[private mail!] Dear Forest,
seems promising. But I'm a bit sceptical concerning IPDA. Can you prove it? Yours, Jobst PS: Can we object anything to Mike's truncation examples? > Here's a Monotone method (UncDMC) that chooses from the uncovered > set, and always picks the DMC winner in the three candidate case: > > 1. List the candidates in approval order, highest to lowest, top to > bottom. > > 2. Modify the list according to the following rule: as long as some > candidate in the list is pairwise defeated by its immediate inferior > in the list, swap the members of the highest such pair in the list. > > 3. Initialize a set S with the highest member of the modified list. > As long as no current member of S is uncovered, add to S the highest > member of the modified list that covers each of the current members > of S. > > 4. The last candidate added to S is the winner. > > This UncDMC method is monotone, clone proof, independent from Pareto > dominated alternatives, and independent from Smith dominated > alternatives, and always picks from the uncovered set. > > If I am not mistaken, previously, the only known deterministic method > to satisfy all of these criteria was Jobst's TACC. > > A careful comparison of UncDMC and TACC in the three candidate case > would be helpful. > > The UncDMC winner is either the DMC winner or a candidate that covers > the DMC winner. In the three candidate case the DMC winner is always > uncovered, so it is also the UncDMC winner. > > We ought to examine three candidate cases where DMC and TACC produce > different winners. > > Now a proof of UncDMC's monotonicity: > > Suppose that the UncDMC winner X improves in approval or in pairwise > defeats relative to the other candidates (which retain their same > relative approvals and pairwise defeats relative to each other). > > Then X is still uncovered, X still covers all of the candidates that > it covered before, and the part of the modified list above X is a > subset (in the same order) of the part of the modified list that was > above X before X's improvement. > > So X will still be the last member added to the set S, retaining the > win. > > Thanks, > > Forest > ---- > election-methods mailing list - see http://electorama.com/em for list > info
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