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