====================================================================== SOURCE FILE: bv2138_cxrf8v_star.yaml TABULATED FILE: bv2138_cxrf8v_star_tabulated.txt ====================================================================== election_title: "No Condorcet Winner — STAR (ranks→scores): Brad wins the runoff" scenario_description: |- One of four races in the 'One Ranked Electorate, Many Tabulations' election (BV2138, bvid cxrf8v; BV-confirmed). 921 voters, five candidates, NO Condorcet winner (Smith set = Abby, Brad, Dave, Erin). Robert LeGrand's flagship 'the method decides' example: across ~15 methods the win splits five ways. Ranks mapped to 0–5 scores. Abby tops the score round (2836) but Brad wins the automatic runoff head-to-head (463–458) → STAR → Brad (agreeing with BV's Ranked Robin, not LH's). bv_test_id: BV2138 bv_election_id: cxrf8v bv_results_url: https://bettervoting.com/cxrf8v/results voting_method: STAR num_winners: 1 ballots: |- Abby,Brad,Cora,Dave,Erin 98: 5,1,4,2,3 64: 4,5,2,1,3 12: 4,5,1,2,3 98: 3,5,2,1,4 13: 3,5,1,2,4 125: 2,5,1,3,4 124: 4,1,5,2,3 76: 3,1,5,2,4 21: 4,3,1,5,2 30: 3,4,1,5,2 98: 1,4,2,5,3 139: 3,2,4,5,1 23: 2,3,4,5,1 expected_winners: - Brad # file: bv2138_cxrf8v_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === No Condorcet Winner — STAR (ranks→scores): Brad wins the runoff === One of four races in the 'One Ranked Electorate, Many Tabulations' election (BV2138, bvid cxrf8v; BV-confirmed). 921 voters, five candidates, NO Condorcet winner (Smith set = Abby, Brad, Dave, Erin). Robert LeGrand's flagship 'the method decides' example: across ~15 methods the win splits five ways. Ranks mapped to 0–5 scores. Abby tops the score round (2836) but Brad wins the automatic runoff head-to-head (463–458) → STAR → Brad (agreeing with BV's Ranked Robin, not LH's). --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Abby | * Brad | Cora | Dave | Erin | ----------------------------------------------------------------------------------------------------------- * Abby > | --- |458 - 0 - 463 |461 - 0 - 460 |485 - 0 - 436 |511 - 0 - 410 | * Brad > | 463 - 0 - 458 | --- |461 - 0 - 460 |312 - 0 - 609 |623 - 0 - 298 | Cora > | 460 - 0 - 461 |460 - 0 - 461 | --- |460 - 0 - 461 |460 - 0 - 461 | Dave > | 436 - 0 - 485 |609 - 0 - 312 |461 - 0 - 460 | --- |311 - 0 - 610 | Erin > | 410 - 0 - 511 |298 - 0 - 623 |461 - 0 - 460 |610 - 0 - 311 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: Abby > Dave > Brad > Abby) [Condorcet Loser] Condorcet Loser: Cora — loses every head-to-head matchup [Divergence from STAR] STAR = Brad RCV-IRV = Dave (differs from STAR) Approval = Erin (differs from STAR) RCV-RR = Abby (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/bv2138_cxrf8v_star_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/bv2138_cxrf8v_star_RCV-RR_tabulated.txt [Runoff Reversal] - Score Round Winner(s) = (Abby) - Runoff Round Winner = (Brad) Candidate Abby earned the highest total score, but Candidate Brad 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 921 ballots. Count × Abby,Brad,Cora,Dave,Erin 139 × 3, 2, 4, 5, 1 125 × 2, 5, 1, 3, 4 124 × 4, 1, 5, 2, 3 98 × 5, 1, 4, 2, 3 98 × 3, 5, 2, 1, 4 98 × 1, 4, 2, 5, 3 76 × 3, 1, 5, 2, 4 64 × 4, 5, 2, 1, 3 30 × 3, 4, 1, 5, 2 23 × 2, 3, 4, 5, 1 21 × 4, 3, 1, 5, 2 13 × 3, 5, 1, 2, 4 12 × 4, 5, 1, 2, 3 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Abby 98 221 356 148 98 0 | 2836 3.1 Brad 312 128 44 139 298 0 | 2780 3.0 Cora 200 260 0 260 201 0 | 2761 3.0 Dave 311 0 125 323 162 0 | 2738 3.0 Erin 0 312 396 51 162 0 | 2700 2.9 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Abby -- 2836 -- First place Brad -- 2780 -- Second place Cora -- 2761 Dave -- 2738 Erin -- 2700 Abby and Brad advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Brad -- 463 -- First place Abby -- 458 Equal Support -- 0 Brad wins. Runoff math: 921 ballots cast − 0 Equal Support (no preference between the two finalists) ─── 921 voters with a preference (majority = 461) Brad 463 (50%) · Abby 458 (50%) [STAR Voting: Winner — STAR Voting Method (single winner)] Brad