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RCV-IRV (Baldwin & Nanson) — Borda-elimination hybrids

Two instant-runoff variants that eliminate by Borda score instead of first choices. Both are Condorcet-consistent — they always elect the head-to-head winner — and both come from the same E. J. Nanson who described center squeeze in 1882.

→ Family: Which RCV-IRV? · the default they fix: RCV-IRV (Hare)

First, the Borda score

Give each ballot position points — with N candidates, a 1st choice = N−1, 2nd = N−2, …, last = 0 — and add them up. A candidate's Borda score rewards being ranked high by many, not just first by a few. Baldwin and Nanson both use this score to decide who to eliminate, then recompute it on the smaller field each round.

Baldwin — drop the lowest Borda score

  1. Compute every candidate's Borda score.
  2. Eliminate the single candidate with the lowest score.
  3. Recompute Borda among those remaining; repeat until one is left.

Nanson — drop everyone below average

  1. Compute Borda scores and their average.
  2. Eliminate every candidate at or below the average Borda score (can remove several at once).
  3. Recompute among the survivors; repeat.

Both are Condorcet methods: a candidate who beats everyone head-to-head always has an above-average Borda score and the highest of any pair, so they're never eliminated.

Worked example — the same 27-voter squeeze

12  Left   > Center > Right
 9  Right  > Center > Left
 6  Center > Left   > Right

Borda (3 candidates → 1st = 2, 2nd = 1, 3rd = 0):

  • Left: 12·2 + 6·1 + 9·0 = 30
  • Center: 6·2 + 12·1 + 9·1 = 33
  • Right: 9·2 + 0 + 0 = 18

Baldwin: lowest is Right (18) → eliminate. Recompute on {Left, Center}: Center is preferred 15–12, so Left has the lower score → eliminate Left → Center wins.

Nanson: average = (30+33+18)/3 = 27. At or below 27 → Right (18) only; eliminate it. Recompute on {Left, Center}: scores 12 vs 15, average 13.5, Left ≤ 13.5 → eliminate Left → Center wins.

Same ballots as Hare (Left); both Borda-elimination methods elect Center, the Condorcet winner — no center squeeze.

Strengths & weaknesses

  • ✅ Condorcet-consistent — always elect the head-to-head winner.
  • ✅ Use the whole ballot (every rank contributes), so no center squeeze.
  • ❌ Not monotonic (Baldwin), and Borda components are vulnerable to strategy (burying, clones) and to truncated ballots.
  • ❌ Not summable; more arithmetic than Hare, which hurts explainability/adoption.

Where it's used

Mostly academic and organizational elections (some societies use Nanson). Their real value here is conceptual: they show that bolting a Condorcet-friendly score onto instant-runoff elimination removes the squeeze — the same insight behind BTR.

History rhymes. Nanson laid this out in Methods of Election (1882), the same paper quoted on the center squeeze page warning that Hare ("Ware's method") "may return the next worst." He didn't just diagnose the flaw — he designed a cure.

Sources: Nanson's method — Wikipedia, Borda count — Wikipedia, Descriptions of ranked-ballot voting methods (R. LeGrand)