Instant runoff does not satisfy the Condercet criterion.
Fact: Instant runoff does not satisfy the Condercet criterion.
Proof: We prove this with an example using 5 voters and 3 candidates.
1st Choice A B A B C 2nd Choice C C C C A 3rd Choice B A B A B
There is no majority winner as no candidate has more than 40% of 1st choices. C has only one first choice and would be eliminated in the first round of instant runoff. At this point A would have 3/5 1st place votes and win the instant runoff election.
We see that C is the Condercet winner. C is preferred to B in columns 1, 3, and 5. C is preferred to A in columns 2, 4, and 5.☐
This example also appears in context on my Social Choice Theory page.
