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The Non-Monotonicity Files 🍿 — a (guilty-pleasure) collection

⚠️ House-rules exemption in effect. This page is the repo's guilty pleasure: a deliberately one-sided montage of RCV-IRV punishing candidates for gaining support — and rewarding them for losing it. It breaks the library's own fairness rule on purpose, and it isn't linked from any index. Two honest promises anyway: every example below is real and verified elsewhere in this repo (the curation is the unfair part, never the facts), and the grown-up, even-handed version — rarity stated, STAR's own limits conceded — is always one click away in the monotonicity worked set and the concept page. Read it as a highlight reel, not a courtroom. And for turnabout: we threw the same unfair mud at our own method in the STAR Whoops reel — because every method has one.

Monotonicity is the one property you'd swear any voting method has: ranking a candidate higher can't make them lose, and lower can't make them win. Instant-runoff cheerfully violates both directions, because it eliminates on first-choice counts and elimination order is fragile. Here's the reel.

🥇 Real elections that actually did this

  • Burlington, VT 2009 (Mayor). The certified, real 8,980 ballots. Montroll beats every rival head-to-head (5–0, a Condorcet winner) — and IRV eliminates him in the semifinal. Worse: raise the winner Kiss on 750 of the real ballots and he loses. Burlington repealed IRV the next year. → Burlington 2009, runnable.
  • Alaska 2022 (US House special). Give the winner more: had ~6,000 Palin-only voters ranked the winner Peltola first, Peltola would have lost — the extra first-place votes eliminate Palin first, and Begich beats Peltola. Ranking the winner higher defeats her. → upward monotonicity, Alaska.
  • San Francisco D7 2020 (Supervisor). The mirror, also real: shift the loser Engardio down on ~800 ballots and he wins — the shift eliminates Melgar first (by 3 votes) and Engardio takes the final. Less support, more victory. → downward monotonicity, San Francisco.

🥈 The lab specimens (clean, minimal, runnable)

  • The textbook pair. 4 voters raise X from second to first — X goes from winning to losing, nothing else changed. → monotonicity worked set.
  • Best = worst. A 24-voter election where IRV elects A whether the voters are picking the best candidate or reverse every ballot to pick the worst. Its "best" and "worst" are the same guy. → reversal symmetry.

🥉 …and it's not even rare

A spatial-model study (Ornstein & Norman, Public Choice 2014) estimates a lower bound of ~15% monotonicity failure in competitive three-candidate IRV races — climbing toward 50% as the race tightens. Not a freak coincidence; a structural feature of eliminate-and-transfer. → the concept, with the citation.

The obligatory conscience clause

Okay, fine — the fair version, because the repo insists and it's the honest one:

  • Monotonicity failures are real but concentrated in close, near-three-way races; most IRV elections never trip one.
  • The failure is IRV-specific, not "ranked voting" — Ranked Robin and other whole-ballot methods are monotonic.
  • STAR isn't perfectly clean either — it passes mono-raise but fails the stronger mono-raise-delete in lab constructions (conceded here).
  • Both STAR and IRV beat Choose-One by a mile; the honest debate is between good options.

There. Now you can go back to enjoying the reel — responsibly. For the version you'd actually cite in a debate, use the worked set and read it fairly.