[EM] Simmons Condorcet Cycle geometric example
Warren Smith
warren.wds at gmail.com
Tue Dec 15 08:10:53 PST 2009
> Here's a natural scenario that yields an exact Condorcet Tie:
A together with 39 supporters at the point (0,2)
B together with 19 supporters at (0,0)
C together with 19 supporters at (1,0)
D together with 19 supporters at (4,2)
D is a Condorcet loser.
A beats B beats C beats A, 60 to 40 in every case.
Think of four cities represented by A, B, C, and D respectively, with
the pairwise distances in miles calculated from the above planar
coordinates:
A B C D
D 4 20^(1/2) 14^(1/2)
C 5^(1/2) 1
B 2
Assuming voters prefer candidates closer to them, the ballots are:
40: A>B>C>D
20: B>C>A>D
20: C>B>A>D
20: D>C>A>B
---- See http://rangevoting.org/CondorcetCycles.html
and there is a pretty picture there, basically taken from Poundstone's book,
showing how a Condorcet cycle can arise in a geometrical manner like this.
His cycle maybe is not as nice mathematically as Simmons', but it works.
--
Warren D. Smith
http://RangeVoting.org <-- add your endorsement (by clicking
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and
math.temple.edu/~wds/homepage/works.html
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