# [EM] Geometric Condorcet cycle example, improved

fsimmons at pcc.edu fsimmons at pcc.edu
Tue Dec 29 14:54:13 PST 2009

```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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