====================================================================== SOURCE FILE: 06b_c9_runoff-overturns-leader.yaml TABULATED FILE: 06b_c9_runoff-overturns-leader_tabulated.txt ====================================================================== election_title: Large field (9 candidates) — the runoff OVERTURNS the score leader scenario_description: |- STAR's headline move, in a 9-candidate field with just 3 voters. Andre has the highest score total (9 stars), so he leads the scoring round — but in the automatic runoff a 2-of-3 majority prefers Carmen, so Carmen wins 2–1. STAR elects the majority-preferred Carmen, not the highest-scoring Andre: the runoff is the majority check that stops a high-ceiling / low-floor candidate from winning on intensity alone. (Carmen is also the Condorcet winner.) Discussion (Larry): - "Andre got the most stars — why didn't he win?" (The runoff asks a different question: which finalist do MORE voters prefer? That's Carmen, 2–1.) - Contrast 06a_c9_b3_large-field-equal-support.yaml, where the runoff merely CONFIRMS the scoring leader. Same method, two different jobs the runoff does. voting_method: STAR num_winners: 1 ballots: |- Andre,Blake,Carmen,David,Ella,Fernando,Gabe,Helena,Ira 5,3,0,2,1,1,1,1,0 # intense Andre voter (Andre 5, Carmen 0) 2,0,3,1,0,2,0,1,1 # prefers Carmen over Andre 2,1,3,0,1,0,2,0,1 # prefers Carmen over Andre expected_winners: - Carmen # file: 06b_c9_runoff-overturns-leader.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Large field (9 candidates) — the runoff OVERTURNS the score leader === STAR's headline move, in a 9-candidate field with just 3 voters. Andre has the highest score total (9 stars), so he leads the scoring round — but in the automatic runoff a 2-of-3 majority prefers Carmen, so Carmen wins 2–1. STAR elects the majority-preferred Carmen, not the highest-scoring Andre: the runoff is the majority check that stops a high-ceiling / low-floor candidate from winning on intensity alone. (Carmen is also the Condorcet winner.) Discussion (Larry): - "Andre got the most stars — why didn't he win?" (The runoff asks a different question: which finalist do MORE voters prefer? That's Carmen, 2–1.) - Contrast 06a_c9_b3_large-field-equal-support.yaml, where the runoff merely CONFIRMS the scoring leader. Same method, two different jobs the runoff does. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Andre | Blake | * Carmen | David | Ella | Fernando | Gabe | Helena | Ira | ------------------------------------------------------------------------------------------------------------------------------------------------- * Andre > | --- | 3 - 0 - 0 | 1 - 0 - 2 | 3 - 0 - 0 | 3 - 0 - 0 | 2 - 1 - 0 | 2 - 1 - 0 | 3 - 0 - 0 | 3 - 0 - 0 | Blake > | 0 - 0 - 3 | --- | 1 - 0 - 2 | 2 - 0 - 1 | 1 - 2 - 0 | 2 - 0 - 1 | 1 - 1 - 1 | 2 - 0 - 1 | 1 - 1 - 1 | * Carmen > | 2 - 0 - 1 | 2 - 0 - 1 | --- | 2 - 0 - 1 | 2 - 0 - 1 | 2 - 0 - 1 | 2 - 0 - 1 | 2 - 0 - 1 | 2 - 1 - 0 | David > | 0 - 0 - 3 | 1 - 0 - 2 | 1 - 0 - 2 | --- | 2 - 0 - 1 | 1 - 1 - 1 | 2 - 0 - 1 | 1 - 2 - 0 | 1 - 1 - 1 | Ella > | 0 - 0 - 3 | 0 - 2 - 1 | 1 - 0 - 2 | 1 - 0 - 2 | --- | 1 - 1 - 1 | 0 - 2 - 1 | 1 - 1 - 1 | 1 - 1 - 1 | Fernando > | 0 - 1 - 2 | 1 - 0 - 2 | 1 - 0 - 2 | 1 - 1 - 1 | 1 - 1 - 1 | --- | 1 - 1 - 1 | 1 - 2 - 0 | 2 - 0 - 1 | Gabe > | 0 - 1 - 2 | 1 - 1 - 1 | 1 - 0 - 2 | 1 - 0 - 2 | 1 - 2 - 0 | 1 - 1 - 1 | --- | 1 - 1 - 1 | 2 - 0 - 1 | Helena > | 0 - 0 - 3 | 1 - 0 - 2 | 1 - 0 - 2 | 0 - 2 - 1 | 1 - 1 - 1 | 0 - 2 - 1 | 1 - 1 - 1 | --- | 1 - 1 - 1 | Ira > | 0 - 0 - 3 | 1 - 1 - 1 | 0 - 1 - 2 | 1 - 1 - 1 | 1 - 1 - 1 | 1 - 0 - 2 | 1 - 0 - 2 | 1 - 1 - 1 | --- | [Condorcet Winner] Condorcet Winner: Carmen — matches the STAR winner [Condorcet Loser] No strict Condorcet loser; jointly weak Condorcet losers: Ella, Helena, Ira (winless — pairwise ties) [Runoff Reversal] - Score Round Winner(s) = (Andre) - Runoff Round Winner = (Carmen) Candidate Andre earned the highest total score, but Candidate Carmen 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 3 ballots. Andre,Blake,Carmen,David,Ella,Fernando,Gabe,Helena,Ira 5, 3, 0, 2, 1, 1, 1, 1, 0 2, 0, 3, 1, 0, 2, 0, 1, 1 2, 1, 3, 0, 1, 0, 2, 0, 1 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Andre 1 0 0 2 0 0 | 9 3.0 Blake 0 0 1 0 1 1 | 4 1.3 Carmen 0 0 2 0 0 1 | 6 2.0 David 0 0 0 1 1 1 | 3 1.0 Ella 0 0 0 0 2 1 | 2 0.7 Fernando 0 0 0 1 1 1 | 3 1.0 Gabe 0 0 0 1 1 1 | 3 1.0 Helena 0 0 0 0 2 1 | 2 0.7 Ira 0 0 0 0 2 1 | 2 0.7 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Andre -- 9 -- First place Carmen -- 6 -- Second place Blake -- 4 David -- 3 Fernando -- 3 Gabe -- 3 Ella -- 2 Helena -- 2 Ira -- 2 Andre and Carmen advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Carmen -- 2 -- First place Andre -- 1 Equal Support -- 0 Carmen wins. Runoff math: 3 ballots cast − 0 Equal Support (no preference between the two finalists) ─ 3 voters with a preference (majority = 2) Carmen 2 (67%) · Andre 1 (33%) [STAR Voting: Winner — STAR Voting Method (single winner)] Carmen