====================================================================== SOURCE FILE: bv2171_h93tm4_star.yaml TABULATED FILE: bv2171_h93tm4_star_tabulated.txt ====================================================================== election_title: "Condorcet centrist, minimal form (8 voters) — STAR elects Casey" scenario_description: |- The STAR race (lead of seven) in the minimal Condorcet-centrist election (BV2171, bvid h93tm4; BV-confirmed). The fewest ballots that still reproduce the whole center-squeeze symptom: 8 voters, three candidates — Avery (left pole), Blake (right pole), Casey (centrist). Casey is the Condorcet winner (beats Avery 5–3 and Blake 5–3) but has only 2 first choices, the fewest. Ranks mapped to 0–5 scores (top=5, mid=3, bottom=1): Casey tops the score round 28 (Avery/Blake tie at 22) and wins the automatic runoff 5–3. 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/h93tm4/results Overview: bv2171_h93tm4_all_methods.md · Full 100-voter version: bv2172_bkwfjr_star.yaml (BV2172) · Original 4-method cut: ../symmetric_centrist_bv2170/ bv_test_id: BV2171 bv_election_id: h93tm4 bv_results_url: https://bettervoting.com/h93tm4/results paradoxes: [condorcet-winner] voting_method: STAR num_winners: 1 ballots: |- Count:Avery,Blake,Casey 3:5,1,3 # Avery > Casey > Blake (left pole) 3:1,5,3 # Blake > Casey > Avery (right pole) 1:3,1,5 # Casey > Avery > Blake (centrist, leans left) 1:1,3,5 # Casey > Blake > Avery (centrist, leans right) expected_winners: - Casey # file: bv2171_h93tm4_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Condorcet centrist, minimal form (8 voters) — STAR elects Casey === The STAR race (lead of seven) in the minimal Condorcet-centrist election (BV2171, bvid h93tm4; BV-confirmed). The fewest ballots that still reproduce the whole center-squeeze symptom: 8 voters, three candidates — Avery (left pole), Blake (right pole), Casey (centrist). Casey is the Condorcet winner (beats Avery 5–3 and Blake 5–3) but has only 2 first choices, the fewest. Ranks mapped to 0–5 scores (top=5, mid=3, bottom=1): Casey tops the score round 28 (Avery/Blake tie at 22) and wins the automatic runoff 5–3. 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/h93tm4/results Overview: bv2171_h93tm4_all_methods.md · Full 100-voter version: bv2172_bkwfjr_star.yaml (BV2172) · 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 22 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 > | --- |4 - 0 - 4 |3 - 0 - 5 | Blake > | 4 - 0 - 4 | --- |3 - 0 - 5 | * Casey > | 5 - 0 - 3 |5 - 0 - 3 | --- | [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/bv2171_h93tm4_star_RCV-IRV_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 8 ballots. Count × Avery,Blake,Casey 3 × 5, 1, 3 3 × 1, 5, 3 1 × 3, 1, 5 1 × 1, 3, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Avery 3 0 1 0 4 0 | 22 2.8 Blake 3 0 1 0 4 0 | 22 2.8 Casey 2 0 6 0 0 0 | 28 3.5 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Casey -- 28 -- First place Avery -- 22 -- Tied for second place Blake -- 22 -- 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 -- 4 -- Tied for second place Blake -- 4 -- 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 -- 3 -- Tied for second place Blake -- 3 -- 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 -- 5 -- First place Avery -- 3 Equal Support -- 0 Casey wins. Runoff math: 8 ballots cast − 0 Equal Support (no preference between the two finalists) ─ 8 voters with a preference (majority = 5) Casey 5 (62%) · Avery 3 (38%) [STAR Voting: Winner — STAR Voting Method (single winner)] Casey