A Helpful Vote That Hurts

Twenty-four voters rank candidates A, B and C. The ballots are: - 8 voters: A > B > C - 3 voters: B > A > C - 7 voters: B > C > A - 6 voters: C > B > A The election uses instant-runoff voting (IRV): if no candidate has a majority (more than half) of first-choice votes, the candidate with the fewest first-choice votes is eliminated and each of their ballots moves to its highest-ranked remaining candidate; this repeats until someone has a majority. Currently B wins. What is the smallest number of voters who can change their ballots (each to any ranking they like) so that C wins? A tie for elimination counts as a failure (no winner is declared).

• game theory

Source: Instant-runoff voting and its failures of monotonicity are discussed widely in the social-choice literature (see e.g. Brams and Fishburn); the electorate is invented for AxiomIQ. Statement written for AxiomIQ.