[EM] simple question (I think)
chrisbenham at bigpond.com
Wed Nov 16 21:05:48 PST 2005
rob brown wrote:
> For instance, say there is no Condorcet winner. Candidates A, B and C
> all have 8 pairwise wins. D has 7. Could D still be chosen as the
> winner by any "reasonable" method?
Yes. The method that just counts the number of pairwise wins is called
Copeland. It hopelessly fails Clone Independence (Clone-Loser) and
Imagine that that there are three candidates, each with the same number
of pairwise wins, and the Condorcet method elects X.
Say that the top cycle is X>Z>Y>X
Now say we add a clone of Y, that every voter ranks directly below Y.
Now Y and Z will each have an extra pairwise win, one more than X and so
now (by the "Copeland criterion") X must lose to Z or Y.
Adding a clone of a losing candidate (not to say adding a
Pareto-dominated candidate) has changed the winner.
Parties and factions that run more candidates will have an absurd and
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