====================================================================== SOURCE FILE: ex15_approval_pairwise.yaml TABULATED FILE: ex15_approval_pairwise_tabulated.txt ====================================================================== election_title: Exercise 15a, second look — the same Yes/No ballots read pairwise scenario_description: |- The SAME 35 ballots as ex15_approval_yes_no.yaml, with each approval written as a 5 and each non-approval as a 0, so the engine prints the pairwise matrix and names the Condorcet winner. The magnitudes carry no information here — every head-to-head count depends only on the two-class order (approved above not-approved), which is what makes this a DICHOTOMOUS PROFILE. The payoff: the head-to-head order reproduces the approval order exactly. Blair beats Cosmo 13-7 (15 voters approved both, so they express no preference) and beats Ada 20-7; Cosmo beats Ada 15-8. Blair > Cosmo > Ada, the same ranking as the approval totals 28 > 22 > 15. That is guaranteed, not luck. On a dichotomous profile "more voters strictly prefer x to y" reduces to "more voters approve x than y", so a Condorcet winner always exists and approval voting agrees with every Condorcet method. The caveat lives one folder over: real approval ballots are compressed from richer opinions, and the Condorcet winner of the uncompressed opinions can be someone else — see method_comparisons/black_curtain/condorcet_compression.md. Exercise page: ../ex15_read_the_ballot.md Live results: https://bettervoting.com/d4v2dh/results (BV2258, race 2 of 2 — the same 35 ballots as race 1, cast as 5/0 scores; BV's STAR count agrees: Blair. The frozen export sits beside the sibling yaml, ex15_approval_yes_no_bv_export.json — one export covers both races.) bv_test_id: BV2258 bv_election_id: d4v2dh bv_results_url: https://bettervoting.com/d4v2dh/results voting_method: STAR num_winners: 1 ballots: |- Count:Ada,Blair,Cosmo 15:0,5,5 8:5,5,0 7:5,0,5 5:0,5,0 expected_winners: - Blair # file: ex15_approval_pairwise.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Exercise 15a, second look — the same Yes/No ballots read pairwise === The SAME 35 ballots as ex15_approval_yes_no.yaml, with each approval written as a 5 and each non-approval as a 0, so the engine prints the pairwise matrix and names the Condorcet winner. The magnitudes carry no information here — every head-to-head count depends only on the two-class order (approved above not-approved), which is what makes this a DICHOTOMOUS PROFILE. The payoff: the head-to-head order reproduces the approval order exactly. Blair beats Cosmo 13-7 (15 voters approved both, so they express no preference) and beats Ada 20-7; Cosmo beats Ada 15-8. Blair > Cosmo > Ada, the same ranking as the approval totals 28 > 22 > 15. That is guaranteed, not luck. On a dichotomous profile "more voters strictly prefer x to y" reduces to "more voters approve x than y", so a Condorcet winner always exists and approval voting agrees with every Condorcet method. The caveat lives one folder over: real approval ballots are compressed from richer opinions, and the Condorcet winner of the uncompressed opinions can be someone else — see method_comparisons/black_curtain/condorcet_compression.md. Exercise page: ../ex15_read_the_ballot.md Live results: https://bettervoting.com/d4v2dh/results (BV2258, race 2 of 2 — the same 35 ballots as race 1, cast as 5/0 scores; BV's STAR count agrees: Blair. The frozen export sits beside the sibling yaml, ex15_approval_yes_no_bv_export.json — one export covers both races.) --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | Ada | * Blair | * Cosmo | ------------------------------------------------------------- Ada > | --- | 7 - 8 - 20 | 8 - 12 - 15 | * Blair > | 20 - 8 - 7 | --- |13 - 15 - 7 | * Cosmo > | 15 - 12 - 8 | 7 - 15 - 13 | --- | [Condorcet Winner] Condorcet Winner: Blair — matches the STAR winner [Condorcet Loser] Condorcet Loser: Ada — loses every head-to-head matchup --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 35 ballots. Count × Ada,Blair,Cosmo 15 × 0, 5, 5 8 × 5, 5, 0 7 × 5, 0, 5 5 × 0, 5, 0 [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 | Total Avg Ada 15 0 0 0 0 20 | 75 2.1 Blair 28 0 0 0 0 7 | 140 4.0 Cosmo 22 0 0 0 0 13 | 110 3.1 [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Blair -- 140 -- First place Cosmo -- 110 -- Second place Ada -- 75 Blair and Cosmo advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Blair -- 13 -- First place Cosmo -- 7 Equal Support -- 15 Blair wins. Runoff math: 35 ballots cast − 15 Equal Support (no preference between the two finalists) ── 20 voters with a preference (majority = 11) Blair 13 (65%) · Cosmo 7 (35%) [STAR Voting: Winner — STAR Voting Method (single winner)] Blair