====================================================================== SOURCE FILE: monotonicity_star_after.yaml TABULATED FILE: monotonicity_star_after_tabulated.txt ====================================================================== election_title: Monotonicity — STAR counterpart (AFTER — X still wins) scenario_description: |- The ONLY change from _before: 4 voters raise X to the top (their ballot goes from Y>Z to X>Y, i.e. scores 0,5,3 → 5,3,0). X gained support. STAR still elects X — raising the winner did not hurt them. Compare the RCV-IRV twin (method_comparisons/monotonicity/cases/monotonicity_irv_after.yaml), where the same change makes X LOSE to Z. The [Divergence from STAR] block below shows RCV-IRV electing Z on these very ballots: STAR is monotone, RCV-IRV is not. See 07_Concepts/monotonicity.md. paradoxes: [non-monotonicity] voting_method: STAR num_winners: 1 ballots: |- Count:X,Y,Z 16:5,3,0 # X>Y (12 + the 4 who raised X) 8:0,5,3 # Y>Z 10:3,0,5 # Z>X expected_winners: - X # file: monotonicity_star_after.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Monotonicity — STAR counterpart (AFTER — X still wins) === The ONLY change from _before: 4 voters raise X to the top (their ballot goes from Y>Z to X>Y, i.e. scores 0,5,3 → 5,3,0). X gained support. STAR still elects X — raising the winner did not hurt them. Compare the RCV-IRV twin (method_comparisons/monotonicity/cases/monotonicity_irv_after.yaml), where the same change makes X LOSE to Z. The [Divergence from STAR] block below shows RCV-IRV electing Z on these very ballots: STAR is monotone, RCV-IRV is not. See 07_Concepts/monotonicity.md. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * X | * Y | Z | ------------------------------------------------------------- * X > | --- |26 - 0 - 8 |16 - 0 - 18 | * Y > | 8 - 0 - 26 | --- |24 - 0 - 10 | Z > | 18 - 0 - 16 |10 - 0 - 24 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: X > Y > Z > X) [Divergence from STAR] STAR = X RCV-IRV = Z (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/monotonicity_star_after_RCV-IRV_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 34 ballots. Count × X,Y,Z 16 × 5,3,0 10 × 3,0,5 8 × 0,5,3 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg X 16 0 10 0 0 8 | 110 3.2 Y 8 0 16 0 0 10 | 88 2.6 Z 10 0 8 0 0 16 | 74 2.2 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. X -- 110 -- First place Y -- 88 -- Second place Z -- 74 X and Y advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. X -- 26 -- First place Y -- 8 Equal Support -- 0 X wins. Runoff math: 34 ballots cast − 0 Equal Support (no preference between the two finalists) ── 34 voters with a preference (majority = 18) X 26 (76%) · Y 8 (24%) [STAR Voting: Winner — STAR Voting Method (single winner)] X