====================================================================== SOURCE FILE: pets_gov_ranked_robin.yaml TABULATED FILE: pets_gov_ranked_robin_tabulated.txt ====================================================================== election_title: "Pets Governance — Mayor by Ranked Robin (1 seat): the Condorcet winner" scenario_description: |- One of six races in the Pets Governance election (BV2134, bvid kcf8vf; BV-confirmed). Same 22 voters, a 13-voter MAJORITY (Dog, Cat, Fish) and a 9-voter MINORITY (Bird, Rabbit, Hamster), voting ranked ballots. This single-seat Mayor race uses Ranked Robin (RCV-RR / Copeland). Because the 13-voter majority ranks Dog first and outnumbers the minority, Dog beats every rival head-to-head — the Condorcet winner. So the executive (Mayor) goes to the majority's choice even as the proportional Council races (STAR-PR, STV) seat the minority. bv_test_id: BV2134 bv_election_id: kcf8vf bv_results_url: https://bettervoting.com/kcf8vf/results voting_method: RankedRobin num_winners: 1 lot_numbers: [Dog, Cat, Fish, Bird, Rabbit, Hamster] ballots: |- 13:Dog>Cat>Fish>Bird>Rabbit>Hamster 9:Bird>Rabbit>Hamster>Fish>Cat>Dog expected_winners: - Dog # file: pets_gov_ranked_robin.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 22 ballots (ranked ballots). Ballots: 13 × Dog > Cat > Fish > Bird > Rabbit > Hamster 9 × Bird > Rabbit > Hamster > Fish > Cat > Dog Round-Robin — every pair, head-to-head (For – Against): Dog beats Cat 13 – 9 Dog beats Fish 13 – 9 Dog beats Bird 13 – 9 Dog beats Rabbit 13 – 9 Dog beats Hamster 13 – 9 Cat beats Fish 13 – 9 Cat beats Bird 13 – 9 Cat beats Rabbit 13 – 9 Cat beats Hamster 13 – 9 Fish beats Bird 13 – 9 Fish beats Rabbit 13 – 9 Fish beats Hamster 13 – 9 Bird beats Rabbit 22 – 0 Bird beats Hamster 22 – 0 Rabbit beats Hamster 22 – 0 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | Dog | Cat | Fish | Bird | Rabbit | Hamster | -------------------------------------------------------------------------------------------------- Dog > | --- |13 - 0 - 9 |13 - 0 - 9 |13 - 0 - 9 |13 - 0 - 9 |13 - 0 - 9 | Cat > | 9 - 0 - 13 | --- |13 - 0 - 9 |13 - 0 - 9 |13 - 0 - 9 |13 - 0 - 9 | Fish > | 9 - 0 - 13 | 9 - 0 - 13 | --- |13 - 0 - 9 |13 - 0 - 9 |13 - 0 - 9 | Bird > | 9 - 0 - 13 | 9 - 0 - 13 | 9 - 0 - 13 | --- |22 - 0 - 0 |22 - 0 - 0 | Rabbit > | 9 - 0 - 13 | 9 - 0 - 13 | 9 - 0 - 13 | 0 - 0 - 22 | --- |22 - 0 - 0 | Hamster > | 9 - 0 - 13 | 9 - 0 - 13 | 9 - 0 - 13 | 0 - 0 - 22 | 0 - 0 - 22 | --- | 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 Dog 5–0–0 5 +20 Cat, Fish, Bird, Rabbit, Hamster 2 Cat 4–1–0 4 +12 Fish, Bird, Rabbit, Hamster 3 Fish 3–2–0 3 +4 Bird, Rabbit, Hamster 4 Bird 2–3–0 2 +32 Rabbit, Hamster 5 Rabbit 1–4–0 1 -12 Hamster 6 Hamster 0–5–0 0 -56 — Winner — Ranked Robin (RCV-RR): Dog 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 6): Dog Outside (5): Cat, Fish, Bird, Rabbit, Hamster One member ⇒ Dog is the Condorcet winner, beating every rival head-to-head. Ranked Robin (RCV-RR) winner Dog 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