====================================================================== SOURCE FILE: crowded_field_c3_star.yaml TABULATED FILE: crowded_field_c3_star_tabulated.txt ====================================================================== election_title: "Crowded field, rung 3 — 3 candidates, 65 voters, counted by STAR" scenario_description: |- RUNG 1 of the crowded-field ladder — three candidates, and all six methods agree. Diego stands at 11 on a 0–24 spectrum, near the middle of where the voters are. He beats both rivals head-to-head, so he is the Condorcet winner; he leads the scoring round 266 to Greta's 123 and Ana's 119, and takes the runoff 50–15 with nobody undecided. He even holds an outright majority of first choices, 34 of 65. Ranked Robin, Score, Approval, RCV-IRV and Choose-One elect him too. That is the point of this rung: with a small field there is nothing to argue about, so any disagreement further up the ladder was caused by the candidates who joined — the voters never move. 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: STAR num_winners: 1 lot_numbers: [Ana, Diego, Greta] ballots: |- Count:Ana,Diego,Greta 6:5,3,0 # bloc at 0 10:5,4,0 # bloc at 4 13:3,5,0 # bloc at 8 9:0,5,0 # bloc at 12 12:0,5,4 # bloc at 16 8:0,3,5 # bloc at 20 7:0,2,5 # bloc at 24 expected_winners: - Diego # file: crowded_field_c3_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Crowded field, rung 3 — 3 candidates, 65 voters, counted by STAR === RUNG 1 of the crowded-field ladder — three candidates, and all six methods agree. Diego stands at 11 on a 0–24 spectrum, near the middle of where the voters are. He beats both rivals head-to-head, so he is the Condorcet winner; he leads the scoring round 266 to Greta's 123 and Ana's 119, and takes the runoff 50–15 with nobody undecided. He even holds an outright majority of first choices, 34 of 65. Ranked Robin, Score, Approval, RCV-IRV and Choose-One elect him too. That is the point of this rung: with a small field there is nothing to argue about, so any disagreement further up the ladder was caused by the candidates who joined — the voters never move. 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. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | Ana | * Diego | * Greta | ------------------------------------------------------------- Ana > | --- |16 - 0 - 49 |29 - 9 - 27 | * Diego > | 49 - 0 - 16 | --- |50 - 0 - 15 | * Greta > | 27 - 9 - 29 |15 - 0 - 50 | --- | [Condorcet Winner] Condorcet Winner: Diego — matches the STAR winner [Condorcet Loser] Condorcet Loser: Greta — loses every head-to-head matchup --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 65 ballots. Count × Ana,Diego,Greta 13 × 3, 5, 0 12 × 0, 5, 4 10 × 5, 4, 0 9 × 0, 5, 0 8 × 0, 3, 5 7 × 0, 2, 5 6 × 5, 3, 0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Ana 16 0 13 0 0 36 | 119 1.8 Diego 34 10 14 7 0 0 | 266 4.1 Greta 15 12 0 0 0 38 | 123 1.9 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Diego -- 266 -- First place Greta -- 123 -- Second place Ana -- 119 Diego and Greta advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Diego -- 50 -- First place Greta -- 15 Equal Support -- 0 Diego wins. Runoff math: 65 ballots cast − 0 Equal Support (no preference between the two finalists) ── 65 voters with a preference (majority = 33) Diego 50 (77%) · Greta 15 (23%) [STAR Voting: Winner — STAR Voting Method (single winner)] Diego