Dear Ted! You wrote: > At first, I didn't understand what Frest meant by 'transitive, but I gather > what he mans is, start a chain by adding the first candidate from the sorted > list (Call that candidate A_i), to the new chain (call that B_j). When adding > a new candidate, start at the winning end, and test to see if the candidate > defeats the first B_j. If not, follow the list down to the next weaker > candidate and test again. Repeat until you find a defeated candidate. Mark > the location, but don't insert the A into the B list. > > Then start testing from the losing end of the B list. If the A candidate > defeats the B candidate, continue following links to stronger B candidates. > > If you end up at the same spot each time, the A candidate isn't in a cycle, > and can be inserted. Otherwise, you're effectively eliminating it from > further consideration.
Right. > Thanks to both of your responses, I have an idea now that I think will work, > and it should have (my) desired quality of encouraging generous approval > cutoff and ranking of candidates below the cutoff. > > Basically, the idea is simply Beatpath: Break each cycle at the weakest link. > But what should be the weakest link? Why not call it the defeat made by the > candidate with lowest approval? We could call this Total Approval > Beatpath (TAB), but suggest a better name if you want. I was thinking about this when writing the grand compromise proposal but didn't propose it for some reason I don't remember, so I should give it another thought. Did you prove any nice properties yet? > This is similar to Jobst's grand compromise and James Green-Armytage's > Approval-weighted Pairwise, but it isn't necessary to carry along a second > pairwise array. Right. > Why might this be preferable to the other schemes mentioned? > > - There is a strong disincentive to bullet vote or truncate (an exercise for > the reader, but consider the 35:A>B>>C, 25:B, 40:C, in which B voters ahve > truncated their true preference 25:B>A>>C). > > - There is a strong incentive to be generous with approval cutoff -- you want > your nearest neighbors, if you will, to be considered earliest in the list. > > - Much less strategic incentive to equal rank due to the approval cutoff. > Voters can express true preferences above the approval cutoff, AND below, > without fear of hurting their candidate. Sounds promising, I'll think about that! Yours, Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info
