====================================================================== SOURCE FILE: ex01_district_west.yaml TABULATED FILE: ex01_district_west_tabulated.txt ====================================================================== election_title: "Exercise 1 — Two districts, one mayor: WEST district" bv_test_id: BV2188 bv_election_id: d3b9wc bv_results_url: https://bettervoting.com/d3b9wc/results scenario_description: |- West District's nine ballots, tallied on their own. Scoring round: Avery 35, Blake 33, Carmen 32, Elena 25, Diego 0 — Avery and Blake advance. Eight of the nine ballots score the two finalists identically (Equal Support), and the one decided voter prefers Avery. West's winner: Avery. Part 1 of 3 of the consistency exercise (ex01_two_districts.md): East 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 BV2188): https://bettervoting.com/d3b9wc/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 3,3,4,0,5 # 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 — the only decided runoff vote expected_winners: - Avery # file: ex01_district_west.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Exercise 1 — Two districts, one mayor: WEST district === West District's nine ballots, tallied on their own. Scoring round: Avery 35, Blake 33, Carmen 32, Elena 25, Diego 0 — Avery and Blake advance. Eight of the nine ballots score the two finalists identically (Equal Support), and the one decided voter prefers Avery. West's winner: Avery. Part 1 of 3 of the consistency exercise (ex01_two_districts.md): East 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 BV2188): https://bettervoting.com/d3b9wc/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 > | --- |1 - 8 - 0 |4 - 0 - 5 |9 - 0 - 0 |4 - 0 - 5 | * Blake > | 0 - 8 - 1 | --- |3 - 1 - 5 |9 - 0 - 0 |4 - 0 - 5 | Carmen > | 5 - 0 - 4 |5 - 1 - 3 | --- |9 - 0 - 0 |4 - 0 - 5 | Diego > | 0 - 0 - 9 |0 - 0 - 9 |0 - 0 - 9 | --- |0 - 4 - 5 | Elena > | 5 - 0 - 4 |5 - 0 - 4 |5 - 0 - 4 |5 - 4 - 0 | --- | [Condorcet Winner] Condorcet Winner: Elena — STAR elected Avery instead (Elena was eliminated in the scoring round) [Condorcet Loser] Condorcet Loser: Diego — 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_west_RCV-IRV_tabulated.txt RCV-RR round-robin: cases_tabulated/ex01_district_west_RCV-RR_tabulated.txt --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 9 ballots. Count × Avery,Blake,Carmen,Diego,Elena 5 × 3, 3, 4, 0, 5 3 × 5, 5, 3, 0, 0 1 × 5, 3, 3, 0, 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 3 0 6 0 0 0 | 33 3.7 Carmen 0 5 4 0 0 0 | 32 3.6 Diego 0 0 0 0 0 9 | 0 0.0 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 Blake -- 33 -- Second place Carmen -- 32 Elena -- 25 Diego -- 0 Avery and Blake advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Avery -- 1 -- First place Blake -- 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%) · Blake 0 (0%) [STAR Voting: Winner — STAR Voting Method (single winner)] Avery