The Condorcet loser paradox¶
A Condorcet loser loses to every other candidate head-to-head. The Condorcet loser paradox is a voting method electing that candidate anyway — the one contender the electorate pairwise-rejects against all comers. (A simple paradox in Felsenthal's taxonomy: no hypothetical change is needed; the ballots as cast do it.)
→ Glossary: Condorcet loser · Felsenthal's taxonomy: README
The 7-voter demonstration¶
In BV2144 — Felsenthal Example 1, Ana loses to Bo 3–4 and to Cal 3–4 — Ana is the Condorcet loser. Choose-One elects Ana anyway, because Ana's 3 first-choice votes top Bo's 2 and Cal's 2. Every voter who didn't put Ana first put Ana last, and the count never looks.
In the same election Ana is also the absolute loser (a majority ranks Ana last) — the stronger form, with its own page. Every absolute loser is a Condorcet loser; the reverse doesn't hold.
Which methods are vulnerable¶
| Method | Vulnerable? | Why |
|---|---|---|
| Choose-One (Plurality) | Yes | A cohesive minority's favorite can top a split majority — BV2144 |
| Approval | Yes (possible) | Approval counts don't consult pairwise preferences |
| RCV-IRV | No | The final round is a head-to-head; a Condorcet loser loses it |
| STAR | No | Same shield: the automatic runoff is a head-to-head the Condorcet loser cannot win |
| Ranked Robin | No | A Condorcet loser has zero pairwise wins and can never have the most |
This is a paradox where RCV-IRV genuinely does well — the repo's critiques of IRV (center squeeze, exhausted ballots, non-monotonicity) are about other failures, and fair treatment means saying so. See reading_these_fairly.md.
Why it matters¶
Electing a Condorcet loser is the clearest possible "wrong winner": for every alternative individually, a majority of expressed preferences said "not this one." Choose-One is the only widely used method that can do it — and it does it with just 7 voters.