====================================================================== SOURCE FILE: bv2146_krk2px_star.yaml TABULATED FILE: bv2146_krk2px_star_tabulated.txt ====================================================================== election_title: "Felsenthal Ex.2 after the raise — STAR: unmoved, still Ada" scenario_description: |- Race 3 of 3 in the Felsenthal runoff-paradoxes election, part 2 of 2 (BV2146, bvid krk2px; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 2 (continued) — see bv2146_krk2px_irv.yaml for the setup. The same 17 voters after the raise, ranks mapped 5/3/1. Ben's two raised ballots move him 51 → 55 and Cleo 49 → 45; Ada stays 53. Finalists are now Ben and Ada — and Ada still wins the automatic runoff 9–8, exactly as in BV2145. Giving Ben more support changed STAR's finalist pair but not its winner: no more-is-less here, while the same raise flips the IRV race. Live results: https://bettervoting.com/krk2px/results bv_test_id: BV2146 bv_election_id: krk2px bv_results_url: https://bettervoting.com/krk2px/results paradoxes: [non-monotonicity] 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 1,5,3 1,5,3 expected_winners: - Ada # file: bv2146_krk2px_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Felsenthal Ex.2 after the raise — STAR: unmoved, still Ada === Race 3 of 3 in the Felsenthal runoff-paradoxes election, part 2 of 2 (BV2146, bvid krk2px; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 2 (continued) — see bv2146_krk2px_irv.yaml for the setup. The same 17 voters after the raise, ranks mapped 5/3/1. Ben's two raised ballots move him 51 → 55 and Cleo 49 → 45; Ada stays 53. Finalists are now Ben and Ada — and Ada still wins the automatic runoff 9–8, exactly as in BV2145. Giving Ben more support changed STAR's finalist pair but not its winner: no more-is-less here, while the same raise flips the IRV race. Live results: https://bettervoting.com/krk2px/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 | --- |11 - 0 - 6 | Cleo > | 8 - 0 - 9 | 6 - 0 - 11 | --- | [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) [Runoff Reversal] - Score Round Winner(s) = (Ben) - Runoff Round Winner = (Ada) Candidate Ben earned the highest total score, but Candidate Ada 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 17 ballots. Count × Ada,Ben,Cleo 4 × 3, 5, 1 4 × 1, 5, 3 4 × 3, 1, 5 3 × 5, 3, 1 2 × 5, 1, 3 [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 8 0 3 0 6 0 | 55 3.2 Cleo 4 0 6 0 7 0 | 45 2.6 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Ben -- 55 -- First place Ada -- 53 -- Second place Cleo -- 45 Ben and Ada 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