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BV2156 — STAR misses the Condorcet winner — STAR's own signature failure

Method: STAR (single winner) · 1 seat · Expected winner: Ada · full count →

▶ Live on BetterVoting: vote · results ↗ (election 3grpbb, Test ID BV2156; STAR is race 1, and every race matches the LH tabulation below).

Level 301 · the one where STAR stumbles. No method is perfect, and this is STAR's signature failure. Cleo is the Condorcet winner — she beats Ada and Bruno one-on-one — yet STAR elects Ada, because Cleo is a low-scored compromise who never reaches the runoff. Same family as IRV's center squeeze: the broadly-acceptable middle is excluded before the decisive comparison.

→ the three "winners" STAR can name: STAR_three_winner_notions · STAR's limits: AR hub · the ranked cousin: center squeeze · fairness test: Reading these fairly — the test for an honest "whoops". ↔ BV QA tracker: BV149 (STAR fails to elect the Condorcet winner).

The ballots (100 voters)

Ada, Bruno, Cleo
40 × 5, 1, 2      # Ada > Cleo > Bruno
35 × 1, 5, 2      # Bruno > Cleo > Ada
25 × 3, 3, 5      # Cleo > (Ada = Bruno)

Cleo is everyone's acceptable middle — but the two wings only score her a 2. Source: bv2156_3grpbb_star_misses_condorcet.yaml.

Cleo wins every head-to-head — and still loses

  • Cleo vs Ada: 60–40 for Cleo (the 35 Bruno voters + 25 Cleo voters prefer her).
  • Cleo vs Bruno: 65–35 for Cleo.
  • So Cleo is the Condorcet winner — a majority prefers her to each rival.

But STAR's first step is the score total, and the wings' stingy 2s sink her:

[Condorcet Winner] Cleo — STAR elected Ada instead (Cleo was eliminated in the scoring round)
[Divergence from STAR]  STAR = Ada   ·   Condorcet = Cleo

Scoring Round:    Ada 310 · Bruno 290 · Cleo 275   → Cleo finishes 3rd, misses the runoff
Automatic Runoff: Ada 40 (53%) vs Bruno 35 (47%)   (Cleo isn't in it) → Ada wins

Cleo (275) lands just behind Ada (310) and Bruno (290), so the two polarizing wings advance instead of the consensus pick, and the runoff is held between them. The candidate a majority actually preferred over both finalists never got to the final.

Full audit copy: _tabulated.

Why this one matters (don't bury it)

This is the honest counterweight to STAR's usual win over IRV. STAR's scoring round can exclude the Condorcet winner from the runoff for the very same reason IRV eliminates a centrist early: she's many people's strong second, few people's first/high. STAR is much better at avoiding this than IRV — but "better" is not "immune," and a fair gallery says so out loud.

Reading this fairly - How common: rare but structural. STAR elects the Condorcet winner in roughly 98%+ of spatial-model elections; this is the residual case where a low-scored compromise is squeezed out of the top two. Real, not a knife-edge — but uncommon. - Sincere or strategic: fully sincere. No one gamed anything; honest stingy scores from the wings are enough. - What STAR does well: usually does elect the Condorcet winner, keeps an expressive ballot honest, and guarantees a majority-of-the-final-two winner. The miss is the exception, not the rule. - The symmetric whoops: this is the score-method twin of IRV center squeeze (RCV_IRV_center_squeeze). Different mechanism, same victim: the broadly-liked middle.