Warren Smith wrote:
>see http://groups.yahoo.com/group/RangeVoting/message/2934 >for counterexample (plus linear program explainign how I found the >counterexample) >wds > > Ballots: > 6: A>B>C > 3: C>A>B > 4: B>C>A > > A wins under Simmons voting since > A beats B pairwise ==> 6 ballots count against B > C beats A pairwise ==> 3 ballots count against A > B beats C pairwise ==> 4 ballots count against C > > Now add two clones of A in a Condorcet cycle. > > Then A1 is beat pairwise by A2 with 1/3 of the 6 of the > A-top ballots, i.e. 3, and ditto A2 and A3, all have 2 > A-top ballots against them. > Plus, all the Ak have got C's toprank votes > against them, which is 3. So in total, each A-clone > has 5 ballots against it, while C has only 4 > ballots against it. > > Hence C is now the winner thanks to A's cloning. > > So SIMMONS IS NOT CLONEPROOF!! > If we agree only to clone non-winners, > or if, when cloning a winner, all voters agree to rank the clones > EQUALLY, THEN Simmons is cloneproof. > > Proof: > After cloning, > the A-beats-B relations are unaffected under these constraints, > and the number of top-rank-votes-against X are either unaltered - > or increased (increase is only possible for nonwinner X since > winning-X clones never pairwise-beat each other). > QED > > However... this weakened kind of cloneproofness is a good > deal less impressive than genuine cloneproofness. So Simmons meets Clone-Loser, but can fail Clone-Winner when there are three or more factions in a top cycle and the candidates in one of those factions are in a sub-cycle. That is a very very mild failure of Clone-Independence and arguably not a practical worry. If that is the full extent of the bad news (and maybe even if it isn't) then I think this method remains a great contender (for "best practical Condorcet method") because of its tremendous Burial resistance and simplicity. Chris Benham ---- election-methods mailing list - see http://electorama.com/em for list info