====================================================================== SOURCE FILE: rr_district_B.yaml TABULATED FILE: rr_district_B_tabulated.txt ====================================================================== election_title: "Summability demo — District B, counted by Ranked Robin" scenario_description: |- District B of the two-district summability demo, counted by Ranked Robin. Same ranked ballots as irv_district_B. B again beats both A and C head-to-head (the Condorcet winner). Its pairwise matrix ADDS to District A's to give the combined result (rr_combined) — no ballot pooling required. voting_method: RankedRobin num_winners: 1 ballots: |- 6:C 4:B 3:A>B>C expected_winners: - B ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 13 ballots (ranked ballots). Ballots: 6 × C 4 × B 3 × A > B > C Round-Robin — every pair, head-to-head (For – Against): B beats C 7 – 6 C beats A 6 – 3 B beats A 4 – 3 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | C | B | A | ----------------------------------------- C > | --- |6 - 0 - 7 |6 - 4 - 3 | B > | 7 - 0 - 6 | --- |4 - 6 - 3 | A > | 3 - 4 - 6 |3 - 6 - 4 | --- | 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 B 2–0–0 2 +2 C, A 2 C 1–1–0 1 +2 A 3 A 0–2–0 0 -4 — Winner — Ranked Robin (RCV-RR): B 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 3): B Outside (2): C, A One member ⇒ B is the Condorcet winner, beating every rival head-to-head. Ranked Robin (RCV-RR) winner B 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