====================================================================== SOURCE FILE: bv2145_6fj2kg_star.yaml TABULATED FILE: bv2145_6fj2kg_star_tabulated.txt ====================================================================== election_title: "Felsenthal Ex.2 — STAR (ranks→scores): elects the Condorcet winner" scenario_description: |- Race 3 of 3 in the Felsenthal runoff-paradoxes election, part 1 of 2 (BV2145, bvid 6fj2kg; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 2 — see bv2145_6fj2kg_irv.yaml for the full citation and setup. The same 17 voters with ranks mapped to 0–5 scores (house map, N=3: top=5, mid=3, bottom=1). Scores: Ada 53, Ben 51, Cleo 49 — Ada and Ben advance, and Ada wins the automatic runoff 9–8. STAR elects the Condorcet winner that the runoff procedure (the IRV race) eliminated first. Live results: https://bettervoting.com/6fj2kg/results bv_test_id: BV2145 bv_election_id: 6fj2kg bv_results_url: https://bettervoting.com/6fj2kg/results paradoxes: [condorcet-winner] voting_method: STAR num_winners: 1 ballots: |- Ada,Ben,Cleo 5,3,1 5,3,1 5,3,1 5,1,3 5,1,3 3,5,1 3,5,1 3,5,1 3,5,1 1,5,3 1,5,3 3,1,5 3,1,5 3,1,5 3,1,5 1,3,5 1,3,5 expected_winners: - Ada # file: bv2145_6fj2kg_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Felsenthal Ex.2 — STAR (ranks→scores): elects the Condorcet winner === Race 3 of 3 in the Felsenthal runoff-paradoxes election, part 1 of 2 (BV2145, bvid 6fj2kg; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 2 — see bv2145_6fj2kg_irv.yaml for the full citation and setup. The same 17 voters with ranks mapped to 0–5 scores (house map, N=3: top=5, mid=3, bottom=1). Scores: Ada 53, Ben 51, Cleo 49 — Ada and Ben advance, and Ada wins the automatic runoff 9–8. STAR elects the Condorcet winner that the runoff procedure (the IRV race) eliminated first. Live results: https://bettervoting.com/6fj2kg/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Ada | * Ben | Cleo | ----------------------------------------------------- * Ada > | --- |9 - 0 - 8 |9 - 0 - 8 | * Ben > | 8 - 0 - 9 | --- |9 - 0 - 8 | Cleo > | 8 - 0 - 9 |8 - 0 - 9 | --- | [Condorcet Winner] Condorcet Winner: Ada — matches the STAR winner [Condorcet Loser] Condorcet Loser: Cleo — loses every head-to-head matchup [Divergence from STAR] STAR = Ada Choose-One (Plurality) = Ben (differs from STAR) RCV-IRV = Ben (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/bv2145_6fj2kg_star_RCV-IRV_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 17 ballots. Count × Ada,Ben,Cleo 4 × 3, 5, 1 4 × 3, 1, 5 3 × 5, 3, 1 2 × 5, 1, 3 2 × 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 Ada 5 0 8 0 4 0 | 53 3.1 Ben 6 0 5 0 6 0 | 51 3.0 Cleo 6 0 4 0 7 0 | 49 2.9 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Ada -- 53 -- First place Ben -- 51 -- Second place Cleo -- 49 Ada and Ben advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Ada -- 9 -- First place Ben -- 8 Equal Support -- 0 Ada wins. Runoff math: 17 ballots cast − 0 Equal Support (no preference between the two finalists) ── 17 voters with a preference (majority = 9) Ada 9 (53%) · Ben 8 (47%) [STAR Voting: Winner — STAR Voting Method (single winner)] Ada