STAR Is Monotone — More Support Never Backfires¶

One line: under STAR, raising a candidate's score can never cause them to lose, and lowering it can never cause them to win. Honest support always helps the candidate it's given to. STAR satisfies the monotonicity criterion.

→ The method that fails this is RCV-IRV — see IRV non-monotonicity (where more first-place votes can defeat the winner). Glossary: monotonicity.

Why STAR can't fail it¶

STAR's winner comes entirely from sums: add up each candidate's scores to find the two finalists, then take the pairwise majority between those two. There is no elimination order to perturb.

Raising a candidate's score can only increase their total, so it can never push them out of the top two.
In the runoff, scoring a finalist higher can only move your vote toward them, never away.

Because every step is additive and there's nothing to "transfer," the backwards paradox that hits IRV simply has no mechanism to occur.

Worked example — the same profile that breaks IRV¶

Take the exact ballots that make RCV-IRV fail (see the IRV page), translated to 0–5 scores (1st → 5, 2nd → 3, unranked → 0), and run STAR before and after 4 voters raise X:

→ monotonicity_star_before.yaml · monotonicity_star_after.yaml

            BEFORE                         AFTER (4 voters raise X)
  12: 5,3,0  (X>Y)               16: 5,3,0  (X>Y)
  12: 0,5,3  (Y>Z)                8: 0,5,3  (Y>Z)
  10: 3,0,5  (Z>X)               10: 3,0,5  (Z>X)
  STAR winner: X                  STAR winner: X

STAR elects X both before and after — raising the winner can't hurt them. The after file's [Divergence from STAR] block makes the contrast self-documenting on the very same ballots:

STAR    = X
RCV-IRV = Z   (differs from STAR)

Same voters, same change: RCV-IRV flips X → Z; STAR doesn't budge. (Verified on the engine: STAR elects X in both files.)

The 301 nuance — a stronger variant STAR doesn't pass¶

Everything above is the standard monotonicity criterion (formally mono-raise: raising a candidate's score, and changing nothing else, never hurts them). STAR passes it without exception. But mathematician D. R. Woodall catalogued several monotonicity properties, and STAR fails a stronger one, mono-raise-delete: "a candidate X should not be harmed if X is raised on some ballots and all candidates now below X on those ballots are deleted from them" (for a score ballot, "deleted" means "dropped to the lowest score").

The catch is that this bundles two moves — raise X and bury everyone the voter placed below X — and only the first is safe. Raising X's own score can never push X out of the top two; but which candidate joins X in the runoff depends on everyone's totals. Burying the also-rans can change X's runoff opponent — from a Y that X beats to a Z that beats X. X was "raised," yet ended up losing. The soft spot isn't the arithmetic of X's own score; it's finalist selection.

This doesn't walk back STAR's monotonicity. The everyday promise — "score your favorite at the top, it can only help them" — holds exactly, because that's the standard criterion, and voters don't perform the composite raise-and-delete operation. It's simply the honest, precise statement: STAR satisfies mono-raise; it does not satisfy every stronger monotonicity variant. (The same care cuts the other way for IRV — which fails even plain mono-raise, the far more damaging failure.)

See it, runnable: a worked before/after pair where raising X and deleting the loser below X flips the winner from X to Z — mono_raise_delete_before.yaml (X wins) · mono_raise_delete_after.yaml (X raised, Y deleted → Z wins). The only change is nine ballots going Z=5,X=3,Y=2 → Z=5,X=4,Y=0; burying Y drops it below Z, so the runoff becomes X vs Z, which X loses.

Source: D. R. Woodall, "Monotonicity and Single-Seat Election Rules", Voting Matters, Issue 6 (1996).

Why this matters¶

Monotonicity is what lets you tell a voter, truthfully, "score your favorite at the top — it can only help them." Under IRV that advice can backfire; under STAR it always holds. It's a quieter virtue than the spoiler story, but it's the one that keeps honest voting safe.

Sources: monotonicity criterion (Wikipedia).