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Center Squeeze — one electorate, four tabulations, two answers (BV2137)

▶ Live on BetterVoting: vote · results ↗ (election ywckmg).

The textbook "center squeeze," from Robert LeGrand's ranked-ballot calculator. One hundred voters rank three candidates. The broadly-liked centrist is the Condorcet winner — yet Instant-Runoff throws him out first. The same ballots, counted four ways on BetterVoting, split two-to-two. This is the single clearest "the tabulation, not the ballot, decides" lesson in the repo.

→ Level: 301 · deep dive — Curriculum 301.11. See also: the ranked-ballot method zoo · center squeeze topic hub · what makes a good winner?.

The electorate

One hundred voters, three candidates — a polarizing right (Reagan), a polarizing left (Carter), and a broadly-liked centrist (Anderson) who is almost everyone's second choice but few voters' first:

45:Reagan>Anderson>Carter
20:Anderson>Carter>Reagan
35:Carter>Anderson>Reagan

Head-to-head, Anderson is the Condorcet winner — he beats Reagan 55–45 and Carter 65–35. But he holds the fewest first-choices (20), which is exactly what a first-choice-elimination method punishes.

The result: four methods, two winners

The same ballots run through the four tabulations BetterVoting supports. All four agree with LeGrand's calculator, pref_voting, and the LH engine:

Method (race) Winner Why Engines agreeing
IRV (Hare) Carter Anderson has fewest first-choices → eliminated round 1; Carter beats Reagan 55–45 LeGrand · pref_voting · LH · BV
STV, 1 seat Carter single-seat STV is IRV LeGrand · LH · BV
Ranked Robin (Copeland) Anderson wins every head-to-head — the Condorcet winner LeGrand · pref_voting · LH · BV
STAR (ranks→scores) Anderson tops the score round (340) and wins the automatic runoff LH · BV

The split is the lesson: the two elimination methods (IRV/STV) throw the centrist out; the two whole-ballot methods (Ranked Robin, STAR) keep him. On LeGrand's full calculator, 13 of the ~15 methods elect Anderson — only Hare (IRV) and Carey pick Carter. IRV is the outlier, not the norm.

The center squeeze, in the LH engine

Instant-Runoff eliminates the consensus candidate first:

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 100 ballots (ranked ballots).
Winner(s) — RCV / Instant-Runoff Voting
  Carter

Ranked Robin counts every head-to-head and finds the Condorcet winner IRV discarded:

Round-Robin — every pair, head-to-head (For – Against):
   Anderson  beats Reagan     55 – 45
   Carter    beats Reagan     55 – 45
   Anderson  beats Carter     65 – 35
Winner — Ranked Robin (RCV-RR): Anderson
   beats every opponent head-to-head — the Condorcet winner.

STAR agrees with Ranked Robin (not IRV): Anderson tops the score round with 340 and wins the automatic runoff. Full detail in the _tabulated mirror.

The rank→score conversion (STAR race)

BetterVoting's STAR race needs 0–5 scores, but this is a ranked electorate, so we map each voter's ranking to scores linearly, top rank → 5, bottom rank → 1:

score(rank) = round( 1 + 4·(N − rank) / (N − 1) ) → for N = 3 candidates: 5, 3, 1.

So Reagan>Anderson>Carter becomes Reagan 5, Anderson 3, Carter 1. This is a modeling choice (a sincere linear voter), documented so the STAR result is reproducible — it is not a claim about how real STAR voters would score. Even so, STAR lands on the Condorcet winner.

Which methods are on BetterVoting — and which aren't

BetterVoting natively tabulates four of LeGrand's ~15 methods: IRV, Ranked Robin, STV, and STAR (via the score conversion above). The other eleven — Borda, Bucklin, Coombs, Dodgson, Simpson, Schulze, Tideman, Nanson, Baldwin, Raynaud, Small — have no BetterVoting equivalent; they are verified with the pref_voting library and LeGrand's calculator. All eleven elect Anderson here. That BV-vs-others split is a property of BetterVoting's method menu, not of the election — see the method zoo for the full field.

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