====================================================================== SOURCE FILE: crowded_field_c5_ranked_robin.yaml TABULATED FILE: crowded_field_c5_ranked_robin_tabulated.txt ====================================================================== election_title: "Crowded field, rung 5 — 5 candidates, 65 voters, counted by Ranked Robin" scenario_description: |- RUNG 2, counted by Ranked Robin. Two candidates joined; Diego still beats all four rivals, so the Smith set is still {Diego} and the electorate's answer has not moved. Hold this next to crowded_field_c5_star.yaml, where STAR agrees — and against crowded_field_c5_irv.yaml, where instant runoff and Choose-One do not. Same 65 voters and the same fixed candidate positions as crowded_field_c5_star.yaml; this file hands them a ranked ballot instead of a 0–5 one. Construction: build_ladder.py in this folder. 65 voters in seven blocs at 0, 4, 8, 12, 16, 20, 24 (sizes 6, 10, 13, 9, 12, 8, 7); candidates fixed at Ana 1 · Bruno 6 · Clara 9 · Diego 11 · Elsa 14 · Felix 16 · Greta 22; utility = minus distance; scores = each bloc's own min-max scaling onto 0–5. Nothing is tuned, and no count at any rung is settled by a tie-break. voting_method: RankedRobin num_winners: 1 lot_numbers: [Ana, Bruno, Diego, Elsa, Greta] ballots: |- 6:Ana>Bruno>Diego>Elsa>Greta # bloc at 0 10:Bruno>Ana>Diego>Elsa>Greta # bloc at 4 13:Bruno>Diego>Elsa>Ana>Greta # bloc at 8 9:Diego>Elsa>Bruno>Greta>Ana # bloc at 12 12:Elsa>Diego>Greta>Bruno>Ana # bloc at 16 8:Greta>Elsa>Diego>Bruno>Ana # bloc at 20 7:Greta>Elsa>Diego>Bruno>Ana # bloc at 24 expected_winners: - Diego ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 65 ballots (ranked ballots). Ballots: 6 × Ana > Bruno > Diego > Elsa > Greta 10 × Bruno > Ana > Diego > Elsa > Greta 13 × Bruno > Diego > Elsa > Ana > Greta 9 × Diego > Elsa > Bruno > Greta > Ana 12 × Elsa > Diego > Greta > Bruno > Ana 15 × Greta > Elsa > Diego > Bruno > Ana Round-Robin — every pair, head-to-head (For – Against): Bruno beats Ana 59 – 6 Diego beats Ana 49 – 16 Elsa beats Ana 49 – 16 Greta beats Ana 36 – 29 Diego beats Bruno 36 – 29 Elsa beats Bruno 36 – 29 Bruno beats Greta 38 – 27 Diego beats Elsa 38 – 27 Diego beats Greta 50 – 15 Elsa beats Greta 50 – 15 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | Ana | Bruno | Diego | Elsa | Greta | ---------------------------------------------------------------------------------- Ana > | --- | 6 - 0 - 59 |16 - 0 - 49 |16 - 0 - 49 |29 - 0 - 36 | Bruno > | 59 - 0 - 6 | --- |29 - 0 - 36 |29 - 0 - 36 |38 - 0 - 27 | Diego > | 49 - 0 - 16 |36 - 0 - 29 | --- |38 - 0 - 27 |50 - 0 - 15 | Elsa > | 49 - 0 - 16 |36 - 0 - 29 |27 - 0 - 38 | --- |50 - 0 - 15 | Greta > | 36 - 0 - 29 |27 - 0 - 38 |15 - 0 - 50 |15 - 0 - 50 | --- | 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 Diego 4–0–0 4 +86 Elsa, Bruno, Greta, Ana 2 Elsa 3–1–0 3 +64 Bruno, Greta, Ana 3 Bruno 2–2–0 2 +50 Greta, Ana 4 Greta 1–3–0 1 -74 Ana 5 Ana 0–4–0 0 -126 — Winner — Ranked Robin (RCV-RR): Diego 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 5): Diego Outside (4): Ana, Bruno, Elsa, Greta One member ⇒ Diego is the Condorcet winner, beating every rival head-to-head. Ranked Robin (RCV-RR) winner Diego 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