[EM] mutual majority set

[Kevin Venzke]

Hi Kristofer,

--- En date de : Lun 7.2.11, Kristofer Munsterhjelm <km-elmet at broadpark.no> a écrit :
> > DEFINITION:
> > An ordinary (not mutual) majority set shall mean a
> candidate-subset
> > such that every member of the set is preferred
> pairwise versus every
> > candidate outside the set, by a majority (but the
> majorities as voter
> > subsets can vary).
> 
> Is that the same as the CDTT set? The CDTT set is like the
> Schwartz set, but the relation is "beats by a majority"
> rather than just "beats". You could make a ranking of sets
> by first having the top set, then the top set with these
> excluded, then the top set with those excluded, and so on.

This is more similar to Smith and CGTT than Schwartz and CDTT. As far
as I know you can't define the latter two with the wording "the (one and
only) smallest set that beats everyone outside the set." You have to
either use beatpaths in the definition or else speak of the "union of
all minimal non-empty subsets that don't lose to anyone outside."

The difference between Smith and Schwartz is usually small because they
only differ in the presence of pairwise ties, but the difference between
CGTT and CDTT is pretty large. For example if you have 3+ candidates
and only one majority-strength win, the CGTT always contains all the
candidates while CDTT already evicts the loser of that win.

Kevin