====================================================================== SOURCE FILE: bv2164_xbqq8t_star.yaml TABULATED FILE: bv2164_xbqq8t_star_tabulated.txt ====================================================================== election_title: "Coombs Ex.17 — STAR: Bree tops the scores, the Condorcet winner Arlo wins the runoff" scenario_description: |- Race 1 of 3 in the Coombs Condorcet-failure election (BV2164, bvid xbqq8t; BV-confirmed). Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A7 (Coombs' procedure: eliminate whoever is ranked LAST by the most voters), Example 17. 33 voters, four candidates: 11×(Arlo>Bree>Cole>Dana), 12×(Bree>Cole>Dana>Arlo), 2×(Bree>Arlo>Dana>Cole), 4×(Cole>Arlo>Dana>Bree), 4×(Dana>Arlo>Bree>Cole). Arlo is the Condorcet winner (beats Bree 19–14, Cole 17–16, Dana 17–16). Coombs — worked on the case page; no tabulator on BetterVoting or in the LH engine — deletes ARLO first (ranked last by 12, the most) and elects Bree. This STAR race (ranks mapped 5/4/2/1): Arlo 107, Bree 126, Cole 96, Dana 67 — Bree tops the scoring round, but Arlo wins the automatic runoff 19–14. No IRV race: its first elimination is a random Cole/Dana 4–4 tie on BV. Live results: https://bettervoting.com/xbqq8t/results bv_test_id: BV2164 bv_election_id: xbqq8t bv_results_url: https://bettervoting.com/xbqq8t/results paradoxes: [condorcet-winner] voting_method: STAR num_winners: 1 ballots: |- Arlo,Bree,Cole,Dana 11: 5,4,2,1 12: 1,5,4,2 # 2× Bree>Arlo>Dana>Cole and 4× Cole>Arlo>Dana>Bree and 4× Dana>Arlo>Bree>Cole: 4,5,1,2 4,5,1,2 4,1,5,2 4,1,5,2 4,1,5,2 4,1,5,2 4,2,1,5 4,2,1,5 4,2,1,5 4,2,1,5 expected_winners: - Arlo # file: bv2164_xbqq8t_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Coombs Ex.17 — STAR: Bree tops the scores, the Condorcet winner Arlo wins the runoff === Race 1 of 3 in the Coombs Condorcet-failure election (BV2164, bvid xbqq8t; BV-confirmed). Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A7 (Coombs' procedure: eliminate whoever is ranked LAST by the most voters), Example 17. 33 voters, four candidates: 11×(Arlo>Bree>Cole>Dana), 12×(Bree>Cole>Dana>Arlo), 2×(Bree>Arlo>Dana>Cole), 4×(Cole>Arlo>Dana>Bree), 4×(Dana>Arlo>Bree>Cole). Arlo is the Condorcet winner (beats Bree 19–14, Cole 17–16, Dana 17–16). Coombs — worked on the case page; no tabulator on BetterVoting or in the LH engine — deletes ARLO first (ranked last by 12, the most) and elects Bree. This STAR race (ranks mapped 5/4/2/1): Arlo 107, Bree 126, Cole 96, Dana 67 — Bree tops the scoring round, but Arlo wins the automatic runoff 19–14. No IRV race: its first elimination is a random Cole/Dana 4–4 tie on BV. Live results: https://bettervoting.com/xbqq8t/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Arlo | * Bree | Cole | Dana | --------------------------------------------------------------------------- * Arlo > | --- |19 - 0 - 14 |17 - 0 - 16 |17 - 0 - 16 | * Bree > | 14 - 0 - 19 | --- |29 - 0 - 4 |25 - 0 - 8 | Cole > | 16 - 0 - 17 | 4 - 0 - 29 | --- |27 - 0 - 6 | Dana > | 16 - 0 - 17 | 8 - 0 - 25 | 6 - 0 - 27 | --- | [Condorcet Winner] Condorcet Winner: Arlo — matches the STAR winner [Condorcet Loser] Condorcet Loser: Dana — loses every head-to-head matchup [Divergence from STAR] STAR = Arlo Choose-One (Plurality) = Bree (differs from STAR) Approval = Bree (differs from STAR) [Runoff Reversal] - Score Round Winner(s) = (Bree) - Runoff Round Winner = (Arlo) Candidate Bree earned the highest total score, but Candidate Arlo 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 33 ballots. Count × Arlo,Bree,Cole,Dana 12 × 1, 5, 4, 2 11 × 5, 4, 2, 1 4 × 4, 1, 5, 2 4 × 4, 2, 1, 5 2 × 4, 5, 1, 2 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Arlo 11 10 0 0 12 0 | 107 3.2 Bree 14 11 0 4 4 0 | 126 3.8 Cole 4 12 0 11 6 0 | 96 2.9 Dana 4 0 0 18 11 0 | 67 2.0 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Bree -- 126 -- First place Arlo -- 107 -- Second place Cole -- 96 Dana -- 67 Bree and Arlo advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Arlo -- 19 -- First place Bree -- 14 Equal Support -- 0 Arlo wins. Runoff math: 33 ballots cast − 0 Equal Support (no preference between the two finalists) ── 33 voters with a preference (majority = 17) Arlo 19 (58%) · Bree 14 (42%) [STAR Voting: Winner — STAR Voting Method (single winner)] Arlo