====================================================================== SOURCE FILE: bv2176_p8dp28_ranked_robin.yaml TABULATED FILE: bv2176_p8dp28_ranked_robin_tabulated.txt ====================================================================== election_title: "The Post-it RCV example (20 voters) — Ranked Robin: a cycle, a 2-1 tie, and two ladders" scenario_description: |- One of three races in the Post-it RCV example (BV2176, bvid p8dp28; BV-confirmed). The same 20 ranked ballots as the RCV-IRV race, compared every-pair head-to-head. The pairwise picture is a genuine Condorcet cycle — Purple beats Green 9-8, Green beats Blue 7-4, Blue beats Purple 10-9 (and Pink beats Purple 12-8) — so no candidate beats all others, and Green and Blue tie on record at 2-1 (Copeland 2). This is the documented spot where the two engines' tiebreak ladders part ways (05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md), and BOTH stay deterministic here: BetterVoting's ladder (exactly 2 tied -> their own head-to-head) elects GREEN, who beats Blue 7-4 — BV-confirmed, freezable; the LH ladder below (total margin, then lot) elects BLUE (+5 vs Green's +4). Same ballots, same 2-1 tie, two defensible winners — the first live BetterVoting election to exhibit the ladder divergence. expected_winners records the LH result (Blue); the frozen BV export records Green. Live results: https://bettervoting.com/p8dp28/results Companion races: bv2176_p8dp28_star.yaml, bv2176_p8dp28_irv.yaml. Overview page: bv2176_p8dp28_postit_rcv_example.md bv_test_id: BV2176 bv_election_id: p8dp28 bv_results_url: https://bettervoting.com/p8dp28/results paradoxes: [condorcet-cycle] voting_method: RankedRobin num_winners: 1 lot_numbers: [Purple, Green, Blue, Pink] ballots: |- Purple Purple Purple Purple Purple Purple Purple Green>Blue>Pink Green>Blue>Pink Green>Blue>Pink Green>Blue>Pink Green>Blue>Pink Green>Blue>Pink Blue>Pink Blue>Pink Blue>Green>Pink Blue>Purple Pink>Green>Purple Pink>Purple Pink expected_winners: - Blue # LH ladder (margin +5); BetterVoting's ladder (head-to-head among the tied pair) elects Green # file: bv2176_p8dp28_ranked_robin.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 20 ballots (ranked ballots). Ballots: 7 × Purple 6 × Green > Blue > Pink 2 × Blue > Pink 1 × Blue > Green > Pink 1 × Blue > Purple 1 × Pink > Green > Purple 1 × Pink > Purple 1 × Pink Round-Robin — every pair, head-to-head (For – Against): Purple beats Green 9 – 8 Blue beats Purple 10 – 9 Pink beats Purple 12 – 8 Green beats Blue 7 – 4 Green beats Pink 7 – 5 Blue beats Pink 10 – 3 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | Purple | Green | Blue | Pink | --------------------------------------------------------------------- Purple > | --- | 9 - 3 - 8 | 9 - 1 - 10 | 8 - 0 - 12 | Green > | 8 - 3 - 9 | --- | 7 - 9 - 4 | 7 - 8 - 5 | Blue > | 10 - 1 - 9 | 4 - 9 - 7 | --- |10 - 7 - 3 | Pink > | 12 - 0 - 8 | 5 - 8 - 7 | 3 - 7 - 10 | --- | 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 Blue 2–1–0 2 +5 Purple, Pink 2 Green 2–1–0 2 +4 Blue, Pink 3 Purple 1–2–0 1 -4 Green 4 Pink 1–2–0 1 -5 Purple Winner — Ranked Robin (RCV-RR): Blue *** 2 candidates tie for the most wins (Green, Blue) — 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): Green, Blue, Purple, Pink 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 (Green, Blue) are only part of the set — the win–loss table's top block understates how wide the contention is. Ranked Robin (RCV-RR) winner Blue 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