[EM] mutual majority set

[Kevin Venzke]

Hi Kristofer,

--- En date de : Lun 7.2.11, Kristofer Munsterhjelm <km-elmet at broadpark.no> a écrit :
> > Hi Kristofer,
> > 
> > --- En date de : Lun 7.2.11, Kristofer Munsterhjelm
> <km-elmet at broadpark.no>
> a écrit :
> 
> >> 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."
> 
> According to the Electorama wiki, the CDTT set is "the
> union of all minimal nonempty sets of candidates such that
> no candidate in each set has a majority-strength pairwise
> loss to any candidate outside of the set". That sounds more
> like the Schwartz set (union of minimal nonempty sets) than
> the Smith set (smallest set that beats all outside it).
> 
> Is the wiki wrong? I haven't investigated CDTT in detail,
> but it seemed similar.

No, it is correct. CDTT is to Schwartz as CGTT is to Smith. But regarding
this idea (that I think I am reading correctly) that you might find a
hierarchy of (mutual) majority-like sets, I doubt it can be applied to
CDTT or Schwartz. Mutual Majority's definition is a lot more like Smith
and CGTT.

Kevin