A 9-voter 3-candidate election example suggesting something is wrong with
both instant runoff and Condorcet

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.