Warren,Thanks for upgrading my example to be valid for the L^1 through
L^infinity cases. Of course, it's still true that four points are needed,
since the proof that there is no example like this with three relies only on
the triangle inequality, which is satisfied for any metric.Jobst,I remember
that example, and I'm sure that it was a subconscious
influence on my trapezoid example. Certainly, your point in the last
paragraph
Aren't such examples a good reason to always consider more than just onepiece
of the information (like approval or ranks or defeats or directsupport) and
instead combine them to get the whole picture?is the most important lesson to
learn from such examples.Guten Rutsch,Forest
- Original Message -From: Jobst Heitzig Date: Tuesday, December 29,
2009 4:51 amSubject: Re: [EM] Geometric Condorcet cycle example, improvedTo:
Warren Smith Cc: election-methods , Forest W Simmons Hi folks, I just
recalled that four years ago I constructed a sophisticated example which is
somewhat similar: http://lists.electorama.com/htdig.cgi/election-methods-
electorama.com/2005-May/015982.html Happy New Year! Jobst Warren Smith
schrieb: This point-set also works: A=(1,0) B=(0,4) C=(3,5) D=(9,2)
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