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BV2155 — Tennessee capital, four ways — same ballots; Memphis, Knoxville or Nashville by count

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

▶ Live on BetterVoting: vote · results ↗ (election cphxpt, Test ID BV2155; STAR is race 1, and every race matches the LH tabulation below).

Level 201 · the headline whoops. The classic Tennessee state-capital puzzle. Four cities, one set of sincere ballots — and three different methods crown three different cities. It's the cleanest demonstration that "the winner" isn't a property of the voters; it's a property of the rule.

→ fairness test: Reading these fairly — the test for an honest "whoops" · the set: README · GLOSSARY. ↔ BV QA tracker: BV150 (Lanphier — STAR/IRV/Condorcet give different winners; ABIF Tennessee example).

The setup (100 voters on a map)

Tennessee wants one capital. Everyone wants it close to home, so preferences track geography: Memphis (far west), Nashville (central), Chattanooga (southeast), Knoxville (east).

Memphis, Nashville, Chattanooga, Knoxville
42 × 5, 2, 1, 0      # Memphis voters
26 × 1, 5, 3, 2      # Nashville voters
15 × 0, 3, 5, 4      # Chattanooga voters
17 × 0, 3, 4, 5      # Knoxville voters

Scores are a simple distance model (home city 5, falling off with distance). Source: bv2155_cphxpt_tennessee_four_ways.yaml.

Three methods, three winners

  • Plurality → Memphis. Memphis has the most first-choices (42%) — and only 42%. A clear majority (58%) would rather have almost anywhere else, but Plurality never asks.
  • RCV-IRV → Knoxville. Chattanooga is eliminated first (fewest firsts) and flows to Knoxville; then Nashville is eliminated and also flows east; Knoxville wins 58–42. The central compromise (Nashville) is squeezed out before the final count.
  • Condorcet & STAR → Nashville. Nashville beats every other city head-to-head and has the highest score total — the geographic compromise nobody is far from. STAR advances it to the runoff on strength of support and it wins.
[Condorcet Winner] Nashville — matches the STAR winner
[Divergence from STAR]
  STAR                   = Nashville
  Choose-One (Plurality) = Memphis     (differs)
  RCV-IRV                = Knoxville    (differs)

Scoring Round:   Nashville 310 · Chattanooga 263 · Memphis 236 · Knoxville 197
Automatic Runoff: Nashville 68 (68%) vs Chattanooga 32 (32%)  → Nashville wins

Full audit copy: _tabulated.

Why it's the perfect opener

No one voted strategically; the ballots are honest geography. The disagreement is purely about what question each method asks — most-first-choices (Plurality), last-one- standing (IRV), or beats-everyone-else (Condorcet/STAR). Same data, three answers.

Reading this fairly - How common: structural — three-way disagreements are routine whenever a centrist sits between two larger wings; Tennessee is the canonical illustration, not a one-off. - Sincere or strategic: fully sincere — no manipulation needed. - What each does well: Plurality is dead simple; IRV guarantees a majority of the final two and handles many fields fine. The catch here is specific to the centrist geometry. - The symmetric whoops: STAR isn't immune to weird results either — it just gets this one right. See Whoops 02, where STAR is the one that stumbles.