On Wed, Jun 13, 2012 at 1:39 AM, Nicholas Buckner <[email protected]>wrote:
> Actually, on a weird second thought, wouldn't a method that refused to > identify a winner in a three-way tie (Condorcet paradox) be compatible > with both? It would be I guess case 5 (A, B, C, D, no winner). It > wouldn't be a very practical method, as we need our voting methods to > decide ties, but isn't deciding the tie what breaks the Participation > criterion? My voting method only made the mistake of picking a winner > in the first place (a mistake I'd happily do again). > Occasionally we talk about methods that refuse to identify winners in some situations. After all, "unrestricted domain" _is_ one of the conditions of Arrow's impossibility theorem. But usually that criterion is considered so obvious that we don't talk about it. I don't even mention "unrestricted domain" when I explain Arrow's theorem to someone for the first time. If you only consider the domain where there are no cycles, then "Condorcet" is a single method and it meets Arrow's other criteria perfectly. ~ Andy
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