====================================================================== SOURCE FILE: bv2149_byk9v2_star.yaml TABULATED FILE: bv2149_byk9v2_star_tabulated.txt ====================================================================== election_title: "Felsenthal Ex.3 Combined — STAR: Bruno, consistent with both districts" scenario_description: |- Race 2 of 2 in the Combined stage of the Felsenthal Reinforcement-paradox trio (BV2149, bvid byk9v2; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 3 — see bv2149_byk9v2_irv.yaml for the setup. The same 32 ballots with ranks mapped 5/3/1. Scores: Alma 88, Bruno 98, Cora 102 — Cora and Bruno advance, and Bruno wins the automatic runoff 18–14. STAR elects Bruno in District I, District II, AND the combined electorate — consistent where the runoff procedure flips to Alma. (Honesty note: STAR is consistent in THIS election, but methods with a runoff stage are not reinforcement-proof in general.) Live results: https://bettervoting.com/byk9v2/results bv_test_id: BV2149 bv_election_id: byk9v2 bv_results_url: https://bettervoting.com/byk9v2/results paradoxes: [multiple-districts] voting_method: STAR num_winners: 1 ballots: |- Alma,Bruno,Cora 5,3,1 5,3,1 5,3,1 5,3,1 5,1,3 5,1,3 5,1,3 5,1,3 5,1,3 5,1,3 3,5,1 1,5,3 1,5,3 1,5,3 1,5,3 1,5,3 1,5,3 1,5,3 1,5,3 1,5,3 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 3,1,5 3,1,5 1,3,5 expected_winners: - Bruno # file: bv2149_byk9v2_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Felsenthal Ex.3 Combined — STAR: Bruno, consistent with both districts === Race 2 of 2 in the Combined stage of the Felsenthal Reinforcement-paradox trio (BV2149, bvid byk9v2; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 3 — see bv2149_byk9v2_irv.yaml for the setup. The same 32 ballots with ranks mapped 5/3/1. Scores: Alma 88, Bruno 98, Cora 102 — Cora and Bruno advance, and Bruno wins the automatic runoff 18–14. STAR elects Bruno in District I, District II, AND the combined electorate — consistent where the runoff procedure flips to Alma. (Honesty note: STAR is consistent in THIS election, but methods with a runoff stage are not reinforcement-proof in general.) Live results: https://bettervoting.com/byk9v2/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | Alma | * Bruno | * Cora | ------------------------------------------------------------- Alma > | --- |17 - 0 - 15 |11 - 0 - 21 | * Bruno > | 15 - 0 - 17 | --- |18 - 0 - 14 | * Cora > | 21 - 0 - 11 |14 - 0 - 18 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: Alma > Bruno > Cora > Alma) [Divergence from STAR] STAR = Bruno RCV-IRV = Alma (differs from STAR) Approval = Cora (differs from STAR) RCV-RR = Cora (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/bv2149_byk9v2_star_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/bv2149_byk9v2_star_RCV-RR_tabulated.txt [Runoff Reversal] - Score Round Winner(s) = (Cora) - Runoff Round Winner = (Bruno) Candidate Cora earned the highest total score, but Candidate Bruno 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 32 ballots. Count × Alma,Bruno,Cora 13 × 1, 5, 3 7 × 3, 1, 5 6 × 5, 1, 3 4 × 5, 3, 1 1 × 3, 5, 1 1 × 1, 3, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Alma 10 0 8 0 14 0 | 88 2.8 Bruno 14 0 5 0 13 0 | 98 3.1 Cora 8 0 19 0 5 0 | 102 3.2 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Cora -- 102 -- First place Bruno -- 98 -- Second place Alma -- 88 Cora and Bruno advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Bruno -- 18 -- First place Cora -- 14 Equal Support -- 0 Bruno wins. Runoff math: 32 ballots cast − 0 Equal Support (no preference between the two finalists) ── 32 voters with a preference (majority = 17) Bruno 18 (56%) · Cora 14 (44%) [STAR Voting: Winner — STAR Voting Method (single winner)] Bruno