====================================================================== SOURCE FILE: bv2280_37yf8x_star.yaml TABULATED FILE: bv2280_37yf8x_star_tabulated.txt ====================================================================== election_title: "Nine candidates, 25 voters — the 0–5 score ballot" scenario_description: |- THE COARSE BALLOT GETS IT RIGHT. Finn beats all eight rivals head-to-head, and STAR elects them from a ballot that cannot even rank the field. Nine candidates will not fit on six rungs — 0, 1, 2, 3, 4 and 5 hold six distinct places, so every voter here must give at least two candidates the same score. They actually tie far more than that minimum: about 16% of all candidate pairs go equal on this paper, against a pigeonhole floor of 8%. Most of the flattening is rounding, not the hard limit. And it does not matter. The preference that decides this election — Finn over everyone — survives the rounding, so STAR returns the Condorcet winner anyway. Read this file against bv2280_37yf8x_rr_top5.yaml, where the same 25 voters fill in a RANKED ballot capped at five names, the cap New York City and Maine actually use, and the count elects Gus instead. The ballot usually called "more expressive" loses the answer that these six rungs kept. Construction: build_cases.py in this folder. 25 voters and 9 candidates at frozen positions on one spectrum — Ada −0.73 · Ben −0.37 · Cleo −0.18 · Dev −0.17 · Emma −0.11 · Finn +0.24 · Gus +0.41 · Hugo +0.80 · Iris +0.84; utility = minus the distance; scores = each voter's own min-max scaling onto 0–5; rankings = those same utilities in order. Nothing is tuned to the result, and **no count in this folder is settled by a tie-break** — that was a search constraint, so every winner here survives any lot rule. voting_method: STAR num_winners: 1 bv_test_id: BV2280 bv_election_id: 37yf8x bv_results_url: https://bettervoting.com/37yf8x/results lot_numbers: [Ada, Ben, Cleo, Dev, Emma, Finn, Gus, Hugo, Iris] ballots: |- Ada,Ben,Cleo,Dev,Emma,Finn,Gus,Hugo,Iris 4,5,4,4,4,2,2,0,0 # voter at -0.43 0,2,2,2,3,4,5,5,5 # voter at +0.60 5,4,4,3,3,2,1,0,0 # voter at -0.67 0,1,2,2,2,3,4,5,5 # voter at +0.89 0,2,3,3,4,5,4,2,1 # voter at +0.18 2,4,5,5,5,3,2,0,0 # voter at -0.13 0,2,2,2,3,4,5,5,5 # voter at +0.59 0,1,2,2,2,4,4,5,5 # voter at +0.72 0,2,3,3,3,5,5,3,3 # voter at +0.34 0,1,2,2,2,4,4,5,5 # voter at +0.69 0,2,3,3,3,5,4,2,2 # voter at +0.23 3,5,5,5,4,3,2,0,0 # voter at -0.30 5,5,4,4,4,2,2,0,0 # voter at -0.51 0,1,2,2,2,3,4,5,5 # voter at +0.89 1,3,5,5,5,4,3,0,0 # voter at -0.05 0,2,2,2,3,4,5,5,5 # voter at +0.60 0,2,3,3,3,5,5,2,2 # voter at +0.28 4,5,4,4,4,2,2,0,0 # voter at -0.40 0,2,2,2,3,4,5,5,5 # voter at +0.62 5,4,4,4,3,2,2,0,0 # voter at -0.63 0,2,3,3,3,5,4,2,2 # voter at +0.27 5,5,4,4,4,2,2,0,0 # voter at -0.61 5,4,3,3,3,2,1,0,0 # voter at -1.33 3,5,5,5,5,3,2,0,0 # voter at -0.23 5,4,3,3,3,2,1,0,0 # voter at -1.82 expected_winners: - Finn # file: bv2280_37yf8x_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Nine candidates, 25 voters — the 0–5 score ballot === THE COARSE BALLOT GETS IT RIGHT. Finn beats all eight rivals head-to-head, and STAR elects them from a ballot that cannot even rank the field. Nine candidates will not fit on six rungs — 0, 1, 2, 3, 4 and 5 hold six distinct places, so every voter here must give at least two candidates the same score. They actually tie far more than that minimum: about 16% of all candidate pairs go equal on this paper, against a pigeonhole floor of 8%. Most of the flattening is rounding, not the hard limit. And it does not matter. The preference that decides this election — Finn over everyone — survives the rounding, so STAR returns the Condorcet winner anyway. Read this file against bv2280_37yf8x_rr_top5.yaml, where the same 25 voters fill in a RANKED ballot capped at five names, the cap New York City and Maine actually use, and the count elects Gus instead. The ballot usually called "more expressive" loses the answer that these six rungs kept. Construction: build_cases.py in this folder. 25 voters and 9 candidates at frozen positions on one spectrum — Ada −0.73 · Ben −0.37 · Cleo −0.18 · Dev −0.17 · Emma −0.11 · Finn +0.24 · Gus +0.41 · Hugo +0.80 · Iris +0.84; utility = minus the distance; scores = each voter's own min-max scaling onto 0–5; rankings = those same utilities in order. Nothing is tuned to the result, and **no count in this folder is settled by a tie-break** — that was a search constraint, so every winner here survives any lot rule. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | Ada | Ben | Cleo | Dev | * Emma | * Finn | Gus | Hugo | Iris | ------------------------------------------------------------------------------------------------------------------------------------------------- Ada > | --- | 4 - 2 - 19 | 6 - 2 - 17 | 6 - 2 - 17 | 6 - 2 - 17 | 8 - 2 - 15 |10 - 1 - 14 |12 - 0 - 13 |12 - 0 - 13 | Ben > | 19 - 2 - 4 | --- | 6 - 8 - 11 | 7 - 7 - 11 | 9 - 1 - 15 |11 - 0 - 14 |11 - 1 - 13 |12 - 4 - 9 |13 - 3 - 9 | Cleo > | 17 - 2 - 6 |11 - 8 - 6 | --- | 1 - 24 - 0 | 3 - 17 - 5 |12 - 0 - 13 |12 - 0 - 13 |16 - 1 - 8 |16 - 1 - 8 | Dev > | 17 - 2 - 6 |11 - 7 - 7 | 0 - 24 - 1 | --- | 2 - 18 - 5 |12 - 0 - 13 |12 - 0 - 13 |16 - 1 - 8 |16 - 1 - 8 | * Emma > | 17 - 2 - 6 |15 - 1 - 9 | 5 - 17 - 3 | 5 - 18 - 2 | --- |12 - 0 - 13 |12 - 1 - 12 |16 - 1 - 8 |16 - 1 - 8 | * Finn > | 15 - 2 - 8 |14 - 0 - 11 |13 - 0 - 12 |13 - 0 - 12 |13 - 0 - 12 | --- |10 - 9 - 6 |17 - 0 - 8 |17 - 0 - 8 | Gus > | 14 - 1 - 10 |13 - 1 - 11 |13 - 0 - 12 |13 - 0 - 12 |12 - 1 - 12 | 6 - 9 - 10 | --- |17 - 4 - 4 |17 - 4 - 4 | Hugo > | 13 - 0 - 12 | 9 - 4 - 12 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 0 - 17 | 4 - 4 - 17 | --- | 1 - 24 - 0 | Iris > | 13 - 0 - 12 | 9 - 3 - 13 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 0 - 17 | 4 - 4 - 17 | 0 - 24 - 1 | --- | [Condorcet Winner] Condorcet Winner: Finn — matches the STAR winner [Condorcet Loser] Condorcet Loser: Ada — loses every head-to-head matchup — elected by Choose-One (Plurality)! [Divergence from STAR] STAR = Finn Choose-One (Plurality) = Ada (differs from STAR) Approval = Emma (differs from STAR) --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 25 ballots. Count × Ada,Ben,Cleo,Dev,Emma,Finn,Gus,Hugo,Iris 4 × 0, 2, 2, 2, 3, 4, 5, 5, 5 2 × 4, 5, 4, 4, 4, 2, 2, 0, 0 2 × 0, 1, 2, 2, 2, 3, 4, 5, 5 2 × 0, 1, 2, 2, 2, 4, 4, 5, 5 2 × 0, 2, 3, 3, 3, 5, 4, 2, 2 2 × 5, 5, 4, 4, 4, 2, 2, 0, 0 2 × 5, 4, 3, 3, 3, 2, 1, 0, 0 1 × 5, 4, 4, 3, 3, 2, 1, 0, 0 1 × 0, 2, 3, 3, 4, 5, 4, 2, 1 1 × 2, 4, 5, 5, 5, 3, 2, 0, 0 1 × 0, 2, 3, 3, 3, 5, 5, 3, 3 1 × 3, 5, 5, 5, 4, 3, 2, 0, 0 1 × 1, 3, 5, 5, 5, 4, 3, 0, 0 1 × 0, 2, 3, 3, 3, 5, 5, 2, 2 1 × 5, 4, 4, 4, 3, 2, 2, 0, 0 1 × 3, 5, 5, 5, 5, 3, 2, 0, 0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Ada 6 2 2 1 1 13 | 47 1.9 Ben 6 5 1 9 4 0 | 75 3.0 Cleo 4 6 7 8 0 0 | 81 3.2 Dev 4 5 8 8 0 0 | 80 3.2 Emma 3 6 12 4 0 0 | 83 3.3 Finn 5 7 5 8 0 0 | 84 3.4 Gus 6 7 1 8 3 0 | 80 3.2 Hugo 8 0 1 4 0 12 | 51 2.0 Iris 8 0 1 3 1 12 | 50 2.0 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Finn -- 84 -- First place Emma -- 83 -- Second place Cleo -- 81 Dev -- 80 Gus -- 80 Ben -- 75 Hugo -- 51 Iris -- 50 Ada -- 47 Finn and Emma advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Finn -- 13 -- First place Emma -- 12 Equal Support -- 0 Finn wins. Runoff math: 25 ballots cast − 0 Equal Support (no preference between the two finalists) ── 25 voters with a preference (majority = 13) Finn 13 (52%) · Emma 12 (48%) [STAR Voting: Winner — STAR Voting Method (single winner)] Finn