IRV Non-Monotonicity — When More Support Makes You Lose¶

One line: under RCV-IRV, giving the eventual winner more first-choice support can cause them to lose — and moving a loser down can make them win. This isn't a glitch; it's baked into eliminate-and-transfer.

Applies to: Hare and the other sequential-elimination variants — BTR, Coombs, and Baldwin/Nanson are non-monotonic too, because eliminate-and-transfer is the cause. (So this is not Hare-specific the way center squeeze is.) The non-eliminating Condorcet methods like Ranked Robin are monotonic. See Which RCV-IRV?.

Why this page matters: most people are never told this. "Rank your honest favorite first, it can't backfire" is the core promise of IRV — and non-monotonicity is the case where that promise breaks. It's the single most underappreciated structural problem with the method.

→ STAR doesn't have this failure — see STAR is monotone. Glossary: monotonicity.

What "monotone" means¶

A voting method is monotone if ranking a candidate higher can never cause them to lose, and ranking them lower can never cause them to win. It's the most basic sanity check you'd expect from any election: support should help, not hurt.

RCV-IRV fails it. STAR (and any additive, summable method) passes it.

Why IRV fails it¶

IRV doesn't add support up — it eliminates the candidate with the fewest first-choices, round by round, and transfers their ballots. The winner depends entirely on who gets eliminated, and in what order.

That's the trap: changing how many first-choices a candidate has changes who is eliminated first — which changes who their ballots transfer to — which can flip the final result backwards. Adding support to your favorite can knock out the opponent who would have lost to them, leaving behind the opponent who beats them.

Worked example — run it yourself¶

The classic 3-candidate case, as two elections that differ by one change: 4 voters raise X from second to first.

→ monotonicity_irv_before.yaml · monotonicity_irv_after.yaml

BEFORE                              AFTER  (4 voters raise X: Y>Z → X>Y)
  12: X>Y                             16: X>Y
  12: Y>Z                              8: Y>Z
  10: Z>X                             10: Z>X
R1: X12  Y12  Z10  → Z eliminated    R1: X16  Y8  Z10  → Y eliminated
    Z>X transfers → X 22             Y>Z transfers → Z 18
    ✅ X WINS                          ❌ X LOSES — Z wins

X went from 12 first-choices and a win to 16 first-choices and a loss — and nothing else changed. The four extra first-place votes for X eliminated Y instead of Z; Y's ballots flowed to Z; Z then beat X. (Verified on the RCV-IRV engine: X elected with 22 before, Z elected with 18 after.)

How often does this happen? Not rare¶

A spatial-model study (Ornstein & Norman, Public Choice 2014) estimates a lower bound of ~15% monotonicity failure in competitive three-candidate IRV races — and the rate climbs as the race gets closer. This is a structural hazard of elimination, not a freak coincidence.

Two real-world flavors (both have happened — and both are runnable here)¶

Per a study of US RCV-IRV elections 2004–2022 (Graham-Squire & McCune, arXiv 2301.12075). Each has a dedicated page with a before/after pair you can run and the Ranked Robin contrast:

Upward paradox ("more is less") — Alaska 2022 (US House special). Had ~6,000 Palin-only voters instead ranked the winner Peltola first, Peltola would have lost — those extra first-place votes eliminate Palin first, and Begich then beats Peltola. Raising the winner defeats the winner. (Ranked Robin elects the Condorcet winner Begich both times, unmoved.)
Downward paradox ("less is more") — San Francisco 2020 (D7 Supervisor). Shifting the loser Engardio down on ~800 ballots would have made him win — the shift eliminates Melgar first (by 3 votes), and Engardio then beats Nguyen. Less support, more victory. (Ranked Robin elects the Condorcet winner Melgar both times.)

(See also the Alaska 2022 case study for the full election.)

A textbook real election¶

Burlington, VT 2009 (mayor). Kiss won, but the result was non-monotonic — and it was also a center squeeze: the Condorcet winner Montroll (who beat every rival head-to-head) was eliminated early. Voters who ranked Kiss lower could have made him win. Burlington repealed IRV in 2010 over this race.

A sharper critique — and where it overreaches (reading advocacy critically)¶

A well-known argument from rangevoting.org ("The logic behind IRV is flawed", after Blake Cretney) puts the point aggressively: IRV advocates spend their breath arguing that most first-choices ≠ best — then, without justification, IRV eliminates on fewest first-choices, as if fewest first-choices = worst. And IRV is "not self-consistent": use IRV to pick who to eliminate and you can eliminate the IRV winner. Range/Score voting, by contrast, is self-consistent — drop the lowest-scored candidate and the score winner still wins.

The kernel is right — and this page is the proof. IRV's fewest-first-choices elimination is the mechanical root of center squeeze and non-monotonicity, and there's a genuine tension between IRV's anti-plurality rhetoric and its plurality-based first cut. We agree, and demonstrate it above.

But it overreaches three ways, and the fairness cuts our way too: - It strawmans IRV's premise. IRV doesn't claim "fewest first-choices = worst"; it claims "fewest current support can't win this round, so transfer those voters' next preference" — ordinary runoff logic. The result can still cut the best candidate (the valid complaint), but that's not what IRV asserts. - "Not self-consistent" is a method-class distinction, not "bogus logic." Self-consistency is a property of additive methods (drop the lowest total, the winner's total is untouched); elimination methods lack it because eliminating a candidate transfers votes. That's an argument for additive methods, not proof IRV is irrational. - The "magician's trick" framing imputes deliberate deception — polemic, not argument.

Disclose the lean: rangevoting.org is Warren Smith / the Center for Range Voting — the most aggressive pro-Range advocacy source (advocacy-adjacent; strong for mechanics, weak for verdicts — see how to read the sources). And note it cuts against STAR as well: STAR's scoring round is additive/self-consistent, but its runoff is a non-additive pairwise step, so a Range purist levels the same charge at STAR. This isn't a pro-STAR argument — it's a Score-maximalist jab at every method with an elimination or runoff. We include it because the library checks pro-Range anti-IRV arguments by the same standard it checks the pro-RCV ones.

Don't confuse it with Later-No-Harm¶

A frequent mix-up: monotonicity asks "can raising a candidate ever hurt them?" Later-No-Harm asks "can adding a lower preference ever hurt your top choice?" They're different criteria. IRV passes Later-No-Harm but fails monotonicity; STAR is the opposite shape. (Worked out in Favorite Betrayal — Does Only RCV Avoid It?.)

→ More source notes: RCV-IRV monotonicity group in LINKS — source-of-truth registry.

Sources: Ornstein & Norman 2014 (Public Choice), Graham-Squire & McCune, RCV in the US 2004–2022 (arXiv), Burlington 2009 (Wikipedia), monotonicity criterion (Wikipedia).