====================================================================== SOURCE FILE: bv2162_4htk44_star.yaml TABULATED FILE: bv2162_4htk44_star_tabulated.txt ====================================================================== election_title: "Nurmi Ex.16 sincere — STAR: elects the Condorcet winner B" scenario_description: |- Race 1 of 3 in the RCV-IRV truncation pair, part 1 of 2 (BV2162, bvid 4htk44; BV-confirmed; the pair is BV2162/63). 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 A6 (instant-runoff — Felsenthal's "Alternative Vote" is the British name for RCV-IRV), Example 16, due to Nurmi (1999: 63). 103 voters, four candidates, everyone ranking all four: 33×(A>B>C>D), 29×(B>A>C>D), 24×(C>B>A>D), 17×(D>C>B>A). B is the Condorcet winner (beats A 70–33, C 62–41, D 86–17). This STAR race (ranks mapped 5/4/2/1) scores A 346, B 407, C 312, D 171 — B wins the automatic runoff 70–33. The IRV race elects A instead (a Condorcet winner failure); part 2 (BV2163) shows 17 voters improving their result by TRUNCATING. Live results: https://bettervoting.com/4htk44/results bv_test_id: BV2162 bv_election_id: 4htk44 bv_results_url: https://bettervoting.com/4htk44/results paradoxes: [truncation, condorcet-winner] voting_method: STAR num_winners: 1 ballots: |- A,B,C,D 33: 5,4,2,1 29: 4,5,2,1 24: 2,4,5,1 17: 1,2,4,5 expected_winners: - B # file: bv2162_4htk44_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Nurmi Ex.16 sincere — STAR: elects the Condorcet winner B === Race 1 of 3 in the RCV-IRV truncation pair, part 1 of 2 (BV2162, bvid 4htk44; BV-confirmed; the pair is BV2162/63). 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 A6 (instant-runoff — Felsenthal's "Alternative Vote" is the British name for RCV-IRV), Example 16, due to Nurmi (1999: 63). 103 voters, four candidates, everyone ranking all four: 33×(A>B>C>D), 29×(B>A>C>D), 24×(C>B>A>D), 17×(D>C>B>A). B is the Condorcet winner (beats A 70–33, C 62–41, D 86–17). This STAR race (ranks mapped 5/4/2/1) scores A 346, B 407, C 312, D 171 — B wins the automatic runoff 70–33. The IRV race elects A instead (a Condorcet winner failure); part 2 (BV2163) shows 17 voters improving their result by TRUNCATING. Live results: https://bettervoting.com/4htk44/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * A | * B | C | D | --------------------------------------------------------------------------- * A > | --- |33 - 0 - 70 |62 - 0 - 41 |86 - 0 - 17 | * B > | 70 - 0 - 33 | --- |62 - 0 - 41 |86 - 0 - 17 | C > | 41 - 0 - 62 |41 - 0 - 62 | --- |86 - 0 - 17 | D > | 17 - 0 - 86 |17 - 0 - 86 |17 - 0 - 86 | --- | [Condorcet Winner] Condorcet Winner: B — matches the STAR winner [Condorcet Loser] Condorcet Loser: D — loses every head-to-head matchup [Divergence from STAR] STAR = B Choose-One (Plurality) = A (differs from STAR) RCV-IRV = 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. 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/bv2162_4htk44_star_RCV-IRV_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 103 ballots. Count × A,B,C,D 33 × 5,4,2,1 29 × 4,5,2,1 24 × 2,4,5,1 17 × 1,2,4,5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg A 33 29 0 24 17 0 | 346 3.4 B 29 57 0 17 0 0 | 407 4.0 C 24 17 0 62 0 0 | 312 3.0 D 17 0 0 0 86 0 | 171 1.7 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. B -- 407 -- First place A -- 346 -- Second place C -- 312 D -- 171 B and A advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. B -- 70 -- First place A -- 33 Equal Support -- 0 B wins. Runoff math: 103 ballots cast − 0 Equal Support (no preference between the two finalists) ─── 103 voters with a preference (majority = 52) B 70 (68%) · A 33 (32%) [STAR Voting: Winner — STAR Voting Method (single winner)] B