====================================================================== SOURCE FILE: bv2172_bkwfjr_star.yaml TABULATED FILE: bv2172_bkwfjr_star_tabulated.txt ====================================================================== election_title: "Condorcet centrist, full form (100 voters, 47/47/3/3) — STAR elects Casey" scenario_description: |- The STAR race (lead of seven) in the full Condorcet-centrist election (BV2172, bvid bkwfjr; BV-confirmed) — the profile as drawn in the "Should we always elect the Condorcet winner?" explainer (youtu.be/NlisR8vbpN4). 100 voters, three candidates — Avery (left pole), Blake (right pole), Casey (centrist). Casey is the Condorcet winner (beats Avery 53–47 and Blake 53–47) but has only 6 first choices. Ranks mapped to 0–5 scores (top=5, mid=3, bottom=1): Casey tops the score round 312 (Avery/Blake tie at 294) and wins the automatic runoff 53–47. Seven methods, one electorate. Whole-ballot methods — STAR, STAR-PR (1 seat), Approval (approve top two), Ranked Robin — elect Casey. First-choice methods — RCV-IRV, STV (1 seat), Choose-One — eliminate Casey first and, because the poles are a mirror image, deadlock Avery vs Blake in an exact tie (random on BV, not freezable). See the overview page for all seven. Live results: https://bettervoting.com/bkwfjr/results Overview: bv2172_bkwfjr_all_methods.md · Minimal 8-voter version: bv2171_h93tm4_star.yaml (BV2171) · Original 4-method cut: ../symmetric_centrist_bv2170/ bv_test_id: BV2172 bv_election_id: bkwfjr bv_results_url: https://bettervoting.com/bkwfjr/results paradoxes: [condorcet-winner] voting_method: STAR num_winners: 1 ballots: |- Count:Avery,Blake,Casey 47:5,1,3 # Avery > Casey > Blake (left pole) 47:1,5,3 # Blake > Casey > Avery (right pole) 3:3,1,5 # Casey > Avery > Blake (centrist, leans left) 3:1,3,5 # Casey > Blake > Avery (centrist, leans right) expected_winners: - Casey # file: bv2172_bkwfjr_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Condorcet centrist, full form (100 voters, 47/47/3/3) — STAR elects Casey === The STAR race (lead of seven) in the full Condorcet-centrist election (BV2172, bvid bkwfjr; BV-confirmed) — the profile as drawn in the "Should we always elect the Condorcet winner?" explainer (youtu.be/NlisR8vbpN4). 100 voters, three candidates — Avery (left pole), Blake (right pole), Casey (centrist). Casey is the Condorcet winner (beats Avery 53–47 and Blake 53–47) but has only 6 first choices. Ranks mapped to 0–5 scores (top=5, mid=3, bottom=1): Casey tops the score round 312 (Avery/Blake tie at 294) and wins the automatic runoff 53–47. Seven methods, one electorate. Whole-ballot methods — STAR, STAR-PR (1 seat), Approval (approve top two), Ranked Robin — elect Casey. First-choice methods — RCV-IRV, STV (1 seat), Choose-One — eliminate Casey first and, because the poles are a mirror image, deadlock Avery vs Blake in an exact tie (random on BV, not freezable). See the overview page for all seven. Live results: https://bettervoting.com/bkwfjr/results Overview: bv2172_bkwfjr_all_methods.md · Minimal 8-voter version: bv2171_h93tm4_star.yaml (BV2171) · Original 4-method cut: ../symmetric_centrist_bv2170/ --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist Note: Avery and Blake tied at 294 in the Scoring Round, and the lot rung (the ballots could not separate them) advanced Avery. The * marks who advanced, not who scored highest. | * Avery | Blake | * Casey | ------------------------------------------------------------- * Avery > | --- |50 - 0 - 50 |47 - 0 - 53 | Blake > | 50 - 0 - 50 | --- |47 - 0 - 53 | * Casey > | 53 - 0 - 47 |53 - 0 - 47 | --- | [Condorcet Winner] Condorcet Winner: Casey — matches the STAR winner [Condorcet Loser] No strict Condorcet loser; jointly weak Condorcet losers: Avery, Blake (winless — pairwise ties) — Avery elected by Choose-One (Plurality)! [Divergence from STAR] STAR = Casey Choose-One (Plurality) = Avery (differs from STAR) RCV-IRV = Avery (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/bv2172_bkwfjr_star_RCV-IRV_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 100 ballots. Count × Avery,Blake,Casey 47 × 5, 1, 3 47 × 1, 5, 3 3 × 3, 1, 5 3 × 1, 3, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Avery 47 0 3 0 50 0 | 294 2.9 Blake 47 0 3 0 50 0 | 294 2.9 Casey 6 0 94 0 0 0 | 312 3.1 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Casey -- 312 -- First place Avery -- 294 -- Tied for second place Blake -- 294 -- Tied for second place Casey advances, but there's a two-way tie for second. [STAR Voting: Scoring Round: First tiebreaker] The candidate preferred in the most head-to-head matchups advances. Avery -- 50 -- Tied for second place Blake -- 50 -- Tied for second place Equal Support -- 0 There's still a two-way tie for second. [STAR Voting: Scoring Round: Second tiebreaker] The candidate with the most votes of score 5 advances. Avery -- 47 -- Tied for second place Blake -- 47 -- Tied for second place There's still a two-way tie for second. *** No official tie-breaking lot numbers were provided. Ties are resolved using a fallback order: CSV column order. Lot-number priority order: ['Avery', 'Blake', 'Casey'] [Tiebreaker: Lot Number Priority] Tie among: ['Avery', 'Blake'] Resolved: ['Avery'] (selected by lot-number priority). [Lot-decided tie — rare] ⚠ The ballots did not break this tie: the deterministic rungs (pairwise / score, then five-star) all came back equal, so the pre-published LOT order chose among the tied candidates — the result here was set by lot, not by the votes. Usually the "dead rung": no tied candidate held a score-5 vote (five-star counts fives, not fours). Verify the tied candidates' 5-counts. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Casey -- 53 -- First place Avery -- 47 Equal Support -- 0 Casey wins. Runoff math: 100 ballots cast − 0 Equal Support (no preference between the two finalists) ─── 100 voters with a preference (majority = 51) Casey 53 (53%) · Avery 47 (47%) [STAR Voting: Winner — STAR Voting Method (single winner)] Casey