[EM] Three rounds

[Raph Frank]

On Sat, Nov 15, 2008 at 8:36 PM, Kristofer Munsterhjelm
<km-elmet at broadpark.no> wrote:
> The single-winner criterion corresponding to the DPC is the mutual majority
> criterion. Any method that's Smith also passes mutual majority, and since
> Condorcet is just the case of the Smith set being a singleton, any Condorcet
> method passes the criterion when there's a CW.

Mutual majority looks the same as the Droop criterion, but for single
winner cases.

I wouldn't think much of a condorcet method that doesn't meet Smith,
but the two criteria aren't the same.

> But what would this multi-winner Condorcet criterion be? That's the
> question. One may also ask whether it's a desirable criterion (like
> Condorcet), or if it's too strict (like Participation).

If the objective is to find a multi-winner equivalent of the condorcet
criterion rather the Smith criterion, I am not so sure how useful that
is.

It would be a criterion that covers less cases than the Droop criterion.

Maybe

An outcome is not a valid outcome if there is any non-elected
candidate who is preferred to all the winning candidates by a Droop
quota of the voters.  No invalid outcome may be used unless there are
no valid outcomes.

This would be similar to re-defining the condorcet criterion as

A candidate shall be deemed an invalid winner if a majority prefer any
other candidate to that candidate.  An invalid candidate may not be
declared the winner unless there are no valid candidates.