Best-is-worst paradox

Condorcet methods Positional voting Cardinal voting Quota-remainder methods Approval-based committees Fractional social choice Semi-proportional representation By ballot type Pathological response Strategic voting Paradoxes of majority rule Positive results In social choice theory, the best-is-worst paradox occurs when a voting rule declares the same candidate to be both the best and worst possible winner.

Methods that satisfy reversal symmetry include the Borda count, ranked pairs, Kemeny–Young, and Schulze.

Best-is-worst paradoxes can occur in ranked-choice runoff voting (RCV) and minimax.

A well-known example is the 2022 Alaska special election, where candidate Mary Peltola was both the winner and anti-winner.

Assume four candidates A, B, C and D with 14 voters with the following preferences: Since all preferences are strict rankings (no equals are present), all three Minimax methods (winning votes, margins and pairwise opposite) elect the same winners.

D benefits from that since its two losses are relatively close and therefore D's biggest defeat is the closest of all candidates.

Therefore D's biggest defeat is the closest of all candidates, and D is elected Minimax winner.