[Election-Methods] RE : Landau and Schwartz set

[Kevin Venzke]

John,

--- John Wong <johnwong00 at hotmail.com> a écrit :
> I know that the Landau set is a subset of the Smith set, and I know that
> Schwartz set is a subset of the Smith set, but is Landau set the subset
> of the Schwartz set, or is the Schwartz set the subset of the Landau set?
> Or is it entirely something else?

The Landau set is a subset of the Schwartz set, also. Any candidate who
has a beatpath of length 1 or 2 to every other candidate (Landau 
requirement) also has a beatpath of any length to them (Schwartz 
requirement).

> Does the Schwartz set violate anything that the Smith doesn't violate?

Not that I'm aware of. Schwartz is a little "better" than Smith because
it excludes candidates who are only in the Smith set due to pairwise ties.

> How important is the Schwartz criterion?

This is a difficult question. Criteria related to pairwise wins (such
as Condorcet, Smith, Schwartz) do a lot to reduce voters' need to vote
insincerely. There are some criteria related to certain scenarios or
certain types of insincere voting that are too strong to be compatible
with Schwartz. If you're insistent on one of these criteria, then that
might be a good reason to not use Schwartz. In general though, Schwartz
etc. are very useful.

Kevin Venzke


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