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RCV-IRV (Coombs) — eliminate the most-hated, not the least-loved

A mirror image of Hare: instead of dropping the candidate with the fewest first choices, Coombs drops the one with the most last choices each round. It tends to protect a broadly-acceptable moderate.

→ Family: Which RCV-IRV? · the default it contrasts with: RCV-IRV (Hare)

In one line

Same instant-runoff shape, opposite elimination rule. Each round, if no one has a majority of first choices, eliminate the candidate ranked last by the most voters, transfer those ballots, and repeat. Where Hare asks "who has the weakest core?", Coombs asks "who is the most widely rejected?" — and removes them.

How the count works, step by step

  1. Tally first choices. Majority? → winner.
  2. Otherwise, count last-place rankings for each candidate.
  3. Eliminate the candidate with the most last-place rankings.
  4. Transfer their ballots to next choices; repeat.

Because it looks at the bottom of the ballot, Coombs leans toward consensus: a polarizing candidate that many voters rank dead-last is removed early, even if they have lots of first-place support.

Worked example — the same 27-voter squeeze

12  Left   > Center > Right     (Right is last)
 9  Right  > Center > Left      (Left  is last)
 6  Center > Left   > Right     (Right is last)

No majority. Last-place tally: Right 18 (the 12 + 6), Left 9, Center 0.

  • Most last-place is Right (18) → eliminate Right.
  • Right's 9 ballots go to Center → first choices now Left 12, Center 15.
  • Center has 15 of 27 (majority) → Center wins.

Same ballots as Hare (which elected Left); Coombs elects Center, the Condorcet winner, because Center is nobody's last choice.

What happens when the last-place counts tie

Step 3 says "eliminate the candidate with the most last-place rankings" — and, exactly as with Hare, that is undefined when several candidates are tied for most. The convention used by the academic statements of Coombs (and by pref_voting's implementation) is to remove all of them in one step. Usually a shortcut; occasionally the whole field, at which point the count stops and every remaining candidate ties for the win.

On a perfectly symmetric three-way rotation — where each candidate is ranked last by exactly one voter — that is precisely what happens, and Hare empties at the same moment from the other end of the ballot. Worth knowing because it is where Coombs' one structural advantage shows up: reading the bottom of the ballot gives the elimination step a different signal, so it survives some profiles on which Hare's first-choice counts have already tied. → Batch elimination — what happens when the batch is everyone.

Strengths & weaknesses

  • ✅ Resists center squeeze and usually elects the Condorcet/centrist candidate.
  • ❌ Not formally Condorcet (it can still miss in constructed cases), unlike BTR / Baldwin / Nanson.
  • ❌ Leans hard on last-place data, so it's very sensitive to truncated ballots (voters who don't rank everyone) and to burying/strategy.
  • ❌ Still not monotonic or summable in general.

Where it's used

Essentially academic / classroom — named for Clyde Coombs (1964). It's the textbook foil to Hare ("if you like the Alternative Vote, you should know about Coombs"), rarely used in public elections, but valuable for showing that which end of the ballot you read completely changes the outcome.

Sources: Coombs' method — Wikipedia, If You Like the Alternative Vote… You Ought to Know about the Coombs Rule (Grofman & Feld), Descriptions of ranked-ballot voting methods (R. LeGrand)