====================================================================== SOURCE FILE: vote_splitting2.yaml TABULATED FILE: vote_splitting2_tabulated.txt ====================================================================== election_title: Vote splitting — two chocolates split the majority scenario_description: |- Election: pick ONE dessert for the party. 360 voters. 220 of the 360 are chocolate lovers — a clear 61% majority. But there are TWO chocolates on the menu, DarkChoco and MilkChoco, and 140 voters prefer Vanilla. Under Choose-One Plurality each voter may name only one flavor, so the chocolate majority splits its vote — 120 for DarkChoco, 100 for MilkChoco — and Vanilla wins with just 140 of 360 (38.9%), a dessert a 61% majority actively dislikes. That is vote splitting / the spoiler effect. STAR fixes it without asking chocolate to drop a flavor: every voter scores all three 0–5, so a chocolate lover can give BOTH chocolates a high score instead of choosing between them. The two highest totals advance to an automatic runoff, and the winner has majority support head-to-head. blocs: Chocolate: [DarkChoco, MilkChoco] voting_method: STAR # STAR Voting - Single-winner num_winners: 1 ballots: |- Count:DarkChoco,MilkChoco,Vanilla 120:5,4,0 # love dark, like milk, no vanilla 100:4,5,0 # love milk, like dark, no vanilla 140:2,1,5 # love vanilla, mild on chocolate expected_winners: - DarkChoco # file: vote_splitting2.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Vote splitting — two chocolates split the majority === Election: pick ONE dessert for the party. 360 voters. 220 of the 360 are chocolate lovers — a clear 61% majority. But there are TWO chocolates on the menu, DarkChoco and MilkChoco, and 140 voters prefer Vanilla. Under Choose-One Plurality each voter may name only one flavor, so the chocolate majority splits its vote — 120 for DarkChoco, 100 for MilkChoco — and Vanilla wins with just 140 of 360 (38.9%), a dessert a 61% majority actively dislikes. That is vote splitting / the spoiler effect. STAR fixes it without asking chocolate to drop a flavor: every voter scores all three 0–5, so a chocolate lover can give BOTH chocolates a high score instead of choosing between them. The two highest totals advance to an automatic runoff, and the winner has majority support head-to-head. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * DarkChoco | * MilkChoco | Vanilla | ------------------------------------------------------------------------- * DarkChoco > | --- |260 - 0 - 100 |220 - 0 - 140 | * MilkChoco > | 100 - 0 - 260 | --- |220 - 0 - 140 | Vanilla > | 140 - 0 - 220 |140 - 0 - 220 | --- | [Condorcet Winner] Condorcet Winner: DarkChoco — matches the STAR winner [Condorcet Loser] Condorcet Loser: Vanilla — loses every head-to-head matchup — elected by Choose-One (Plurality)! [Divergence from STAR] STAR = DarkChoco Choose-One (Plurality) = Vanilla (differs from STAR) [Vote-splitting check] Choose-One first choices: Vanilla 140, DarkChoco 120, MilkChoco 100 Plurality winner: Vanilla (140, 38.9%) Bloc 'Chocolate' = DarkChoco, MilkChoco: combined 220 (61.1%); winner Vanilla is OUTSIDE it. => VOTE SPLITTING: the 'Chocolate' bloc is an outright majority (220 vs Vanilla's 140) but split across 2 candidates, so Vanilla won Choose- One. STAR elected DarkChoco. --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 360 ballots. Count × DarkChoco,MilkChoco,Vanilla 140 × 2, 1, 5 120 × 5, 4, 0 100 × 4, 5, 0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg DarkChoco 120 100 0 140 0 0 | 1280 3.6 MilkChoco 100 120 0 0 140 0 | 1120 3.1 Vanilla 140 0 0 0 0 220 | 700 1.9 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. DarkChoco -- 1280 -- First place MilkChoco -- 1120 -- Second place Vanilla -- 700 DarkChoco and MilkChoco advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. DarkChoco -- 260 -- First place MilkChoco -- 100 Equal Support -- 0 DarkChoco wins. Runoff math: 360 ballots cast − 0 Equal Support (no preference between the two finalists) ─── 360 voters with a preference (majority = 181) DarkChoco 260 (72%) · MilkChoco 100 (28%) [STAR Voting: Winner — STAR Voting Method (single winner)] DarkChoco