====================================================================== SOURCE FILE: cycle_family_splits_c5_b77.yaml TABULATED FILE: cycle_family_splits_c5_b77_tabulated.txt ====================================================================== election_title: "The whole Condorcet family splits — Minimax & Schulze pick Ava, Ranked Pairs picks Ben, on one set of ballots" scenario_description: |- The five-candidate profile behind the "…but they don't always agree" table in 05_Ranked_Robin/01_Learn/cycle_resolution.md. 77 members of a program committee rank five finalists, and majority preference is knotted about as badly as it can be: there is no Condorcet winner and the Smith set is ALL FIVE candidates — every finalist is in a beat-cycle with the rest. On these identical ballots the Condorcet family gives four different answers: Copeland (Ranked Robin) Ava, Ben (tie — both go 2-2; LH breaks it by margin) Minimax Ava Schulze (beat path) Ava Ranked Pairs Ben Split Cycle Ava, Ben Minimax and Schulze land on Ava (her worst defeat is the mildest); Ranked Pairs locks the biggest margins first and they carry Ben; Copeland can't separate the two, and Split Cycle deliberately returns both. That is the entire lesson of the cycle-resolution page in one election: "Condorcet method" names a FAMILY, and inside a cycle the family stops agreeing. The LH engine tabulates the Copeland column (= Ranked Robin) and breaks the Ava/Ben tie by total margin, then lot. The other four rules are printed by: uv run STARVote_LH_tabulation_engine/tools_adam/pref_voting_tabulation_engine/cycle_resolution_report.py \ method_comparisons/cycle_resolution/cases/cycle_family_splits_c5_b77.yaml LH-only (no BetterVoting election): the result is a Copeland tie, and BV breaks Copeland ties at random, so this can't be frozen on BV. Constructed by search and verified with pref_voting (it is NOT a profile from the literature — an earlier draft mis-attributed a 100-voter version to Heitzig; this replaces it with a real, reproducible one). Companion: cycle_schulze_vs_ranked_pairs_c4_b40.yaml. paradoxes: [condorcet-cycle] voting_method: RankedRobin num_winners: 1 lot_numbers: [Ava, Ben, Cole, Dana, Ezra] ballots: |- 12:Ezra>Ava>Dana>Ben>Cole 7:Ezra>Cole>Ava>Dana>Ben 14:Ben>Ava>Ezra>Cole>Dana 8:Dana>Ben>Ava>Ezra>Cole 5:Cole>Ava>Dana>Ezra>Ben 11:Dana>Ben>Ava>Cole>Ezra 13:Ezra>Cole>Ava>Ben>Dana 7:Ben>Ava>Cole>Ezra>Dana expected_winners: - Ava ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 77 ballots (ranked ballots). Ballots: 12 × Ezra > Ava > Dana > Ben > Cole 7 × Ezra > Cole > Ava > Dana > Ben 14 × Ben > Ava > Ezra > Cole > Dana 8 × Dana > Ben > Ava > Ezra > Cole 5 × Cole > Ava > Dana > Ezra > Ben 11 × Dana > Ben > Ava > Cole > Ezra 13 × Ezra > Cole > Ava > Ben > Dana 7 × Ben > Ava > Cole > Ezra > Dana Round-Robin — every pair, head-to-head (For – Against): Ava beats Ezra 45 – 32 Ezra beats Dana 53 – 24 Ben beats Ezra 40 – 37 Ezra beats Cole 54 – 23 Ava beats Dana 58 – 19 Ben beats Ava 40 – 37 Ava beats Cole 52 – 25 Dana beats Ben 43 – 34 Cole beats Dana 46 – 31 Ben beats Cole 52 – 25 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | Ezra | Ava | Dana | Ben | Cole | --------------------------------------------------------------------------------- Ezra > | --- |32 - 0 - 45 |53 - 0 - 24 |37 - 0 - 40 |54 - 0 - 23 | Ava > | 45 - 0 - 32 | --- |58 - 0 - 19 |37 - 0 - 40 |52 - 0 - 25 | Dana > | 24 - 0 - 53 |19 - 0 - 58 | --- |43 - 0 - 34 |31 - 0 - 46 | Ben > | 40 - 0 - 37 |40 - 0 - 37 |34 - 0 - 43 | --- |52 - 0 - 25 | Cole > | 23 - 0 - 54 |25 - 0 - 52 |46 - 0 - 31 |25 - 0 - 52 | --- | 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 Ava 3–1–0 3 +76 Ezra, Cole, Dana 2 Ben 3–1–0 3 +24 Ava, Ezra, Cole 3 Ezra 2–2–0 2 +44 Cole, Dana 4 Cole 1–3–0 1 -70 Dana 5 Dana 1–3–0 1 -74 Ben Winner — Ranked Robin (RCV-RR): Ava *** 2 candidates tie for the most wins (Ava, Ben) — 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 (5 of 5): Ava, Ben, Ezra, Dana, Cole 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 (Ava, Ben) are only part of the set — the win–loss table's top block understates how wide the contention is. Ranked Robin (RCV-RR) winner Ava 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