====================================================================== SOURCE FILE: reversal_star_reversed.yaml TABULATED FILE: reversal_star_reversed_tabulated.txt ====================================================================== election_title: "Reversal symmetry — STAR, reversed: A (differs from original B — no winner=loser)" scenario_description: |- The STAR original (reversal_star_original) with every preference reversed (scores re-mapped 5/3/0 to the reversed ranking). STAR elects A — different from the original winner B — so unlike RCV-IRV (which elects A both ways), STAR's "best" and "worst" here are not the same candidate. Scope note per ../README.md: this demonstrates STAR avoiding the winner=loser on this example, not a general reversal-symmetry proof. Condorcet cycle electorate. paradoxes: [condorcet-cycle] voting_method: STAR num_winners: 1 ballots: |- Count:A,B,C 9:5,0,3 8:0,3,5 7:3,5,0 expected_winners: - A # file: reversal_star_reversed.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Reversal symmetry — STAR, reversed: A (differs from original B — no winner=loser) === The STAR original (reversal_star_original) with every preference reversed (scores re-mapped 5/3/0 to the reversed ranking). STAR elects A — different from the original winner B — so unlike RCV-IRV (which elects A both ways), STAR's "best" and "worst" here are not the same candidate. Scope note per ../README.md: this demonstrates STAR avoiding the winner=loser on this example, not a general reversal-symmetry proof. Condorcet cycle electorate. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * A | B | * C | ------------------------------------------------------------- * A > | --- | 9 - 0 - 15 |16 - 0 - 8 | B > | 15 - 0 - 9 | --- | 7 - 0 - 17 | * C > | 8 - 0 - 16 |17 - 0 - 7 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: A > C > B > A) [Divergence from STAR] STAR = A Approval = C (differs from STAR) [Runoff Reversal] - Score Round Winner(s) = (C) - Runoff Round Winner = (A) Candidate C earned the highest total score, but Candidate A won the automatic runoff — not a malfunction, STAR working as designed: the runoff elects the finalist preferred by the majority (of voters with a preference). --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 24 ballots. Count × A,B,C 9 × 5,0,3 8 × 0,3,5 7 × 3,5,0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg A 9 0 7 0 0 8 | 66 2.8 B 7 0 8 0 0 9 | 59 2.5 C 8 0 9 0 0 7 | 67 2.8 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. C -- 67 -- First place A -- 66 -- Second place B -- 59 C and A advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. A -- 16 -- First place C -- 8 Equal Support -- 0 A wins. Runoff math: 24 ballots cast − 0 Equal Support (no preference between the two finalists) ── 24 voters with a preference (majority = 13) A 16 (67%) · C 8 (33%) [STAR Voting: Winner — STAR Voting Method (single winner)] A