====================================================================== SOURCE FILE: bv2160_r6qc8h_star.yaml TABULATED FILE: bv2160_r6qc8h_star_tabulated.txt ====================================================================== election_title: "Fishburn Ex.14 — STAR: B wins the electorate whose Borda count is truncation-unstable" scenario_description: |- Race 1 of 2 in the Borda-truncation election (BV2160, bvid r6qc8h; BV-confirmed). 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 A5, Example 14 — adapted from Fishburn (1974: 543). 7 voters, four candidates: 3×(A>B>C>D), 1×(B>C>A>D), 1×(B>C>D>A), 2×(C>D>A>B). The Borda paradox lives on the case page (no Borda tabulator on BetterVoting or in the LH engine): Borda awards A 19, B 19, C 20, D 12 → C, but if the three A>B>C>D voters TRUNCATE C, Borda gives 16/16/14/12 — a truncation flips the winner away from C. This STAR race (ranks mapped 5/4/2/1) scores A 22, B 24, C 24, D 14: B and C take both finalist seats and B wins the automatic runoff 5–2. The pairwise preferences are a CYCLE (A>B 5–2, B>C 5–2, C>A 4–3), which is why no Ranked Robin or IRV race exists here (both would hit random ties on BetterVoting). Live results: https://bettervoting.com/r6qc8h/results bv_test_id: BV2160 bv_election_id: r6qc8h bv_results_url: https://bettervoting.com/r6qc8h/results paradoxes: [truncation, condorcet-cycle] voting_method: STAR num_winners: 1 ballots: |- A,B,C,D 5,4,2,1 5,4,2,1 5,4,2,1 2,5,4,1 1,5,4,2 2,1,5,4 2,1,5,4 expected_winners: - B # file: bv2160_r6qc8h_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Fishburn Ex.14 — STAR: B wins the electorate whose Borda count is truncation-unstable === Race 1 of 2 in the Borda-truncation election (BV2160, bvid r6qc8h; BV-confirmed). 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 A5, Example 14 — adapted from Fishburn (1974: 543). 7 voters, four candidates: 3×(A>B>C>D), 1×(B>C>A>D), 1×(B>C>D>A), 2×(C>D>A>B). The Borda paradox lives on the case page (no Borda tabulator on BetterVoting or in the LH engine): Borda awards A 19, B 19, C 20, D 12 → C, but if the three A>B>C>D voters TRUNCATE C, Borda gives 16/16/14/12 — a truncation flips the winner away from C. This STAR race (ranks mapped 5/4/2/1) scores A 22, B 24, C 24, D 14: B and C take both finalist seats and B wins the automatic runoff 5–2. The pairwise preferences are a CYCLE (A>B 5–2, B>C 5–2, C>A 4–3), which is why no Ranked Robin or IRV race exists here (both would hit random ties on BetterVoting). Live results: https://bettervoting.com/r6qc8h/results --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | A | * B | * C | D | ----------------------------------------------------------------- A > | --- |5 - 0 - 2 |3 - 0 - 4 |4 - 0 - 3 | * B > | 2 - 0 - 5 | --- |5 - 0 - 2 |5 - 0 - 2 | * C > | 4 - 0 - 3 |2 - 0 - 5 | --- |7 - 0 - 0 | D > | 3 - 0 - 4 |2 - 0 - 5 |0 - 0 - 7 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: A > B > C > A) [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) RCV-RR = C (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/bv2160_r6qc8h_star_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/bv2160_r6qc8h_star_RCV-RR_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 7 ballots. Count × A,B,C,D 3 × 5,4,2,1 2 × 2,1,5,4 1 × 2,5,4,1 1 × 1,5,4,2 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg A 3 0 0 3 1 0 | 22 3.1 B 2 3 0 0 2 0 | 24 3.4 C 2 2 0 3 0 0 | 24 3.4 D 0 2 0 1 4 0 | 14 2.0 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. B -- 24 -- First place C -- 24 -- Second place A -- 22 D -- 14 B and C advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. B -- 5 -- First place C -- 2 Equal Support -- 0 B wins. Runoff math: 7 ballots cast − 0 Equal Support (no preference between the two finalists) ─ 7 voters with a preference (majority = 4) B 5 (71%) · C 2 (29%) [STAR Voting: Winner — STAR Voting Method (single winner)] B