====================================================================== SOURCE FILE: margins_star.yaml TABULATED FILE: margins_star_tabulated.txt ====================================================================== election_title: "Margins matter — STAR on the same twelve ballots (rank converted 5/3/0)" scenario_description: |- The same twelve gelato voters, with each ranking converted to scores on an even 5/3/0 spacing so a SCORE method can run on a RANKED profile. Under a uniform spacing the STAR scoring round IS a Borda count, so round one reproduces Borda's answer — Berry first — and then the automatic runoff runs the head-to-head Borda never runs: Almond beats Berry 7-5, and Almond wins. Honest caveat, stated on the page: unlike Condorcet's 1788 profile, this outcome is NOT robust to the spacing. 5/3/0, 5/4/0, 5/2/0 and 4/2/0 all give Almond, but a polarized 5/1/0 makes Cocoa a finalist instead of Berry and elects Cocoa. With no Condorcet winner to anchor it (the pairwise contests cycle), the rank-to-score mapping is doing real work — which is exactly the objection the Borda page raises against inventing intensities. bv_test_id: BV2251 bv_election_id: kdjjkq bv_results_url: https://bettervoting.com/kdjjkq/results voting_method: STAR num_winners: 1 ballots: |- Almond,Berry,Cocoa 5,3,0 5,3,0 5,3,0 5,3,0 5,3,0 0,5,3 0,5,3 0,5,3 3,0,5 3,0,5 0,3,5 0,3,5 expected_winners: - Almond # file: margins_star.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Margins matter — STAR on the same twelve ballots (rank converted 5/3/0) === The same twelve gelato voters, with each ranking converted to scores on an even 5/3/0 spacing so a SCORE method can run on a RANKED profile. Under a uniform spacing the STAR scoring round IS a Borda count, so round one reproduces Borda's answer — Berry first — and then the automatic runoff runs the head-to-head Borda never runs: Almond beats Berry 7-5, and Almond wins. Honest caveat, stated on the page: unlike Condorcet's 1788 profile, this outcome is NOT robust to the spacing. 5/3/0, 5/4/0, 5/2/0 and 4/2/0 all give Almond, but a polarized 5/1/0 makes Cocoa a finalist instead of Berry and elects Cocoa. With no Condorcet winner to anchor it (the pairwise contests cycle), the rank-to-score mapping is doing real work — which is exactly the objection the Borda page raises against inventing intensities. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Almond | * Berry | Cocoa | ----------------------------------------------------- * Almond > | --- |7 - 0 - 5 |5 - 0 - 7 | * Berry > | 5 - 0 - 7 | --- |8 - 0 - 4 | Cocoa > | 7 - 0 - 5 |4 - 0 - 8 | --- | [Condorcet Winner] No Condorcet winner (majority cycle: Almond > Berry > Cocoa > Almond) [Divergence from STAR] STAR = Almond RCV-IRV = Cocoa (differs from STAR) Approval = Berry (differs from STAR) RCV-RR = Berry (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. Full round-by-round reports (generated for review): RCV-IRV rounds: cases_tabulated/margins_star_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/margins_star_RCV-RR_tabulated.txt [Runoff Reversal] - Score Round Winner(s) = (Berry) - Runoff Round Winner = (Almond) Candidate Berry earned the highest total score, but Candidate Almond 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 12 ballots. Count × Almond,Berry,Cocoa 5 × 5, 3, 0 3 × 0, 5, 3 2 × 3, 0, 5 2 × 0, 3, 5 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Almond 5 0 2 0 0 5 | 31 2.6 Berry 3 0 7 0 0 2 | 36 3.0 Cocoa 4 0 3 0 0 5 | 29 2.4 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Berry -- 36 -- First place Almond -- 31 -- Second place Cocoa -- 29 Berry and Almond advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Almond -- 7 -- First place Berry -- 5 Equal Support -- 0 Almond wins. Runoff math: 12 ballots cast − 0 Equal Support (no preference between the two finalists) ── 12 voters with a preference (majority = 7) Almond 7 (58%) · Berry 5 (42%) [STAR Voting: Winner — STAR Voting Method (single winner)] Almond