BV2154 — Felsenthal Example 8: the absolute loser wins Approval — and three races give three winners

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15 voters. An absolute majority (8 of 15) rank April dead last — April is both the Condorcet loser and the absolute loser. One voter's approval-cutoff choice elects her anyway. And the same 15 ballots return three different winners across the three races: Approval → April, IRV → Clara, Ranked Robin → Bruce.

Source

Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix §A3, Example 8.

The election

No. of voters    Ranking                     Approves
      6          April > Bruce > Clara       {April}
      4          Bruce > Clara > April       {Bruce}
      1          Clara > April > Bruce       {Clara, April}   ← the strategic ballot
      4          Clara > Bruce > April       {Clara}

Social ordering Bruce > Clara > April (Bruce beats April 8–7 and Clara 10–5; Clara beats April 9–6). Approval totals: April 7, Bruce 4, Clara 5 → April, the candidate a majority ranked last — the Condorcet loser and absolute loser paradoxes under Approval, triggered by a single voter approving two. Compare BV2144, where Choose-One does the same with bullet votes only.

The ranked races disagree with Approval and with each other: IRV deletes the Condorcet winner Bruce (fewest first choices, 6/4/5) and elects Clara 9–6 — a Condorcet winner paradox — while Ranked Robin elects Bruce directly. One electorate, three winners: the tabulation, not the ballot, decides.

The races

Race	BetterVoting	LH engine	Agree?
Approval (one strategic two-approval ballot)	April (7/4/5)	April	✓
IRV	Clara (Bruce deleted; 9–6)	Clara	✓
Ranked Robin	Bruce (Condorcet winner)	Bruce	✓

Files: approval yaml · irv yaml · rr yaml · frozen export · mirrors: approval, irv, rr.