====================================================================== SOURCE FILE: bv2150_dxg8pb_star.yaml TABULATED FILE: bv2150_dxg8pb_star_tabulated.txt ====================================================================== election_title: "Felsenthal Ex.4 full electorate — STAR: elects the Condorcet winner Beth" scenario_description: |- Race 3 of 3 in the No-Show-paradox pair, part 1 of 2 (BV2150, bvid dxg8pb; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 4 — see bv2150_dxg8pb_irv.yaml for the setup. The same 11 voters with ranks mapped to 0–5 scores (5/3/1). Scores: Andy 29, Beth 37, Carl 33 — Beth and Carl advance, Beth wins the automatic runoff 7–4. STAR elects the Condorcet winner that the runoff procedure (the IRV race) deleted in round one. Live results: https://bettervoting.com/dxg8pb/results bv_test_id: BV2150 bv_election_id: dxg8pb bv_results_url: https://bettervoting.com/dxg8pb/results paradoxes: [no-show, condorcet-winner] voting_method: STAR num_winners: 1 ballots: |- Andy,Beth,Carl 5,3,1 5,3,1 5,3,1 5,3,1 1,5,3 1,5,3 1,5,3 3,1,5 1,3,5 1,3,5 1,3,5 expected_winners: - Beth # file: bv2150_dxg8pb_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Felsenthal Ex.4 full electorate — STAR: elects the Condorcet winner Beth === Race 3 of 3 in the No-Show-paradox pair, part 1 of 2 (BV2150, bvid dxg8pb; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 4 — see bv2150_dxg8pb_irv.yaml for the setup. The same 11 voters with ranks mapped to 0–5 scores (5/3/1). Scores: Andy 29, Beth 37, Carl 33 — Beth and Carl advance, Beth wins the automatic runoff 7–4. STAR elects the Condorcet winner that the runoff procedure (the IRV race) deleted in round one. Live results: https://bettervoting.com/dxg8pb/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | Andy | * Beth | * Carl | ----------------------------------------------------- Andy > | --- |5 - 0 - 6 |4 - 0 - 7 | * Beth > | 6 - 0 - 5 | --- |7 - 0 - 4 | * Carl > | 7 - 0 - 4 |4 - 0 - 7 | --- | [Condorcet Winner] Condorcet Winner: Beth — matches the STAR winner [Condorcet Loser] Condorcet Loser: Andy — loses every head-to-head matchup — elected by Choose-One (Plurality)! [Divergence from STAR] STAR = Beth Choose-One (Plurality) = Andy (differs from STAR) RCV-IRV = Carl (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. Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone outlier — the classic center-squeeze signature. Full round-by-round reports (generated for review): RCV-IRV rounds: cases_tabulated/bv2150_dxg8pb_star_RCV-IRV_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 11 ballots. Count × Andy,Beth,Carl 4 × 5, 3, 1 3 × 1, 5, 3 3 × 1, 3, 5 1 × 3, 1, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Andy 4 0 1 0 6 0 | 29 2.6 Beth 3 0 7 0 1 0 | 37 3.4 Carl 4 0 3 0 4 0 | 33 3.0 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Beth -- 37 -- First place Carl -- 33 -- Second place Andy -- 29 Beth and Carl advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Beth -- 7 -- First place Carl -- 4 Equal Support -- 0 Beth wins. Runoff math: 11 ballots cast − 0 Equal Support (no preference between the two finalists) ── 11 voters with a preference (majority = 6) Beth 7 (64%) · Carl 4 (36%) [STAR Voting: Winner — STAR Voting Method (single winner)] Beth