BV2162 — Nurmi Example 16 (1 of 2): everyone ranks fully, and RCV-IRV misses the Condorcet winner

▶ Live on BetterVoting: vote · results ↗ (election 4htk44).

103 voters, four candidates, every ballot ranking all four. B beats every rival head-to-head — yet instant runoff elects A. Part 2 (BV2163) is the sting: 17 voters improve their own outcome by ranking fewer candidates. Three races: STAR → B, RCV-IRV → A, Ranked Robin → B.

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 §A6 — the "Alternative Vote" procedure, the British name for instant-runoff / RCV-IRV (used once here; RCV-IRV everywhere else). Example 16, due to Nurmi (1999: 63). Felsenthal's other §A6 paradoxes reuse Examples 2–4, already live as BV2145/46, BV2147–49 and BV2150/51.

The election

No. of voters    Preference ordering
     33          A > B > C > D
     29          B > A > C > D
     24          C > B > A > D
     17          D > C > B > A

B is the Condorcet winner: beats A 70–33, C 62–41, D 86–17. Under RCV-IRV nobody holds a first-count majority (33/29/24/17), so D is eliminated — his 17 ballots transfer to C (41) — then B (29) is eliminated, and A wins 62. A Condorcet winner failure on sincere, complete ballots; STAR (5/4/2/1 map: 346/407/312/171, runoff 70–33) and Ranked Robin both elect B.

Agreement

Race	BetterVoting	LH engine	Agree?
STAR (ranks→scores)	B	B	✓
RCV-IRV	A	A	✓
Ranked Robin	B	B	✓

Files: star · irv · rr · frozen export · mirrors: star, irv, rr · Part 2: BV2163 — the truncation.