====================================================================== SOURCE FILE: succ_elim_ex9_pareto.yaml TABULATED FILE: succ_elim_ex9_pareto_tabulated.txt ====================================================================== election_title: "Successive elimination Ex.9 — the agenda elects B, whom every voter ranks below A" scenario_description: |- Felsenthal's flagship successive-elimination example, and the densest case in the whole appendix: one 11-voter profile that yields four different paradoxes depending on which single datum you vary. 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 A4, Example 9. 11 voters, four candidates: 3×(A>B>C>D), 2×(C>A>B>D), 1×(C>D>A>B), 5×(D>A>B>C). The majority preference cycles (B>C>D>A>B), which is the precondition for everything below. PARETO. Under the agenda D vs A, winner vs C, winner vs B: D beats A 6:5, C beats D 6:5, B beats C 8:3 — B is elected. But all 11 voters rank A above B, unanimously and without exception. A Pareto-dominated candidate wins. PATH INDEPENDENCE. Same ballots, agenda A vs B, winner vs C, winner vs D: A beats B 11:0, A beats C 8:3, then D beats A 6:5 — D wins. Under a cycle the agenda-setter picks the winner, not the electorate. SCC. Delete D, who wins nothing under the first agenda: A beats C 8:3 and then B 11:0, so A wins. A non-winner's mere presence decided the election. NO-SHOW is the companion file succ_elim_ex9_noshow.yaml, where two of the D-first voters stay home and get A, whom they prefer to B. Labels are Felsenthal's own, capitalized; this is an academic reproduction meant to be read beside the paper's table, not a scenario with a cast. Successive elimination exists in neither the LH engine nor BetterVoting — it is a parliamentary procedure, not a ballot-box method — so this file is tabulated as Ranked Robin, which reads the same pairwise matrix the agenda consumes one pair at a time. Ranked Robin elects A, the candidate the agenda buried. Run the procedure itself with tools_adam/pref_voting_tabulation_engine/successive_elimination_report.py, whose --agenda and --drop flags reproduce all four readings above. paradoxes: [pareto, spoiler-scc, condorcet-cycle, no-show] voting_method: RankedRobin num_winners: 1 ballots: |- 3:A>B>C>D 2:C>A>B>D 1:C>D>A>B 5:D>A>B>C expected_winners: - A # file: succ_elim_ex9_pareto.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 11 ballots (ranked ballots). Ballots: 3 × A > B > C > D 2 × C > A > B > D 1 × C > D > A > B 5 × D > A > B > C Round-Robin — every pair, head-to-head (For – Against): A beats B 11 – 0 A beats C 8 – 3 D beats A 6 – 5 B beats C 8 – 3 D beats B 6 – 5 C beats D 6 – 5 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | A | B | C | D | ---------------------------------------------------------------- A > | --- |11 - 0 - 0 | 8 - 0 - 3 | 5 - 0 - 6 | B > | 0 - 0 - 11 | --- | 8 - 0 - 3 | 5 - 0 - 6 | C > | 3 - 0 - 8 | 3 - 0 - 8 | --- | 6 - 0 - 5 | D > | 6 - 0 - 5 | 6 - 0 - 5 | 5 - 0 - 6 | --- | Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order): # Candidate W–L–T Copeland Margin Beats 1 A 2–1–0 2 +15 B, C 2 D 2–1–0 2 +1 A, B 3 B 1–2–0 1 -7 C 4 C 1–2–0 1 -9 D Winner — Ranked Robin (RCV-RR): A *** 2 candidates tie for the most wins (A, D) — tied on the tally, not a cycle (some of them beat others head-to-head, but no loop closes). Resolved by total margin, then lot order. --- Smith Set (the generalized Condorcet winner) --- The smallest group whose every member beats every candidate outside it — the honest answer to "who is even in contention?". Smith set (4 of 4): A, D, B, C Outside (0): — More than one member ⇒ NO Condorcet winner: the top of the tournament is a cycle, so the strongest "candidate" is a set, not a person. Which member of the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md. Note: the Copeland leaders (A, D) are only part of the set — the win–loss table's top block understates how wide the contention is. Ranked Robin (RCV-RR) winner A is INSIDE the Smith set. ✓ Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of the set outscores every outsider, so the top of the win–loss table is always inside the set, however the tie among them is then broken. More: 07_Concepts/topics/smith_set.md