SCC — the spoiler, as a formal paradox

Felsenthal's SCC (subset choice condition) failure: a candidate who cannot win enters or leaves the race, and the winner changes. This is the formal name for the everyday spoiler effect — and in Felsenthal's taxonomy it's the model conditional paradox: hold every ballot's preferences constant, change one datum (who's on the ballot), and the outcome flips.

→ The full intuitive lesson: spoiler_effect.md · Glossary: spoiler effect · Felsenthal's taxonomy: README

The 7-voter demonstration

In BV2144 — Felsenthal Example 1, Choose-One elects Ana 3–2–2. Now let Cal — who finished last-equal and cannot win — withdraw. Cal's 2 voters both prefer Bo to Ana, so the same preferences count as Bo 4, Ana 3: Bo wins. Nothing about any voter's mind changed; a hopeless candidate's mere presence decided the election. Cal spoiled it for Bo.

Conditional, not simple

The other three paradoxes in BV2144 (Condorcet winner, Condorcet loser, absolute loser) are simple: the cast ballots alone produce the surprise. SCC needs the counterfactual — "what if Cal weren't running?" — which is exactly what makes it politically explosive: every real-world third-party candidacy is that counterfactual waiting to be argued about.

Which methods are vulnerable

Choose-One is maximally vulnerable — vote-splitting is the mechanism, demonstrated small in BV2144 and thematically in the split-voting set. RCV-IRV inherits it through center squeeze: a strong-but-eliminated candidate's presence can redirect eliminations (center_squeeze_irv). STAR sharply reduces it (supporting a doomed favorite at 5 doesn't take support away from a compromise you also score), though no method eliminates every variant. A close cousin is clone dependence — adding a copy of a candidate to exploit or suffer the subset effect — covered for Ranked Robin in rr_clone_independence.md.

Why it matters

The spoiler is the paradox voters have personally felt — "don't waste your vote" is SCC internalized as strategy. Showing it in seven ballots, then showing STAR count the same preferences without the spoil, is the shortest path from criterion to conviction.