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The Upward Monotonicity Paradox — when ranking the winner higher makes her lose (Alaska 2022)

A voting method should never punish a candidate for gaining support. RCV-IRV can. In the real Alaska 2022 US House special, had about 6,000 Palin-only voters instead ranked the eventual winner Peltola first — giving her more first-place support and changing nothing else — Peltola would have lost. This is the upward monotonicity paradox, and this page reproduces it on a faithful model of the real ballots, then shows that STAR and Ranked Robin cannot do it.**

→ Part of the monotonicity worked set. Companions: Downward paradox — San Francisco 2020 (its mirror) · Alaska 2022 (the full case) · the burial attack on the same numbers · non-monotonicity (concept) · monotonicity topic hub.

Two flavours of the paradox

Non-monotonicity comes in a matched pair (Graham-Squire & McCune, arXiv:2301.12075):

  • Upward monotonicity paradox ("more is less"): shift the winner up the rankings on some ballots — keeping every other candidate's relative order the same — and the winner loses. Giving a candidate more support defeats them. ← this page.
  • Downward monotonicity paradox ("less is more"): shift a loser down on some ballots and that loser wins. Giving a candidate less support elects them. → San Francisco D7 2020.

Both are failures of the monotonicity criterion: raising a candidate should never hurt them, and lowering one should never help them. (Note: monotonicity is not the same as Later-No-Harm — a common conflation.)

The real example: Alaska 2022

The August 2022 Alaska US House special, reduced ~960:1 to a faithful 200-voter model (the same profile as the full Alaska case). Three candidates: Peltola (D), Begich (R, the moderate), Palin (R). Counted by RCV-IRV:

BEFORE — Peltola wins. (alaska_upward_before)

ROUND 1
Peltola   80   Hopeful
Palin     63   Hopeful
Begich    57   Rejected      ← fewest first-choices, eliminated
Peltola   96   Elected       ← Begich's ballots split; Peltola wins the final
Palin     92   Rejected

AFTER — raise the winner, and she loses. Change 7 of the 23 Palin-only ballots to Peltola > Palin. Nothing else moves — Peltola simply gains 7 first-place votes. (alaska_upward_after)

ROUND 1
Peltola   87   Hopeful       ← Peltola GAINED support (80 → 87)
Begich    57   Hopeful
Palin     56   Rejected      ← Palin now has the fewest, eliminated instead of Begich
Begich    93   Elected       ← Palin's ballots swing to Begich; Begich wins the final
Peltola   91   Rejected      ← the previous winner now LOSES

Peltola gained first-place support and turned from winner into loser.

Why more support backfires

The winner's fate under IRV depends on who gets eliminated first, and that depends on first-place counts — the one thing the extra support changed. In the BEFORE election Begich has the fewest first-choices and is eliminated; his second-choices (which favour Peltola enough) carry her to the win. The 7 shifted ballots pull Palin below Begich, so now Palin is eliminated first instead — and Palin's ballots break heavily to Begich (they're Republican-aligned: Palin > Begich), who then beats Peltola head-to-head. Peltola's extra first-place votes rescued her rival's rival. That is the mechanism, and it is structural to sequential elimination.

Model note. At this 200-voter reduction, moving 6 ballots makes an exact 57–57 Begich/Palin tie in Round 1 (a coarse-model artifact whose outcome hinges on a tie-break); moving 7 clears it cleanly, so we use 7 for a tie-free, engine-independent demonstration. The real election's figure is ~6,000 Palin-only ballots, which crosses the threshold comfortably. Reproduce: uv run python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/monotonicity/cases/alaska_upward_after.yaml.

STAR and Ranked Robin can't do this

Both methods are monotonic in this sense — raising a candidate on some ballots can never cost them the election — so neither has an upward monotonicity paradox.

  • Ranked Robin (Condorcet / Copeland) reads the whole pairwise picture, not just who's eliminated first, so the shift doesn't move it at all. On the same ballots it elects Begich both times — before and after — because Begich is the Condorcet winner who beats each rival head-to-head (Begich > Peltola, Begich > Palin). It's completely unmoved by the raise. (Same ballot as RCV-IRV, a monotonic count — the olive branch to ranked-choice voters.)
  • STAR passes mono-raise: raising your score for a candidate can only ever help them reach and win the runoff. (See the runnable STAR before/after pair and STAR & monotonicity.)

Keep it in proportion — the fair reading

  • This is a real, documented failure, not a hypothetical — Alaska 2022 is one of the clearest real-world monotonicity failures on record, which is exactly why it's worth teaching.
  • But it is rare. Monotonicity failures need a near-three-way race with a specific transfer structure; most IRV elections never trigger one. Don't oversell frequency — sell the structural point: IRV's winner can depend on elimination order, and elimination order can move the wrong way.
  • It is IRV-specific, not "ranked voting" writ large. The same ranked ballots counted by Ranked Robin are monotonic. Saying "ranked voting is non-monotonic" is imprecise; it's instant-runoff that is.
  • STAR is not perfectly immune to every monotonicity variant. It passes mono-raise (no upward paradox), but fails the stronger mono-raise-delete in lab constructions — conceded and shown in the worked set. Honesty is naming both.

The takeaway isn't "IRV is bad." It's that a voter should be able to rank their favourite honestly without the ranking backfiring — and STAR and Ranked Robin deliver that guarantee where instant-runoff can't.

Sources

  • Graham-Squire & McCune, An Examination of the... [monotonicity] Paradoxes in the 2022 Alaska Special Election, arXiv:2301.12075 — the origin of the upward/downward framing and the 6,000-ballot finding.
  • realrcv.equal.vote/alaska22 — an interactive walk-through (Equal Vote; advocacy-adjacent, clear on the mechanics).
  • This library's full Alaska 2022 case (101/201/301) and burial companion — the same real numbers, other pathologies.