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RCV-IRV (BTR) — Bottom-Two-Runoff

An instant-runoff variant that fixes center squeeze: each round, the two lowest candidates meet head-to-head and the loser is eliminated. Because a Condorcet winner beats everyone, BTR can never eliminate them.

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

In one line

Like Hare, BTR eliminates one candidate per round and transfers ballots — but instead of cutting whoever has the fewest first choices, it takes the two candidates with the fewest and eliminates the one who loses their direct head-to-head. This one change makes it Condorcet-efficient: it always elects the candidate who beats every other one-on-one, when such a candidate exists.

How the count works, step by step

  1. Tally first choices (with transfers from any prior rounds).
  2. Find the two candidates with the fewest votes.
  3. Compare those two head-to-head across all ballots; eliminate the loser.
  4. Transfer the loser's ballots to next choices; repeat from step 1 until one remains.

The intuition: Hare can eliminate a strong candidate just because few people rank them first. BTR only ever eliminates a candidate who loses a head-to-head — and the Condorcet winner loses none, so they survive to the end.

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.

  • Two lowest: Center (6) and Right (9). Head-to-head Center vs Right: Center is ranked above Right on 18 ballots, Right above Center on 9 → Center wins, Right is eliminated. (Hare would have cut Center here instead.)
  • Right's 9 ballots go to Center → Center 15, Left 12.
  • Final pair Center vs Left: Center 15, Left 12 → Center wins.

Same ballots as the Hare page, opposite result: BTR elects Center, the Condorcet winner. No center squeeze.

Strengths & weaknesses

  • ✅ Condorcet-efficient — elects the head-to-head winner; no center squeeze.
  • ✅ Keeps the familiar round-by-round runoff "feel" of RCV.
  • ❌ Still not monotonic in general, and still not summable (you need the full ballots to run the head-to-heads).
  • ❌ Slightly more to explain than Hare ("why those two?"), which matters for adoption.

Where it's used

Mostly a reform proposal rather than current law — introduced by Rob LeGrand (2006) as "BTR-STV," and a frequent suggestion for making RCV-IRV Condorcet-compliant with minimal change to how it already works. Compare with the no-elimination Condorcet method, Ranked Robin (RCV-RR).

Sources: Instant-runoff voting — Wikipedia, Descriptions of ranked-ballot voting methods (R. LeGrand, Angelo State), Condorcet method — electowiki