Dear Forest! You wrote: > Unfortunately, reverse TACC is not monotonic with respect to approval. > If the winner moves up to the top approval slot without also becoming > the CW, she will turn into a loser.
That's right. You continued: > However, the following "chain filling" method is monotonic: > > Working from top to bottom of the approval list, fill in a chain by > incorporating each candidate that can be included transitively. The > candidate at the top of the resulting maximal chain is the winner. This is a nice idea, but upon closer inspection it turns out not to be monotonic, unfortunately. Look at this example: Assume the approval list from top to bottom is A,B,C,D,E, and the defeats are A>B>C>D>E>A>D>B<E>C>A. Then the chain filling begins A>B, C is skipped, D is added to give A>D>B, and E is skipped. Hence A wins. Now reverse the defeat C>A into A>C without changing approvals. Then the chain filling begins A>B>C, D is skipped, and E is added to give E>A>B>C. Hence E wins although the original winner A was raised. > As mentioned above, I wanted to work top down so that I would come to > the Pareto dominators before getting to the Pareto dominated candidates. > Then it doesn't matter if the Pareto dominated candidates are eliminated > at the beginning; the rest of the chain will be the same, including the > top candidate. That's a good point! I think that for this reason, we should proceed trying to find a variation which works top down. Yours, Jobst ---- Election-methods mailing list - see http://electorama.com/em for list info
