====================================================================== SOURCE FILE: crowded_field_c7_ranked_robin.yaml TABULATED FILE: crowded_field_c7_ranked_robin_tabulated.txt ====================================================================== election_title: "Crowded field, rung 7 — 7 candidates, 65 voters, counted by Ranked Robin" scenario_description: |- RUNG 3, counted by Ranked Robin — the control for the whole ladder. Diego beats all SIX rivals head-to-head. The electorate's answer has not budged since rung 1, and Ranked Robin returns it, because a ranked ballot at seven candidates can still say which of Clara and Diego a voter prefers: **Diego beats Clara 36–29** right here in the round-robin. The 0–5 score ballot in crowded_field_c7_star.yaml largely cannot — 25 of 65 voters score the two identically there, and Clara takes the runoff 23–17 out of what is left. So this file is the control, and it carries the caveat that goes with being one: it reads a full-resolution ranking while the STAR file reads six rungs. Part of the gap between the two at this rung is ballot expressiveness rather than tabulation rule. A real 0–5 STAR election really does have only six rungs, so the cost still lands on STAR — but it is not the automatic runoff that caused it. The folder README works through both halves of that. Same 65 voters and the same fixed candidate positions as crowded_field_c7_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, Clara, Diego, Elsa, Felix, Greta] ballots: |- 6:Ana>Bruno>Clara>Diego>Elsa>Felix>Greta # bloc at 0 10:Bruno>Ana>Clara>Diego>Elsa>Felix>Greta # bloc at 4 13:Clara>Bruno>Diego>Elsa>Ana>Felix>Greta # bloc at 8 9:Diego>Elsa>Clara>Felix>Bruno>Greta>Ana # bloc at 12 12:Felix>Elsa>Diego>Greta>Clara>Bruno>Ana # bloc at 16 8:Greta>Felix>Elsa>Diego>Clara>Bruno>Ana # bloc at 20 7:Greta>Felix>Elsa>Diego>Clara>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 > Clara > Diego > Elsa > Felix > Greta 10 × Bruno > Ana > Clara > Diego > Elsa > Felix > Greta 13 × Clara > Bruno > Diego > Elsa > Ana > Felix > Greta 9 × Diego > Elsa > Clara > Felix > Bruno > Greta > Ana 12 × Felix > Elsa > Diego > Greta > Clara > Bruno > Ana 15 × Greta > Felix > Elsa > Diego > Clara > Bruno > Ana Round-Robin — every pair, head-to-head (For – Against): Bruno beats Ana 59 – 6 Clara beats Ana 49 – 16 Diego beats Ana 49 – 16 Elsa beats Ana 49 – 16 Felix beats Ana 36 – 29 Greta beats Ana 36 – 29 Clara beats Bruno 49 – 16 Diego beats Bruno 36 – 29 Elsa beats Bruno 36 – 29 Felix beats Bruno 36 – 29 Bruno beats Greta 38 – 27 Diego beats Clara 36 – 29 Elsa beats Clara 36 – 29 Clara beats Felix 38 – 27 Clara beats Greta 38 – 27 Diego beats Elsa 38 – 27 Diego beats Felix 38 – 27 Diego beats Greta 50 – 15 Elsa beats Felix 38 – 27 Elsa beats Greta 50 – 15 Felix 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 | Clara | Diego | Elsa | Felix | Greta | -------------------------------------------------------------------------------------------------------------- Ana > | --- | 6 - 0 - 59 |16 - 0 - 49 |16 - 0 - 49 |16 - 0 - 49 |29 - 0 - 36 |29 - 0 - 36 | Bruno > | 59 - 0 - 6 | --- |16 - 0 - 49 |29 - 0 - 36 |29 - 0 - 36 |29 - 0 - 36 |38 - 0 - 27 | Clara > | 49 - 0 - 16 |49 - 0 - 16 | --- |29 - 0 - 36 |29 - 0 - 36 |38 - 0 - 27 |38 - 0 - 27 | Diego > | 49 - 0 - 16 |36 - 0 - 29 |36 - 0 - 29 | --- |38 - 0 - 27 |38 - 0 - 27 |50 - 0 - 15 | Elsa > | 49 - 0 - 16 |36 - 0 - 29 |36 - 0 - 29 |27 - 0 - 38 | --- |38 - 0 - 27 |50 - 0 - 15 | Felix > | 36 - 0 - 29 |36 - 0 - 29 |27 - 0 - 38 |27 - 0 - 38 |27 - 0 - 38 | --- |50 - 0 - 15 | Greta > | 36 - 0 - 29 |27 - 0 - 38 |27 - 0 - 38 |15 - 0 - 50 |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 6–0–0 6 +104 Elsa, Clara, Felix, Bruno, Greta, Ana 2 Elsa 5–1–0 5 +82 Clara, Felix, Bruno, Greta, Ana 3 Clara 4–2–0 4 +74 Felix, Bruno, Greta, Ana 4 Felix 3–3–0 3 +16 Bruno, Greta, Ana 5 Bruno 2–4–0 2 +10 Greta, Ana 6 Greta 1–5–0 1 -120 Ana 7 Ana 0–6–0 0 -166 — 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 7): Diego Outside (6): Ana, Bruno, Clara, Elsa, Felix, 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