By Toby Pereira, May 2016
| #voters | Their Vote |
|---|---|
| 3 | A>B>C |
| 2 | B>A>C |
| 2 | B>C>A |
| 2 | C>A>B |
A is the Condorcet winner, beating B pairwise by 5:4 and also beating C pairwise by 5:4. Also, A would win using "instant runoff voting" (C eliminated, then A defeats B 5:4). Now: remove two voters each of types "A>B>C," "B>C>A," and "C>A>B" (six removed in all) who all together should constitute a three-way tie. Then you are left with:
| #voters | Their Vote |
|---|---|
| 1 | A>B>C |
| 2 | B>A>C |
whereupon B becomes the Condorcet winner! Namely, B beats A pairwise by 2:1, and B also beats C pairwise by 3:0. And B also is the winner using "instant runoff voting."
This seems to demonstrate a self-contradiction within the Condorcet philosophy. (Also within the instant runoff philosophy.)
However, it does not demonstrate a contradiction for Borda voting; B is the Borda winner in both elections. To see a Borda self-contradiction, consider this.
Fishburn's anti-Condorcet example