IRV favorite betrayal example by Adam Tarr (not involving any "cycle")

(More detailed look)

#voters Their Vote
45 A>B>C
10 B>A>C
10 B>C>A
35 C>B>A

In this 100-voter example election, under IRV, "A" wins. ("B," with the fewest top-rank votes, is eliminated in the first round then A wins 55 to 45 over "C".) This is a fairly realistic scenario of the sort that arises with voters and candidates positioned along a one-dimensional line.

Now suppose eight voters in the bottom faction cleverly (but dishonestly) switch their top-two preference order, "betraying" their favorite C. Result:

#voters Their (new) Vote
45 A>B>C
10 B>A>C
18 B>C>A
27 C>B>A

Then "C" is eliminated in the first round, and then in the second round "B" wins over "A" 55-to-45. From those 8 voters' point of view, this was an improvement. The betrayal worked.

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