====================================================================== SOURCE FILE: ex07_vanishing_votes.yaml TABULATED FILE: ex07_vanishing_votes_tabulated.txt ====================================================================== election_title: "Exercise 7 — The vanishing votes that never vanished (a park-tree ballot drill)" scenario_description: |- A park board picks a tree. Nine ballot papers come back: two score the finalists equal at the top (5-5), one at 3-3, one bullet-votes Cedar (0,0,5), one is all zeros, one is completely blank — and only three express a preference between the finalists Aspen and Birch. The drill: predict every number in the two-line runoff summary before peeking. Scoring round: Aspen 24, Birch 20, Cedar 13. Runoff: Aspen 2, Birch 1, Equal Support 6 — "Voters with a preference: 3 of 9 (6 Equal Support)". The 9 counts every tabulated ballot: the blank abstention folds into Equal Support on this line, and the separate engine Note ("1 of 9 ballots is marked as an abstention") carries the cast-vs-abstained split. No vote vanished: equal scores are counted in full in the scoring round and then have no preference to give between equals. Exercise: ex07_vanishing_votes.md. Ballots and cast are this repo's own. voting_method: STAR num_winners: 1 ballots: |- Aspen,Birch,Cedar 5,5,0 # equal top pair — full weight in scoring, Equal Support in the runoff 5,5,3 # same, with a nod to Cedar 3,3,5 # Cedar first — and equal on the two finalists 5,2,0 # a clear Aspen preference 4,1,0 # a clear Aspen preference 2,4,0 # a clear Birch preference 0,0,5 # bullet vote for Cedar — zero on both finalists is still Equal Support 0,0,0 # all zeros — a CAST ballot that supports no one -,-,- # completely blank — a true abstention, not a cast ballot expected_winners: - Aspen # file: ex07_vanishing_votes.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Exercise 7 — The vanishing votes that never vanished (a park-tree ballot drill) === A park board picks a tree. Nine ballot papers come back: two score the finalists equal at the top (5-5), one at 3-3, one bullet-votes Cedar (0,0,5), one is all zeros, one is completely blank — and only three express a preference between the finalists Aspen and Birch. The drill: predict every number in the two-line runoff summary before peeking. Scoring round: Aspen 24, Birch 20, Cedar 13. Runoff: Aspen 2, Birch 1, Equal Support 6 — "Voters with a preference: 3 of 9 (6 Equal Support)". The 9 counts every tabulated ballot: the blank abstention folds into Equal Support on this line, and the separate engine Note ("1 of 9 ballots is marked as an abstention") carries the cast-vs-abstained split. No vote vanished: equal scores are counted in full in the scoring round and then have no preference to give between equals. Exercise: ex07_vanishing_votes.md. Ballots and cast are this repo's own. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Aspen | * Birch | Cedar | ----------------------------------------------------- * Aspen > | --- |2 - 6 - 1 |5 - 2 - 2 | * Birch > | 1 - 6 - 2 | --- |5 - 2 - 2 | Cedar > | 2 - 2 - 5 |2 - 2 - 5 | --- | [Condorcet Winner] Condorcet Winner: Aspen — matches the STAR winner [Condorcet Loser] Condorcet Loser: Cedar — loses every head-to-head matchup --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 9 ballots. Note: 1 of 9 ballots is marked as an abstention. Aspen,Birch,Cedar 5, 5, 0 5, 5, 3 3, 3, 5 5, 2, 0 4, 1, 0 2, 4, 0 0, 0, 5 0, 0, 0 -, -, - ('-' = left blank / abstained; '0' = scored zero — both count as 0 stars.) [Score Distribution] (how many ballots gave each star rating) Score Candidate 5 4 3 2 1 0 Abs | Total Avg all Avg rated Aspen 3 1 1 1 0 2 1 | 24 2.7 3.0 Birch 2 1 1 1 1 2 1 | 20 2.2 2.5 Cedar 2 0 1 0 0 5 1 | 13 1.4 1.6 Avg all = Total / all ballots — a blank counts as 0, so this is the Total the Scoring Round ranks on, per ballot. Avg rated = Total / the ballots that scored this candidate (Abs excluded) — support among voters who had an opinion. [STAR Voting: Scoring Round] The two highest-scoring candidates advance to the next round. Aspen -- 24 -- First place Birch -- 20 -- Second place Cedar -- 13 Aspen and Birch advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Aspen -- 2 -- First place Birch -- 1 Equal Support -- 6 Aspen wins. Runoff math: 9 ballots cast − 6 Equal Support (no preference between the two finalists) ─ 3 voters with a preference (majority = 2) Aspen 2 (67%) · Birch 1 (33%) [STAR Voting: Winner — STAR Voting Method (single winner)] Aspen