[EM] Three rounds

[Raph Frank]

On Mon, Nov 17, 2008 at 2:35 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> That rule would admit more sets than the DPC. Call the candidates that a
> Droop quota supports above the others, "Droop CWs". Your criterion basically
> says "if you're picking k winners, and there are at least k Droop CWs, all
> the winners have to be Droop CWs; if there are less than k Droop CWs, those
> have to be included in the winning set".

I am not 100% sure that is equivalent to what I suggested, but seems reasonable.

> I guess that shouldn't surprise us; since Condorcet doesn't imply Mutual
> Majority, a multiwinner Condorcet criterion wouldn't imply the DPC either.
> However, the failure mode is different. Condorcet fails MM only when there's
> no CW (and the Condorcet criterion can't say which candidate you should
> elect); however, this fails even when there are Droop CWs (since we know
> Condorcet and the DPC is incompatible, and that a Condorcet winner must also
> be a Droop CW).

Well, it fails multi-winner condorcet when there isn't enough Droop
CWs.  The difference in the single winner case is that only a single
winner is required.

> So we may need a Smith set, and that set would have to be defined so that
> electing from it implies DPC. I have no idea how it would actually be
> defined, though.

Maybe, base it on Copeland;

A candidate shall be deemed to defeat an outcome if he is preferred to
all winning candidates in the outcome by a Droop quota.

The final outcome must be one of the outcomes which ties for fewest defeats.