====================================================================== SOURCE FILE: mono_raise_delete_before.yaml TABULATED FILE: mono_raise_delete_before_tabulated.txt ====================================================================== election_title: "STAR mono-raise-delete — part 1: baseline, X wins" scenario_description: |- Part 1 of the STAR mono-raise-delete pair (a 301 nuance). STAR satisfies the standard monotonicity criterion (mono-raise: raising a candidate's score, and nothing else, never hurts them) — but NOT the stronger mono-raise-delete (D. R. Woodall, Voting Matters 1996): "X should not be harmed if X is raised on some ballots AND all candidates now below X on those ballots are deleted." Baseline: 30 voters. Scoring round makes X (87) and Y (84) the finalists, with Z third (72); the runoff is X vs Y, which X wins 21-9. X WINS. In part 2 (mono_raise_delete_after.yaml), nine voters whose ballots read Z>X>Y raise X (3 -> 4) AND delete the one candidate now below X — Y -> 0. That pure "raise X and bury the losers below X" move drops Y from 84 to 66, below Z's 72, so the finalists become X and Z instead of X and Y. X still leads the scoring, but now faces Z in the runoff and loses. Raising X made X lose: STAR fails mono-raise-delete. The soft spot is finalist selection, not X's own score. See 01_STAR/01_Learn/properties_and_limits/STAR_monotonicity.md. paradoxes: [non-monotonicity] voting_method: STAR num_winners: 1 # Columns X,Y,Z. The middle bloc (Z=5,X=3,Y=2, i.e. "3,2,5") is the one modified # in part 2. Counts are >= 6 to avoid collision with 0-5 scores. ballots: |- X,Y,Z 12: 5,4,0 9: 3,2,5 9: 0,2,3 expected_winners: - X # file: mono_raise_delete_before.yaml ====================================================================== TABULATION RESULTS ====================================================================== === STAR mono-raise-delete — part 1: baseline, X wins === Part 1 of the STAR mono-raise-delete pair (a 301 nuance). STAR satisfies the standard monotonicity criterion (mono-raise: raising a candidate's score, and nothing else, never hurts them) — but NOT the stronger mono-raise-delete (D. R. Woodall, Voting Matters 1996): "X should not be harmed if X is raised on some ballots AND all candidates now below X on those ballots are deleted." Baseline: 30 voters. Scoring round makes X (87) and Y (84) the finalists, with Z third (72); the runoff is X vs Y, which X wins 21-9. X WINS. In part 2 (mono_raise_delete_after.yaml), nine voters whose ballots read Z>X>Y raise X (3 -> 4) AND delete the one candidate now below X — Y -> 0. That pure "raise X and bury the losers below X" move drops Y from 84 to 66, below Z's 72, so the finalists become X and Z instead of X and Y. X still leads the scoring, but now faces Z in the runoff and loses. Raising X made X lose: STAR fails mono-raise-delete. The soft spot is finalist selection, not X's own score. See 01_STAR/01_Learn/properties_and_limits/STAR_monotonicity.md. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * X | * Y | Z | ------------------------------------------------------------- * X > | --- |21 - 0 - 9 |12 - 0 - 18 | * Y > | 9 - 0 - 21 | --- |12 - 0 - 18 | Z > | 18 - 0 - 12 |18 - 0 - 12 | --- | [Condorcet Winner] Condorcet Winner: Z — STAR elected X instead (Z was eliminated in the scoring round) [Condorcet Loser] Condorcet Loser: Y — loses every head-to-head matchup [Divergence from STAR] STAR = X Choose-One (Plurality) = Z (differs from STAR) RCV-IRV = Z (differs from STAR) RCV-RR (Condorcet) = 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) sides with RCV-IRV, so STAR is the outlier here — STAR need not elect the Condorcet candidate. Full round-by-round reports (generated for review): RCV-IRV rounds: cases_tabulated/mono_raise_delete_before_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/mono_raise_delete_before_RCV-RR_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 30 ballots. Count × X,Y,Z 12 × 5,4,0 9 × 3,2,5 9 × 0,2,3 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg X 12 0 9 0 0 9 | 87 2.9 Y 0 12 0 18 0 0 | 84 2.8 Z 9 0 9 0 0 12 | 72 2.4 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. X -- 87 -- First place Y -- 84 -- Second place Z -- 72 X and Y advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. X -- 21 -- First place Y -- 9 Equal Support -- 0 X wins. Runoff math: 30 ballots cast − 0 Equal Support (no preference between the two finalists) ── 30 voters with a preference (majority = 16) X 21 (70%) · Y 9 (30%) [STAR Voting: Winner — STAR Voting Method (single winner)] X