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Does STAR collapse to IRV under strategic "5-1-0" voting? — rb-j's challenge, counted

Robert Bristow-Johnson (rb-j), a longtime Condorcet advocate and the analyst of Burlington 2009, posed a sharp challenge on r/EndFPTP: a rational STAR voter with preferences A > B > C will score A:5, B:1, C:0 — and if everyone votes that way, STAR behaves like IRV and center-squeezes the Condorcet winner the same way. This page takes the argument seriously, runs it, and reports what's true, what's overstated, and where the honest line is. Short version: the mechanism is real — and his "the 1s contribute little" is not.**

→ Related: strategic voting · favorite betrayal (301) · STAR's honest limits · real cases: Alaska 2022, Burlington 2009.

▶ Live on BetterVoting (the 5-1-0 elections each carry a STAR race and an RCV-IRV race on the same voter preferences, side by side): sincere → results ↗ (2kcwbw, BV2221) · thin-moderate 5-1-0 → results ↗ (rfyk46, BV2222) · real-moderate 5-1-0 → results ↗ (dyh93j, BV2223).

The argument (steelmanned)

You prefer A, you're fine with the moderate B, you loathe C. How should you fill in a STAR ballot?

  • Give A a 5 and C a 0 — easy. The only question is B.
  • In the automatic runoff, your B-vs-C preference is worth exactly one vote whether you scored B a 1 or a 4 — you can't give B more than "I prefer B to C." So a 1 is all B needs to beat C in a runoff that A doesn't reach.
  • But raising B in the scoring round can bump B past your own favorite A into the runoff. If your goal is "A wins," you want A — not B — in that runoff, so you keep B as low as possible.

So the rational ballot is 5-1-0: max your favorite, give the lesser-evil the minimum insurance, zero the enemy. rb-j's conclusion: score B higher only if you already fear A can't beat C but B can — which is exactly the center-squeeze case. Under universal 5-1-0, "the first round cares essentially only about the top-scored ballot," so STAR's finalists are basically the first-choice leaders — and the broadly-liked moderate gets squeezed out, just like under IRV.

It's a tight argument. So we ran it.

What the engine says

One 1-D electorate, Beth is the Condorcet winner (she beats Ana 52–48 and Cole 53–47), tabulated five ways:

Electorate Ballot Method Winner CW elected?
Thin moderate (48 / 47 / 5) sincere (poles score Beth a 3) STAR Beth ✅
Thin moderate strategic 5-1-0 STAR Ana (pole) ❌
Thin moderate ranked RCV-IRV Ana (pole) ❌
Real moderate (40 / 35 / 25) strategic 5-1-0 STAR Beth ✅
Real moderate ranked RCV-IRV Ana (pole) ❌

Watch the scoring round do the work.

Sincere STAR (s1) — the poles genuinely rate the moderate a 3, so she leads:

Scoring Round:  Beth 310 · Ana 250 · Cole 235   → Beth & Ana advance
Automatic Runoff:  Beth 52 vs Ana 48            → Beth wins  (the Condorcet winner)

Strategic 5-1-0, thin moderate (s2) — now the moderate gets only 1s from the poles and collapses below both:

Scoring Round:  Ana 245 · Cole 235 · Beth 120   → Ana & Cole advance  (Beth squeezed out)
Automatic Runoff:  Ana 53 vs Cole 47            → Ana wins  (a pole — NOT the CW)

That is identical to RCV-IRV on the same electorate (s3): Beth has the fewest first-choices (5), is eliminated first, and Ana wins 53–47. So rb-j's core claim is confirmed: under coordinated 5-1-0 with a thin moderate base, STAR center-squeezes exactly like IRV — and yes, Burlington 2009 or Alaska 2022 voted 5-1-0 would fail under STAR too. We don't dodge that; it's "strategy-resistant, not strategy-proof" made concrete.

Where the argument overstates itself

The claim that carries all the weight is "the 1 scores contribute little." They don't. Give the moderate a real first-choice base and run the identical 5-1-0 strategy (s4):

Scoring Round:  Ana 225 · Beth 200 · Cole 175   → Ana & Beth advance  (Beth made it — on 1s)
Automatic Runoff:  Beth 60 vs Ana 40            → Beth wins  (the Condorcet winner)

Beth's 75 "insignificant" 1s (plus her 25 fives) lifted her to 200 — past Cole — and into a runoff she wins. Under the same strategic ballot, STAR elects the Condorcet winner here while RCV-IRV eliminates her (s5 → Ana, 65–35). So:

"Everyone votes 5-1-0 ⇒ STAR = IRV" is false as a general statement. 5-1-0 STAR fails only in a sub-region — a moderate whose base is thin enough that even the pooled 1s can't lift them past a pole. Outside that region the 1s carry real weight, and 5-1-0 STAR is strictly more moderate-friendly than IRV. STAR degraded-by-strategy is still not IRV.

The honest bottom line

  • Conceded, squarely: STAR is not strategy-proof (no method is — Gibbard). Under coordinated 5-1-0 min-max voting and a thin moderate base, STAR can fail the Condorcet winner just as IRV does. rb-j is right about the mechanism.
  • But it's a strategic-equilibrium argument, not a sincere-ballot one. On sincere ballots STAR elects the CW (s1); the failure needs universal coordination on min-max, a thin moderate base, and accurate anticipation of who can beat whom. Misjudge it and 5-1-0 backfires — starving a moderate you needed can hand the seat to the candidate you loathe.
  • And the "1s are noise" premise is wrong (s4): they lift moderates into runoffs, which is precisely why STAR ≠ IRV even under the strategic ballot.
  • The 0-5-0 escalation rb-j floats (bullet-vote the moderate, abandon your doomed favorite) is favorite betrayal — which STAR permits and doesn't deny. But it demands even more information and coordination, and the FBC simulation finds attempted betrayal backfires ~98% of the time under STAR. "You can betray your favorite" and "betrayal pays" are different claims; STAR's case rests on the second being rare.

So the fair verdict: rb-j has found a genuine edge of STAR's strategy space and named it precisely — credit to him. What the counting adds is the boundary of that edge (thin base only) and the correction that STAR-under-5-1-0 is IRV-like, not IRV-identical. The Condorcet answer — "just always elect the CW" — carries its own bill: cycles need a completion method (there's no canonical one), and the CW can be a weakly-supported compromise. That's a values trade, honestly stated, not a knockout for either side.

The runnable cases

File Electorate · ballot Method →
s1 thin moderate · sincere STAR Beth (CW)
s2 thin moderate · 5-1-0 STAR Ana
s3 thin moderate · ranked RCV-IRV Ana
s4 real moderate · 5-1-0 STAR Beth (CW)
s5 real moderate · ranked RCV-IRV Ana

Source of the argument: rb-j (Robert Bristow-Johnson), r/EndFPTP, "the restricted case of 3 significant candidates" (2026). Cast renamed (Ana/Beth/Cole) for a clean spatial example; Beth is the center. Every winner above is the engine's, reproducible from the files. BetterVoting's own STAR and IRV counts agree on every race (frozen _bv_export.json beside the yamls) — including dyh93j, where the same 5-1-0 ballots elect Beth under STAR yet Ana under IRV, live.