====================================================================== SOURCE FILE: ex01_district_east.yaml TABULATED FILE: ex01_district_east_tabulated.txt ====================================================================== election_title: "Exercise 1 — Two districts, one mayor: EAST district" bv_test_id: BV2189 bv_election_id: rhbfj7 bv_results_url: https://bettervoting.com/rhbfj7/results scenario_description: |- East District's nine ballots, tallied on their own — a mirror of West with Blake and Diego trading places. Scoring round: Avery 35, Diego 33, Carmen 32, Elena 25, Blake 0 — Avery and Diego advance. Eight of the nine ballots score the two finalists identically (Equal Support), and the one decided voter prefers Avery. East's winner: Avery. Part 2 of 3 of the consistency exercise (ex01_two_districts.md): West also elects Avery, yet the combined city elects Carmen. 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 BV2189): https://bettervoting.com/rhbfj7/results — the election carries a second, Ranked Robin race on the same opinions (equal ranks allowed): Elena, the district's Condorcet winner, wins it 4-0. voting_method: STAR num_winners: 1 ballots: |- Avery,Blake,Carmen,Diego,Elena 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 — the only decided runoff vote expected_winners: - Avery # file: ex01_district_east.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Exercise 1 — Two districts, one mayor: EAST district === East District's nine ballots, tallied on their own — a mirror of West with Blake and Diego trading places. Scoring round: Avery 35, Diego 33, Carmen 32, Elena 25, Blake 0 — Avery and Diego advance. Eight of the nine ballots score the two finalists identically (Equal Support), and the one decided voter prefers Avery. East's winner: Avery. Part 2 of 3 of the consistency exercise (ex01_two_districts.md): West also elects Avery, yet the combined city elects Carmen. 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 BV2189): https://bettervoting.com/rhbfj7/results — the election carries a second, Ranked Robin race on the same opinions (equal ranks allowed): Elena, the district's 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 > | --- |9 - 0 - 0 |4 - 0 - 5 |1 - 8 - 0 |4 - 0 - 5 | Blake > | 0 - 0 - 9 | --- |0 - 0 - 9 |0 - 0 - 9 |0 - 4 - 5 | Carmen > | 5 - 0 - 4 |9 - 0 - 0 | --- |5 - 1 - 3 |4 - 0 - 5 | * Diego > | 0 - 8 - 1 |9 - 0 - 0 |3 - 1 - 5 | --- |4 - 0 - 5 | Elena > | 5 - 0 - 4 |5 - 4 - 0 |5 - 0 - 4 |5 - 0 - 4 | --- | [Condorcet Winner] Condorcet Winner: Elena — STAR elected Avery instead (Elena was eliminated in the scoring round) [Condorcet Loser] Condorcet Loser: Blake — loses every head-to-head matchup [Divergence from STAR] STAR = Avery Choose-One (Plurality) = Elena (differs from STAR) RCV-IRV = Elena (differs from STAR) RCV-RR (Condorcet) = Elena (differs from STAR) Note: 9 of 9 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_east_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/ex01_district_east_RCV-RR_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 9 ballots. Count × Avery,Blake,Carmen,Diego,Elena 5 × 3, 0, 4, 3, 5 3 × 5, 0, 3, 5, 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 4 0 5 0 0 0 | 35 3.9 Blake 0 0 0 0 0 9 | 0 0.0 Carmen 0 5 4 0 0 0 | 32 3.6 Diego 3 0 6 0 0 0 | 33 3.7 Elena 5 0 0 0 0 4 | 25 2.8 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Avery -- 35 -- First place Diego -- 33 -- Second place Carmen -- 32 Elena -- 25 Blake -- 0 Avery and Diego advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Avery -- 1 -- First place Diego -- 0 Equal Support -- 8 Avery wins. Runoff math: 9 ballots cast − 8 Equal Support (no preference between the two finalists) ─ 1 voters with a preference (majority = 1) Avery 1 (100%) · Diego 0 (0%) [STAR Voting: Winner — STAR Voting Method (single winner)] Avery