====================================================================== SOURCE FILE: bv2167_f3dxq9_star.yaml TABULATED FILE: bv2167_f3dxq9_star_tabulated.txt ====================================================================== election_title: "Minimax Ex.29 — STAR: elects B, a top-cycle member, not the universal loser" scenario_description: |- Race 1 of 2 in the Minimax-elects-the-absolute-loser election (BV2167, bvid f3dxq9; 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 A10 (the Condorcet / Minimax / Simpson-Kramer procedure), Example 29. 11 voters, four candidates: 2×(D>A>C>B), 3×(D>B>A>C), 3×(C>B>A>D), 1×(B>A>C>D), 2×(A>C>B>D). A, B, C form a top cycle (B>A 7–4, A>C 8–3, C>B 7–4); D loses every matchup 5–6 — the Condorcet loser AND absolute loser (6 of 11 rank D last). Minimax — worked on the case page; no tabulator on BV or in LH — elects D, whose worst loss (6) is the smallest (A/B/C: 7/7/8). This STAR race (ranks mapped 5/4/2/1): A 34, B 35, C 32, D 31 — B and A advance, B wins the automatic runoff 7–4. No RR race (the A/B/C Copeland tie → BV random) and no IRV race (random transfer tie). Live results: https://bettervoting.com/f3dxq9/results bv_test_id: BV2167 bv_election_id: f3dxq9 bv_results_url: https://bettervoting.com/f3dxq9/results paradoxes: [condorcet-loser, absolute-loser, condorcet-cycle] voting_method: STAR num_winners: 1 ballots: |- A,B,C,D 4,1,2,5 4,1,2,5 2,4,1,5 2,4,1,5 2,4,1,5 2,4,5,1 2,4,5,1 2,4,5,1 4,5,2,1 5,2,4,1 5,2,4,1 expected_winners: - B # file: bv2167_f3dxq9_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Minimax Ex.29 — STAR: elects B, a top-cycle member, not the universal loser === Race 1 of 2 in the Minimax-elects-the-absolute-loser election (BV2167, bvid f3dxq9; 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 A10 (the Condorcet / Minimax / Simpson-Kramer procedure), Example 29. 11 voters, four candidates: 2×(D>A>C>B), 3×(D>B>A>C), 3×(C>B>A>D), 1×(B>A>C>D), 2×(A>C>B>D). A, B, C form a top cycle (B>A 7–4, A>C 8–3, C>B 7–4); D loses every matchup 5–6 — the Condorcet loser AND absolute loser (6 of 11 rank D last). Minimax — worked on the case page; no tabulator on BV or in LH — elects D, whose worst loss (6) is the smallest (A/B/C: 7/7/8). This STAR race (ranks mapped 5/4/2/1): A 34, B 35, C 32, D 31 — B and A advance, B wins the automatic runoff 7–4. No RR race (the A/B/C Copeland tie → BV random) and no IRV race (random transfer tie). Live results: https://bettervoting.com/f3dxq9/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * A | * B | C | D | ----------------------------------------------------------------- * A > | --- |4 - 0 - 7 |8 - 0 - 3 |6 - 0 - 5 | * B > | 7 - 0 - 4 | --- |4 - 0 - 7 |6 - 0 - 5 | C > | 3 - 0 - 8 |7 - 0 - 4 | --- |6 - 0 - 5 | D > | 5 - 0 - 6 |5 - 0 - 6 |5 - 0 - 6 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: A > C > B > A) [Condorcet Loser] Condorcet Loser: D — loses every head-to-head matchup — elected by Choose-One (Plurality)! [Divergence from STAR] STAR = B Choose-One (Plurality) = D (differs from STAR) RCV-IRV = C (differs from STAR) RCV-RR = A (differs from STAR) Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine method difference, not a tie-breaking artifact. Full round-by-round reports (generated for review): RCV-IRV rounds: cases_tabulated/bv2167_f3dxq9_star_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/bv2167_f3dxq9_star_RCV-RR_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 11 ballots. Count × A,B,C,D 3 × 2,4,1,5 3 × 2,4,5,1 2 × 4,1,2,5 2 × 5,2,4,1 1 × 4,5,2,1 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg A 2 3 0 6 0 0 | 34 3.1 B 1 6 0 2 2 0 | 35 3.2 C 3 2 0 3 3 0 | 32 2.9 D 5 0 0 0 6 0 | 31 2.8 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. B -- 35 -- First place A -- 34 -- Second place C -- 32 D -- 31 B and A advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. B -- 7 -- First place A -- 4 Equal Support -- 0 B wins. Runoff math: 11 ballots cast − 0 Equal Support (no preference between the two finalists) ── 11 voters with a preference (majority = 6) B 7 (64%) · A 4 (36%) [STAR Voting: Winner — STAR Voting Method (single winner)] B