====================================================================== SOURCE FILE: bv2178_8kg698_ranked_robin.yaml TABULATED FILE: bv2178_8kg698_ranked_robin_tabulated.txt ====================================================================== election_title: "The Post-it switch, made real — Ranked Robin: Blue, now the outright Condorcet winner" scenario_description: |- One of four races in the Post-it switch election (BV2178, bvid 8kg698; BV-confirmed) — the BV2176/BV2177 electorate with two of the six Green>Blue>Pink voters flipping their top two (Blue>Green>Pink). In the original election the pairwise picture was a Condorcet cycle with Green and Blue tied 2-1 — the race where BetterVoting (head-to-head rung: Green) and LH (margin rung: Blue) famously part ways. The two-ballot flip dissolves all of it: Blue now beats Green 6-5 as well as Purple 10-9 and Pink 10-3 — a clean 3-0 CONDORCET WINNER. No tie, no ladder, no divergence: LH, BetterVoting, and pref_voting's independent Copeland all elect Blue. Cycles are knife-edges; two ballots is all it took to go from "two engines, two defensible winners" to unanimity. See the fairness lesson page: postit_video_fair_and_balanced.md. Live results: https://bettervoting.com/8kg698/results Companion races: bv2178_8kg698_star.yaml, bv2178_8kg698_irv.yaml. Overview page: bv2178_8kg698_switch_made_real.md bv_test_id: BV2178 bv_election_id: 8kg698 bv_results_url: https://bettervoting.com/8kg698/results paradoxes: [condorcet-winner] 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 Blue>Green>Pink Blue>Green>Pink Blue>Pink Blue>Pink Blue>Green>Pink Blue>Purple Pink>Green>Purple Pink>Purple Pink expected_winners: - Blue # file: bv2178_8kg698_ranked_robin.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 20 ballots (ranked ballots). Ballots: 7 × Purple 4 × Green > Blue > Pink 3 × Blue > Green > Pink 2 × Blue > 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 Blue beats Green 6 – 5 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 | --- | 5 - 9 - 6 | 7 - 8 - 5 | Blue > | 10 - 1 - 9 | 6 - 9 - 5 | --- |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 3–0–0 3 +9 Green, Purple, Pink 2 Green 1–2–0 1 +0 Pink 3 Purple 1–2–0 1 -4 Green 4 Pink 1–2–0 1 -5 Purple Winner — Ranked Robin (RCV-RR): Blue beats every opponent head-to-head — the Condorcet winner. --- 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 (1 of 4): Blue Outside (3): Purple, Green, Pink One member ⇒ Blue is the Condorcet winner, beating every rival head-to-head. 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