[Election-Methods] Landau and Schwartz set

[Rob LeGrand]

Kevin Venzke wrote:
> --- Rob LeGrand <honky1998 at yahoo.com> a écrit :
> > 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 what
> > 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?

Yeah, I was a bit hasty as I wrote that.  The above makes rough intuitive
sense, but carefully defining a "Schwartz-Landau" set may be a bit
trickier than I assumed because of the precise way Schwartz must be
defined so as to avoid the empty set.  I'll investigate defining a
Schwartz-Landau set when I can make the time, unless Markus or someone
else has already thought about it.

--
Rob LeGrand, psephologist
rob at approvalvoting.org
Citizens for Approval Voting
http://www.approvalvoting.org/


       
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