====================================================================== SOURCE FILE: bv2170_pp2q4q_star.yaml TABULATED FILE: bv2170_pp2q4q_star_tabulated.txt ====================================================================== election_title: "Symmetric centrist (47/47/3/3) — STAR: elects Casey, the Condorcet winner" scenario_description: |- One of four races in the Symmetric Centrist election (BV2170, bvid pp2q4q; BV-confirmed). 100 voters, three candidates, ONE electorate tabulated four ways. Avery is the left pole, Blake the right pole, Casey the broadly-liked centrist. 47 rank Avery>Casey>Blake, 47 rank Blake>Casey>Avery, and 6 put Casey first (3 leaning each way). Casey is the Condorcet winner — a majority prefers Casey to Avery (53–47) and to Blake (53–47) — yet holds only 6 first choices. Ranks mapped to 0–5 scores (top=5, mid=3, bottom=1): Casey tops the score round 312 (Avery and Blake tie at 294) and wins the automatic runoff 53–47 → STAR → Casey, matching Ranked Robin, unlike IRV and Choose-One (which throw the centrist out first and then deadlock the two poles). Live results: https://bettervoting.com/pp2q4q/results Companion races: bv2170_pp2q4q_irv.yaml, bv2170_pp2q4q_ranked_robin.yaml, bv2170_pp2q4q_plurality.yaml. Overview page: bv2170_pp2q4q_symmetric_centrist.md bv_test_id: BV2170 bv_election_id: pp2q4q bv_results_url: https://bettervoting.com/pp2q4q/results paradoxes: [condorcet-winner] voting_method: STAR num_winners: 1 # Perfectly symmetric between the two poles: Avery and Blake tie at every rung # (score 294=294, pairwise 50–50, five-star 47=47), so the SECOND finalist slot is # lot-decided. Casey is the deterministic winner regardless. lot_numbers pinned to # BV's `perm` for this run so LH reproduces the frozen export. lot_numbers: [Blake, Casey, Avery] 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: bv2170_pp2q4q_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Symmetric centrist (47/47/3/3) — STAR: elects Casey, the Condorcet winner === One of four races in the Symmetric Centrist election (BV2170, bvid pp2q4q; BV-confirmed). 100 voters, three candidates, ONE electorate tabulated four ways. Avery is the left pole, Blake the right pole, Casey the broadly-liked centrist. 47 rank Avery>Casey>Blake, 47 rank Blake>Casey>Avery, and 6 put Casey first (3 leaning each way). Casey is the Condorcet winner — a majority prefers Casey to Avery (53–47) and to Blake (53–47) — yet holds only 6 first choices. Ranks mapped to 0–5 scores (top=5, mid=3, bottom=1): Casey tops the score round 312 (Avery and Blake tie at 294) and wins the automatic runoff 53–47 → STAR → Casey, matching Ranked Robin, unlike IRV and Choose-One (which throw the centrist out first and then deadlock the two poles). Live results: https://bettervoting.com/pp2q4q/results Companion races: bv2170_pp2q4q_irv.yaml, bv2170_pp2q4q_ranked_robin.yaml, bv2170_pp2q4q_plurality.yaml. Overview page: bv2170_pp2q4q_symmetric_centrist.md --- 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 Blake. 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) — Blake elected by Choose-One (Plurality)! [Divergence from STAR] STAR = Casey Choose-One (Plurality) = Blake (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/bv2170_pp2q4q_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. *(Ties are resolved by choosing the tied candidate with the highest-priority official lot number.)* Lot-number priority order: ['Blake', 'Casey', 'Avery'] [Tiebreaker: Lot Number Priority] Tie among: ['Avery', 'Blake'] Resolved: ['Blake'] (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 Blake -- 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%) · Blake 47 (47%) [STAR Voting: Winner — STAR Voting Method (single winner)] Casey