====================================================================== SOURCE FILE: ex04_olympics_1994.yaml TABULATED FILE: ex04_olympics_1994_tabulated.txt ====================================================================== election_title: "Exercise 4 — Lillehammer 1994: nine judges, three skaters, two winners" scenario_description: |- The real final ordinals of the 1994 Winter Olympics ladies figure skating: nine judges ranked Oksana Baiul, Nancy Kerrigan, and Chen Lu — five judges put Baiul first (Kerrigan second), four put Kerrigan first; Lu is ranked third by seven judges and second by two. Ranks are mapped to 0-5 scores with the repo's standard order-preserving map (top=5, mid=3, bottom=1). Scoring round: Kerrigan 35, Baiul 33, Lu 13 — KERRIGAN leads the scores. Automatic runoff: five of the nine judges prefer Baiul, so BAIUL wins 5-4 — matching the real 5-4 judging split that decided the gold medal. Score voting and STAR genuinely diverge on real data; and Chen Lu can never win under ANY honest scoring, because every single judge ranks Kerrigan above her (Pareto dominance). The exercise is ex04_olympics_1994.md. Ordinals as reproduced in Brendan W. Sullivan, "An Introduction to the Math of Voting Methods" (2022), ch. 5. voting_method: STAR num_winners: 1 ballots: |- Baiul,Kerrigan,Lu 5,3,1 # judges 1-5: Baiul > Kerrigan > Lu 5,3,1 5,3,1 5,3,1 5,3,1 3,5,1 # judges 6-7: Kerrigan > Baiul > Lu 3,5,1 1,5,3 # judges 8-9: Kerrigan > Lu > Baiul 1,5,3 expected_winners: - Baiul # file: ex04_olympics_1994.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Exercise 4 — Lillehammer 1994: nine judges, three skaters, two winners === The real final ordinals of the 1994 Winter Olympics ladies figure skating: nine judges ranked Oksana Baiul, Nancy Kerrigan, and Chen Lu — five judges put Baiul first (Kerrigan second), four put Kerrigan first; Lu is ranked third by seven judges and second by two. Ranks are mapped to 0-5 scores with the repo's standard order-preserving map (top=5, mid=3, bottom=1). Scoring round: Kerrigan 35, Baiul 33, Lu 13 — KERRIGAN leads the scores. Automatic runoff: five of the nine judges prefer Baiul, so BAIUL wins 5-4 — matching the real 5-4 judging split that decided the gold medal. Score voting and STAR genuinely diverge on real data; and Chen Lu can never win under ANY honest scoring, because every single judge ranks Kerrigan above her (Pareto dominance). The exercise is ex04_olympics_1994.md. Ordinals as reproduced in Brendan W. Sullivan, "An Introduction to the Math of Voting Methods" (2022), ch. 5. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Baiul | * Kerrigan | Lu | ------------------------------------------------------------- * Baiul > | --- | 5 - 0 - 4 | 7 - 0 - 2 | * Kerrigan > | 4 - 0 - 5 | --- | 9 - 0 - 0 | Lu > | 2 - 0 - 7 | 0 - 0 - 9 | --- | [Condorcet Winner] Condorcet Winner: Baiul — matches the STAR winner [Condorcet Loser] Condorcet Loser: Lu — loses every head-to-head matchup [Divergence from STAR] STAR = Baiul Approval = Kerrigan (differs from STAR) [Runoff Reversal] - Score Round Winner(s) = (Kerrigan) - Runoff Round Winner = (Baiul) Candidate Kerrigan earned the highest total score, but Candidate Baiul 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 9 ballots. Count × Baiul,Kerrigan,Lu 5 × 5, 3, 1 2 × 3, 5, 1 2 × 1, 5, 3 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Baiul 5 0 2 0 2 0 | 33 3.7 Kerrigan 4 0 5 0 0 0 | 35 3.9 Lu 0 0 2 0 7 0 | 13 1.4 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Kerrigan -- 35 -- First place Baiul -- 33 -- Second place Lu -- 13 Kerrigan and Baiul advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Baiul -- 5 -- First place Kerrigan -- 4 Equal Support -- 0 Baiul wins. Runoff math: 9 ballots cast − 0 Equal Support (no preference between the two finalists) ─ 9 voters with a preference (majority = 5) Baiul 5 (56%) · Kerrigan 4 (44%) [STAR Voting: Winner — STAR Voting Method (single winner)] Baiul