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Forced Exhaustion Ceiling — when a ranking cap discards more ballots than the winner gets

Method: RCV-IRV (Instant Runoff) · 1 seat · Expected winner: Ada · full count →

▶ Live on BetterVoting: vote · results ↗ (BV2183, election dfw8rj).

Read this fairly. This is a deliberately constructed worst case, built to show the ceiling of RCV-IRV ballot exhaustion under a ranking cap — not a claim that real elections look like this. Real exhaustion runs milder (roughly 10–27%; see the real rates). The point is what the mechanism permits, and that the cause is the ballot cap, not the voters. It sits in paradoxes_and_whoops/ under the same reading-these-fairly discipline as the Felsenthal/Nurmi cases.

The setup

50 voters, five candidates — but the ballot caps every voter at 2 rankings (like a tight ranking limit; NYC caps at 5, Minneapolis at 3). Three minor candidates (Cleo, Dev, Eli) form a rotating bloc; their voters spend both of their allowed ranks on minor candidates.

15:Ada>Cleo      ← two real contenders, Ada & Ben, lead on first choices
14:Ben>Dev
 8:Cleo>Eli      ← 21 voters rank ONLY minor candidates —
 7:Dev>Cleo         all their ballots will exhaust
 6:Eli>Dev

What happens

ROUND 1   Ada 15 | Ben 14 | Cleo 8 | Dev 7 | Eli 6   → Eli eliminated (Eli>Dev transfers)
ROUND 2   Ada 15 | Ben 14 | Dev 13 | Cleo 8          → Cleo eliminated; its 8 ballots EXHAUST
ROUND 3   Ada 15 | Ben 14 | Dev 13                   → Dev eliminated; its 13 ballots EXHAUST
FINAL     Ada 15 (Elected) | Ben 14 | Blank Votes 21

Winner: Ada, 15 to 14 — a margin of one. And 21 ballots (42%) were exhausted — more than the winner's own 15 votes. Ada's "majority" (15 of the 29 still active) is really 30% of the 50 voters. The margin is 1; the exhaustion is 21.

The kicker: lift the 2-rank cap — let those 21 voters rank all five candidates — and in single-winner IRV no ballot can exhaust at all, because there is always a continuing candidate. The exhaustion here is manufactured entirely by the ballot design, not by anything the voters did. That's forced exhaustion, the involuntary kind — the voters were as expressive as the rules allowed.

BetterVoting confirms it

BV's own IRV tabulation agrees with the LH engine to the number: winner Ada, and exhaustedVoteCount = [0, 0, 8, 21] — 8 exhausted after round 2, 21 by the final round. Frozen export: …_bv_export.json.

The LH tabulation

--- RCV / Instant-Runoff Voting (single winner) ---
 Tabulating 50 ballots (ranked ballots).

ROUND 1   Ada 15 | Ben 14 | Cleo 8 | Dev 7 | Eli 6(Rejected)
ROUND 2   Ada 15 | Ben 14 | Dev 13 | Cleo 8(Rejected)
ROUND 3   Ada 15 | Ben 14 | Dev 13(Rejected) | Blank Votes 8
FINAL     Ada 15 (Elected) | Ben 14 | Blank Votes 21

Winner — RCV / Instant-Runoff Voting: Ada

Full report: …_tabulated.txt.