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RCV-IRV (Contingent & Supplementary Vote) — instant runoff in one round

The "quick" instant runoffs: don't eliminate one candidate at a time — jump straight to the top two in a single transfer. The Supplementary Vote is the same idea with the ballot capped at two choices.

→ Family: Which RCV-IRV? · full Hare version: RCV-IRV (Hare)

Contingent Vote — in one line

Tally first choices. If someone has a majority, they win. If not, eliminate everyone except the top two at once, and transfer every other ballot to whichever of the two finalists it ranks higher. Highest total wins. It's Hare collapsed into a single elimination step.

Supplementary Vote — in one line

A Contingent Vote with only two columns: voters mark a first and second choice, nothing more. Same top-two-runoff logic, but a ballot that named neither finalist simply exhausts. This is the form famously used for the Mayor of London.

How the count works (Contingent)

  1. Count first choices. Majority (> 50%)? → winner.
  2. Otherwise keep the top two; eliminate all others in one batch.
  3. Move each eliminated ballot to whichever finalist it ranks higher (ballots ranking neither are exhausted).
  4. The finalist with more votes wins.

Worked example — the same 27-voter squeeze

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

First choices: Left 12, Right 9, Center 6. No majority.

  • Top two = Left, Right. Center (the bottom one) is eliminated in the single round.
  • Center's 6 ballots (Center > Left > Right) move to Left → Left 18, Right 9.
  • Left wins.

Same result as Hare — and the same center squeeze. With only three candidates, Contingent Vote is Hare, so it inherits the flaw: Center, the Condorcet winner, never even reaches the runoff. These one-shot methods are not Condorcet-safe; the fix is BTR or Baldwin/Nanson.

Strengths & weaknesses

  • ✅ Simple and fast — one transfer, easy to hand-count and explain.
  • ✅ Guarantees the winner has broad (top-two) support, beating plain plurality.
  • ❌ Center squeeze survives (worse with Supplementary's 2-choice cap, which exhausts more ballots).
  • ❌ Can eliminate a candidate who would have won a full Hare count, because it cuts everyone below 2nd place in a single step.

Where it's used

  • Supplementary Vote: Mayor of London and other English mayors + Police & Crime Commissioners — until the Elections Act 2022, which replaced it with first-past-the-post (so the 2024 London election used FPTP).
  • Contingent Vote: the President of Sri Lanka (voters rank up to three); historically Queensland, Australia.

Sources: Supplementary vote — Wikipedia, Contingent vote — Wikipedia, Electoral Commission — Elections Act 2022 voting changes