[EM] Methods which refuse to identify a winner sometimes

[Andy Jennings]

On Wed, Jun 13, 2012 at 1:39 AM, Nicholas Buckner <nlborlcl at gmail.com>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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