Example of Instant Runoff Voting insanity

Let there be 15 voters and four candidates named A, B, C, and D.

#voterstheir vote
3 A>D>C>B
3 B>D>C>A
2 C>D>A>B
2 D>A>B>C
1 A>C>B>D
1 B>C>D>A
1 C>B>D>A
1 C>D>B>A
1 D>B>C>A

With Instant Runoff (IRV) voting, A wins this election. (First D is eliminated, then C, then B.) Thus IRV is saying that A is the best candidate, followed by B, C, and D in that order.

But now suppose C drops out. Now the results are completely reversed: D wins, followed by B and A.

If instead B drops out, then D wins, followed by C and A.

Finally if A drops out, then D wins, followed by C and B.

In short, Instant Runoff says A>B>C>D – but if anybody besides D drops out, then it orders the candidates in exactly reversed order. IRV can say somebody is the best candidate, then turn around and say that same person is the worst. It must have been wrong at least one of those times. And the consequence can be that we elect the worst instead of the best candidate, which is very bad news for your country.

You might want to consider range voting instead.

Actually in this election, there are good arguments that D is the best (not the worst as IRV says) candidate: namely D beats every rival pairwise by at least a 9-to-6 majority and D also is the Borda winner and the winner with approval voting if each voter approves her top-two choices. You can also see a related insanity but instead for plurality voting, and another of similar ilk for Borda voting.

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