====================================================================== SOURCE FILE: ex01_district_combined.yaml TABULATED FILE: ex01_district_combined_tabulated.txt ====================================================================== election_title: "Exercise 1 — Two districts, one mayor: the COMBINED city" bv_test_id: BV2190 bv_election_id: 923q3d bv_results_url: https://bettervoting.com/923q3d/results scenario_description: |- All 18 ballots — West and East together. Both districts separately elect Avery, but combined the runner-ups change: Blake (33) only exists in West and Diego (33) only in East, while Carmen scores 32 in BOTH — so citywide it is Avery 70 vs Carmen 64 in the runoff, and Carmen wins it 10-8 head-to-head. STAR fails the CONSISTENCY criterion: winning every district does not guarantee winning the whole. (Note this is NOT a summability failure — score totals and the preference matrix still add across precincts; what you cannot add is each district's declared winner.) Part 3 of 3 of the consistency exercise (ex01_two_districts.md). Ballots adapted from a RangeVoting.org example, posed as an exercise in Brendan W. Sullivan, "An Introduction to the Math of Voting Methods" (2022), ch. 5. Live on BetterVoting (Test ID BV2190): https://bettervoting.com/923q3d/results — the election carries a second, Ranked Robin race on the same opinions (equal ranks allowed): Elena, the citywide Condorcet winner, wins it 4-0. voting_method: STAR num_winners: 1 ballots: |- Avery,Blake,Carmen,Diego,Elena 3,3,4,0,5 # 5 West voters: Elena first, Carmen second, Avery = Blake 3,3,4,0,5 3,3,4,0,5 3,3,4,0,5 3,3,4,0,5 5,5,3,0,0 # 3 West voters: Avery = Blake at the top, Carmen third 5,5,3,0,0 5,5,3,0,0 5,3,3,0,0 # 1 West voter: Avery over Blake 3,0,4,3,5 # 5 East voters: Elena first, Carmen second, Avery = Diego 3,0,4,3,5 3,0,4,3,5 3,0,4,3,5 3,0,4,3,5 5,0,3,5,0 # 3 East voters: Avery = Diego at the top, Carmen third 5,0,3,5,0 5,0,3,5,0 5,0,3,3,0 # 1 East voter: Avery over Diego expected_winners: - Carmen # file: ex01_district_combined.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Exercise 1 — Two districts, one mayor: the COMBINED city === All 18 ballots — West and East together. Both districts separately elect Avery, but combined the runner-ups change: Blake (33) only exists in West and Diego (33) only in East, while Carmen scores 32 in BOTH — so citywide it is Avery 70 vs Carmen 64 in the runoff, and Carmen wins it 10-8 head-to-head. STAR fails the CONSISTENCY criterion: winning every district does not guarantee winning the whole. (Note this is NOT a summability failure — score totals and the preference matrix still add across precincts; what you cannot add is each district's declared winner.) Part 3 of 3 of the consistency exercise (ex01_two_districts.md). Ballots adapted from a RangeVoting.org example, posed as an exercise in Brendan W. Sullivan, "An Introduction to the Math of Voting Methods" (2022), ch. 5. Live on BetterVoting (Test ID BV2190): https://bettervoting.com/923q3d/results — the election carries a second, Ranked Robin race on the same opinions (equal ranks allowed): Elena, the citywide Condorcet winner, wins it 4-0. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Avery | Blake | * Carmen | Diego | Elena | ----------------------------------------------------------------------------------------- * Avery > | --- |10 - 8 - 0 | 8 - 0 - 10 |10 - 8 - 0 | 8 - 0 - 10 | Blake > | 0 - 8 - 10 | --- | 3 - 1 - 14 | 9 - 0 - 9 | 4 - 4 - 10 | * Carmen > | 10 - 0 - 8 |14 - 1 - 3 | --- |14 - 1 - 3 | 8 - 0 - 10 | Diego > | 0 - 8 - 10 | 9 - 0 - 9 | 3 - 1 - 14 | --- | 4 - 4 - 10 | Elena > | 10 - 0 - 8 |10 - 4 - 4 |10 - 0 - 8 |10 - 4 - 4 | --- | [Condorcet Winner] Condorcet Winner: Elena — STAR elected Carmen instead (Elena was eliminated in the scoring round) [Condorcet Loser] No strict Condorcet loser; jointly weak Condorcet losers: Blake, Diego (winless — pairwise ties) [Divergence from STAR] STAR = Carmen Choose-One (Plurality) = Elena (differs from STAR) RCV-IRV = Elena (differs from STAR) Approval = Avery (differs from STAR) RCV-RR (Condorcet) = Elena (differs from STAR) Note: 18 of 18 ballots (100%) had equal non-zero scores, so their ranks were decided by candidate priority order. The RCV-IRV result may be an artifact of score-to-rank tie-breaking rather than a deep difference. Note: Ranked Robin (RCV-RR) sides with RCV-IRV, so STAR is the outlier here — STAR need not elect the Condorcet candidate. Full round-by-round reports (generated for review): RCV-IRV rounds: cases_tabulated/ex01_district_combined_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/ex01_district_combined_RCV-RR_tabulated.txt [Runoff Reversal] - Score Round Winner(s) = (Avery) - Runoff Round Winner = (Carmen) Candidate Avery 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 18 ballots. Count × Avery,Blake,Carmen,Diego,Elena 5 × 3, 3, 4, 0, 5 5 × 3, 0, 4, 3, 5 3 × 5, 5, 3, 0, 0 3 × 5, 0, 3, 5, 0 1 × 5, 3, 3, 0, 0 1 × 5, 0, 3, 3, 0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Avery 8 0 10 0 0 0 | 70 3.9 Blake 3 0 6 0 0 9 | 33 1.8 Carmen 0 10 8 0 0 0 | 64 3.6 Diego 3 0 6 0 0 9 | 33 1.8 Elena 10 0 0 0 0 8 | 50 2.8 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Avery -- 70 -- First place Carmen -- 64 -- Second place Elena -- 50 Blake -- 33 Diego -- 33 Avery and Carmen advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Carmen -- 10 -- First place Avery -- 8 Equal Support -- 0 Carmen wins. Runoff math: 18 ballots cast − 0 Equal Support (no preference between the two finalists) ── 18 voters with a preference (majority = 10) Carmen 10 (56%) · Avery 8 (44%) [STAR Voting: Winner — STAR Voting Method (single winner)] Carmen