[Election-Methods] Landau and Schwartz set

[Rob LeGrand]

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.

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


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