====================================================================== SOURCE FILE: bv2165_9vxcj7_star.yaml TABULATED FILE: bv2165_9vxcj7_star_tabulated.txt ====================================================================== election_title: "Coombs Ex.19 full — STAR: Boone wins the runoff 8–7" scenario_description: |- Race 1 of 2 in the Coombs No-Show pair, part 1 of 2 (BV2165, bvid 9vxcj7; BV-confirmed; the pair is BV2165/66). 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), Example 19. The full electorate: 15 voters — 4×(Amy>Boone>Cass), 4×(Boone>Cass>Amy), 5×(Cass>Amy>Boone), 2×(Cass>Boone>Amy). Coombs (worked on the case page; no tabulator on BV or in LH): Amy is ranked last by the most voters (6) and is deleted; Boone then holds a majority — Boone wins. This STAR race (5/3/1 map): Amy 41, Boone 43, Cass 51 — Cass tops the scores, but Boone wins the automatic runoff 8–7. Part 2 (BV2166): the two Cass>Boone>Amy voters stay home, and BOTH Coombs and STAR flip to Cass, their favorite. Pairwise is a cycle (Amy>Boone 9–6, Boone>Cass 8–7, Cass>Amy 11–4) — no RR race; IRV's first elimination is a random Amy/Boone tie — no IRV race. Live results: https://bettervoting.com/9vxcj7/results bv_test_id: BV2165 bv_election_id: 9vxcj7 bv_results_url: https://bettervoting.com/9vxcj7/results paradoxes: [no-show, condorcet-cycle] voting_method: STAR num_winners: 1 ballots: |- Amy,Boone,Cass 5,3,1 5,3,1 5,3,1 5,3,1 1,5,3 1,5,3 1,5,3 1,5,3 3,1,5 3,1,5 3,1,5 3,1,5 3,1,5 1,3,5 1,3,5 expected_winners: - Boone # file: bv2165_9vxcj7_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Coombs Ex.19 full — STAR: Boone wins the runoff 8–7 === Race 1 of 2 in the Coombs No-Show pair, part 1 of 2 (BV2165, bvid 9vxcj7; BV-confirmed; the pair is BV2165/66). 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), Example 19. The full electorate: 15 voters — 4×(Amy>Boone>Cass), 4×(Boone>Cass>Amy), 5×(Cass>Amy>Boone), 2×(Cass>Boone>Amy). Coombs (worked on the case page; no tabulator on BV or in LH): Amy is ranked last by the most voters (6) and is deleted; Boone then holds a majority — Boone wins. This STAR race (5/3/1 map): Amy 41, Boone 43, Cass 51 — Cass tops the scores, but Boone wins the automatic runoff 8–7. Part 2 (BV2166): the two Cass>Boone>Amy voters stay home, and BOTH Coombs and STAR flip to Cass, their favorite. Pairwise is a cycle (Amy>Boone 9–6, Boone>Cass 8–7, Cass>Amy 11–4) — no RR race; IRV's first elimination is a random Amy/Boone tie — no IRV race. Live results: https://bettervoting.com/9vxcj7/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | Amy | * Boone | * Cass | ------------------------------------------------------------- Amy > | --- | 9 - 0 - 6 | 4 - 0 - 11 | * Boone > | 6 - 0 - 9 | --- | 8 - 0 - 7 | * Cass > | 11 - 0 - 4 | 7 - 0 - 8 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: Amy > Boone > Cass > Amy) [Divergence from STAR] STAR = Boone Choose-One (Plurality) = Cass (differs from STAR) Approval = Cass (differs from STAR) RCV-RR = Cass (differs from STAR) Full round-by-round reports (generated for review): RCV-RR round-robin: cases_tabulated/bv2165_9vxcj7_star_RCV-RR_tabulated.txt [Runoff Reversal] - Score Round Winner(s) = (Cass) - Runoff Round Winner = (Boone) Candidate Cass earned the highest total score, but Candidate Boone 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 15 ballots. Count × Amy,Boone,Cass 5 × 3, 1, 5 4 × 5, 3, 1 4 × 1, 5, 3 2 × 1, 3, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Amy 4 0 5 0 6 0 | 41 2.7 Boone 4 0 6 0 5 0 | 43 2.9 Cass 7 0 4 0 4 0 | 51 3.4 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Cass -- 51 -- First place Boone -- 43 -- Second place Amy -- 41 Cass and Boone advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Boone -- 8 -- First place Cass -- 7 Equal Support -- 0 Boone wins. Runoff math: 15 ballots cast − 0 Equal Support (no preference between the two finalists) ── 15 voters with a preference (majority = 8) Boone 8 (53%) · Cass 7 (47%) [STAR Voting: Winner — STAR Voting Method (single winner)] Boone