====================================================================== SOURCE FILE: star_district_B.yaml TABULATED FILE: star_district_B_tabulated.txt ====================================================================== election_title: "Summability demo — STAR district B (Oak wins — a runoff reversal)" scenario_description: |- District B of the STAR summability trio — the other half of the star_combined electorate. Publish its per-candidate score sums and pairwise matrix, add them to district A's, and you have the combined election's entire count: that's summability, and it's what makes STAR precinct-friendly and cheap to audit. Contrast the irv_* files, whose district tallies cannot be combined. voting_method: STAR num_winners: 1 expected_winners: [Oak] ballots: |- Maple, Oak, Pine 1,5,4 0,5,3 4,0,5 lot_numbers: [Maple, Oak, Pine] # file: star_district_B.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Summability demo — STAR district B (Oak wins — a runoff reversal) === District B of the STAR summability trio — the other half of the star_combined electorate. Publish its per-candidate score sums and pairwise matrix, add them to district A's, and you have the combined election's entire count: that's summability, and it's what makes STAR precinct-friendly and cheap to audit. Contrast the irv_* files, whose district tallies cannot be combined. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | Maple | * Oak | * Pine | ----------------------------------------------------- Maple > | --- |1 - 0 - 2 |0 - 0 - 3 | * Oak > | 2 - 0 - 1 | --- |2 - 0 - 1 | * Pine > | 3 - 0 - 0 |1 - 0 - 2 | --- | [Condorcet Winner] Condorcet Winner: Oak — matches the STAR winner [Condorcet Loser] Condorcet Loser: Maple — loses every head-to-head matchup [Divergence from STAR] STAR = Oak Approval = Pine (differs from STAR) [Runoff Reversal] - Score Round Winner(s) = (Pine) - Runoff Round Winner = (Oak) Candidate Pine earned the highest total score, but Candidate Oak won the automatic runoff — not a malfunction, STAR working as designed: the runoff elects the finalist preferred by the majority (of voters with a preference). --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 3 ballots. Maple,Oak,Pine 1, 5, 4 0, 5, 3 4, 0, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Maple 0 1 0 0 1 1 | 5 1.7 Oak 2 0 0 0 0 1 | 10 3.3 Pine 1 1 1 0 0 0 | 12 4.0 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Pine -- 12 -- First place Oak -- 10 -- Second place Maple -- 5 Pine and Oak advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Oak -- 2 -- First place Pine -- 1 Equal Support -- 0 Oak wins. Runoff math: 3 ballots cast − 0 Equal Support (no preference between the two finalists) ─ 3 voters with a preference (majority = 2) Oak 2 (67%) · Pine 1 (33%) [STAR Voting: Winner — STAR Voting Method (single winner)] Oak