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Condorcet centrist, full form (100 voters, 47/47/3/3) — every BV method, one electorate

▶ Live on BetterVoting: vote · results ↗ (election bkwfjr, Test ID BV2172).

The profile as drawn in the "Should we always elect the Condorcet winner?" explainer — 100 voters, three candidates, run through all seven methods BetterVoting supports. Avery is the left pole, Blake the right pole, Casey the centrist. Casey is the Condorcet winner (beats each pole 53–47) but has only 6 first choices. The minimal 8-voter twin (BV2171) shows the identical symptom with the fewest possible ballots.

The ballots

# voters 1st 2nd 3rd
47 Avery Casey Blake
47 Blake Casey Avery
3 Casey Avery Blake
3 Casey Blake Avery

First choices: Avery 47, Blake 47, Casey 6. Pairwise: Casey 53–47 over each pole; Avery 50–50 Blake.

Seven methods, two outcomes

Method Ballot type Winner Why
STAR scores 5/3/1 Casey Score round Casey 312 vs 294/294; runoff 53–47
STAR-PR (1 seat) scores 5/3/1 Casey 1 seat ⇒ the STAR winner
Approval (approve top two) 0/1 Casey Everyone's top two include Casey → Casey 100, poles 50
Ranked Robin ranks Casey Condorcet winner, 2–0
RCV-IRV ranks tie 50–50 Casey eliminated (6); poles deadlock — random on BV
STV (1 seat) ranks tie 50–50 = IRV single-winner
Choose-One 0/1 tie 47–47 Casey last (6); poles tie — random on BV

The four whole-ballot methods elect the candidate a majority actually prefers; the three first-choice methods throw the centrist out and deadlock the poles. On BetterVoting the three ties resolve at random (a coin flip, not freezable). STAR-PR at 1 seat and STV at 1 seat are degenerate (= STAR and = IRV) — included to complete the BV method set.

LH engine — the STAR race (the divergence, on one screen)

[Divergence from STAR]
  STAR                   = Casey
  Choose-One (Plurality) = Avery   (differs from STAR)
  RCV-IRV                = Avery   (differs from STAR)
  Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
        method difference, not a tie-breaking artifact.
  Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
        outlier — the classic center-squeeze signature.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/bv2172_bkwfjr_star_RCV-IRV_tabulated.txt

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 100 ballots.
Count × Avery,Blake,Casey
   47 ×     5,    1,    3
   47 ×     1,    5,    3
    3 ×     3,    1,    5
    3 ×     1,    3,    5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Casey         -- 312 -- First place
   Avery         -- 294 -- Tied for second place
   Blake         -- 294 -- Tied for second place
 Casey advances, but there's a two-way tie for second.

[STAR Voting: Scoring Round: First tiebreaker]
 The candidate preferred in the most head-to-head matchups advances.
   Avery         -- 50 -- Tied for second place
   Blake         -- 50 -- Tied for second place
   Equal Support --  0
 There's still a two-way tie for second.

[STAR Voting: Scoring Round: Second tiebreaker]
 The candidate with the most votes of score 5 advances.
   Avery         -- 47 -- Tied for second place
   Blake         -- 47 -- Tied for second place
 There's still a two-way tie for second.

*** No official tie-breaking lot numbers were provided.
    Ties are resolved using a fallback order: CSV column order.
    Lot-number priority order: ['Avery', 'Blake', 'Casey']

[Tiebreaker: Lot Number Priority]
  Tie among: ['Avery', 'Blake']
  Resolved: ['Avery'] (selected by lot-number priority).

[Lot-decided tie — rare]
  ⚠ The ballots did not break this tie: the deterministic rungs
    (pairwise / score, then five-star) all came back equal, so the
    pre-published LOT order chose among the tied candidates — the
    result here was set by lot, not by the votes. Usually the
    "dead rung": no tied candidate held a score-5 vote (five-star
    counts fives, not fours). Verify the tied candidates' 5-counts.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Casey         -- 53 -- First place
   Avery         -- 47
   Equal Support --  0
 Casey wins.
   Runoff math:
     100  ballots cast
   −   0  Equal Support (no preference between the two finalists)
     ───
     100  voters with a preference  (majority = 51)
           Casey 53 (53%)  ·  Avery 47 (47%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Casey

(LH's RCV-IRV breaks the 50–50 tie with a stable seed → Avery; BetterVoting breaks it at random. Same profile, same conclusion — only the coin lands differently.)

Why 47/47/3/3?

The numbers look deliberately chosen: a realistic polarized split (47% / 47% / 6%), a clean but non-landslide pairwise majority for Casey (53–47, not a blowout), a vivid first-choice squeeze (Casey with just 6), and a count that isn't reducible (gcd of 47 and 3 is 1) so it reads like real data rather than a toy. The minimal 3/3/1/1 twin strips all of that away and gets the same result — evidence the effect is structural.

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