottom rules when there are no >stronger preferences than ">". This makes the "flat preferences" case >more similar to traditional Condorcet methods. This might be of >interest if majority of the voters do not bother to use the stronger >preferences but rely on basic Condorcet instead. > >Juho Laatu > >Send instant messages to your online friends http://uk.messenger.yahoo.com ---- election-methods mailing list - see http://electorama.com/em for list info
