The absolute loser paradox

An absolute loser is a candidate whom an outright majority of voters rank dead last. The absolute loser paradox is a voting method electing that candidate anyway. (A simple paradox in Felsenthal's taxonomy — and the most viscerally wrong-feeling one: most voters said "anyone but this one," and got this one.)

→ Glossary: absolute loser · Felsenthal's taxonomy: README

The 7-voter demonstration

In BV2144 — Felsenthal Example 1, 4 of 7 voters — a majority — rank Ana last. Choose-One elects Ana: her 3 first-choice votes beat Bo's 2 and Cal's 2, and the ballot never records what the other 4 voters think of her. The majority's shared bottom choice wins because their first choices split 2–2.

Relation to the Condorcet loser

The absolute loser is the stronger condition: if a majority ranks Ana last, then in every pairwise matchup that same majority prefers Ana's opponent, so an absolute loser is always a Condorcet loser too. The reverse doesn't hold — a Condorcet loser can lose each matchup to different coalitions without any single majority ranking them last.

Which methods are vulnerable

The immunities mirror the Condorcet loser paradox, since electing an absolute loser implies electing a Condorcet loser: Choose-One (Plurality) is vulnerable — BV2144 shows it with 7 voters; RCV-IRV, STAR, and Ranked Robin are not (each ends in, or is built from, head-to-head comparisons an absolute loser cannot survive). Approval sits in between: it can't see "ranked last," but a candidate approved by fewer than half the voters can still win if everyone else is approved by fewer.

Why it matters

"The majority's last choice won" is the one-sentence indictment of choose-one voting — no pairwise table needed, no criterion jargon. It's the sharpest single fact to hand a debate audience, and it takes only seven ballots to make it real: run the case or see it live on BetterVoting.