Skip to content

Condorcet centrist, minimal form (8 voters) — every BV method, one electorate

▶ Live on BetterVoting: vote · results ↗ (election h93tm4, Test ID BV2171).

The smallest electorate that still reproduces the whole center-squeeze symptom — 8 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 5–3) but has the fewest first choices (2). This is the minimal foil to the full 100-voter version (BV2172); proving the effect is structural, not an artifact of big round numbers.

The ballots

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

First choices: Avery 3, Blake 3, Casey 2. Pairwise: Casey 5–3 over each pole; Avery 4–4 Blake.

Seven methods, two outcomes

Method Ballot type Winner Why
STAR scores 5/3/1 Casey Score round Casey 28 vs 22/22; runoff 5–3
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 8, poles 4
Ranked Robin ranks Casey Condorcet winner, 2–0
RCV-IRV ranks tie 4–4 Casey eliminated (2); poles deadlock — random on BV
STV (1 seat) ranks tie 4–4 = IRV single-winner
Choose-One 0/1 tie 3–3 Casey last (2); 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 respectively) — included to complete the BV method set.

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

Abridged for the lesson — not verbatim engine output
[Condorcet Winner]
  Condorcet Winner: Casey — matches the STAR winner

[Divergence from STAR]
  STAR                   = Casey
  Choose-One (Plurality) = Avery   (differs from STAR)
  RCV-IRV                = Avery   (differs from STAR)
  Note: Ranked Robin (RCV-RR) agrees with STAR — RCV-IRV is the lone outlier.

Scoring Round:  Casey 28 · Avery 22 · Blake 22   (Casey advances; poles tie for 2nd)
Automatic Runoff:  Casey 5 vs Avery/Blake 3      (Casey wins)
(LH's RCV-IRV breaks the 4–4 tie with a stable seed → Avery; BetterVoting breaks it at random. Same profile, same conclusion — only the coin lands differently.)

Files