A 100-voter Condorcet election example

By Warren D. Smith, Feb. 2014

#voters Their Vote
35 A>B>C
21 B>A>C
21 B>C>A
21 C>A>B
1 A>C>B
1 C>B>A

A is the Condorcet winner, beating B pairwise by 57:43 and also beating C pairwise by 57:43. Now: one voter each of types "A>C>B," "B>A>C," and "C>B>A" – as well as 21 voters each of the types "B>C>A," "C>A>B," and "A>B>C" (which form a reversed-direction cycle) – all together should constitute a three-way tie. So those votes should cancel out. If we remove those 66=21×3+3 "cancelled out" ballots, then we get:

#voters Their Vote
14 A>B>C
20 B>A>C

whereupon B becomes the Condorcet winner! Namely, B beats A pairwise by 20:14, and B also beats C pairwise by 34:0. (And B is the IRV winner, and also Borda winner, in both elections.)

This seems to demonstrate a self-contradiction within the Condorcet philosophy.

Fishburn's anti-Condorcet example

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