[Election-Methods] RE : Re: Landau and Schwartz set

[Kevin Venzke]

Rob,

--- Rob LeGrand <honky1998 at yahoo.com> a écrit :
> Kevin Venzke wrote:
> > The defeats are A>B, B>C, A=C. What reasoning do you use to find that
> > B and C are in the Landau set? I gather I don't have a complete
> > understanding of what Landau refers to, but I'm very surprised if the
> > definition is such that a Landau winner can fail to be a Schwartz
> > winner.  This makes Landau seem less worthwhile to me, since Schwartz
> > is more intuitive.
> 
> I'm using what I believe is Markus Schulze's definition of Landau
> winners:
> 
> "Candidate A is a Landau winner iff for every other candidate B at least
> one of the following two statements is correct:
> (1) A >= B.
> (2) There is a candidate C such that A >= C >= B."
> 
> where >= means "beats or ties pairwise".  It's the same thing as Smith
> except that the beatpaths can be of length at most two.  You could easily
> define a "Schwartz-Landau" set that may give you want you were expecting
> by changing "beats or ties pairwise" in the above definition to "beats
> pairwise".  Such a set would always be a subset of the Landau set and of
> the Schwartz set.

Ok. In either case, isn't it conceivable that the set is totally empty?

Kevin Venzke


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