====================================================================== SOURCE FILE: abstentions.yaml TABULATED FILE: abstentions_tabulated.txt ====================================================================== election_title: "Abstentions — blank and abstaining ballots in STAR" scenario_description: |- Six ballots tabulated, only three of which can decide the runoff: the 5-5 Equal Support ballot, the all-zero ballot, and the truly blank ballot all express no preference between the finalists. Teaches the runoff denominator: the two-line summary (show_runoff_percent) counts ALL tabulated ballots and folds every no-preference ballot — the blank included — into one Equal Support bucket, so it reads 3 of 6 (3 Equal Support); the cast-vs-abstained split is carried separately by the abstention Note (1 of 6 ballots). Dog beats Cat 2-1 among voters WITH a preference, and the percentages never look like votes went missing. voting_method: STAR num_winners: 1 ballots: |- Dog,Cat 5,0 # Dog — a clear preference (decides the runoff) 4,0 # Dog — a clear preference (decides the runoff) 0,5 # Cat — a clear preference (decides the runoff) 5,5 # Equal Support — a CAST ballot that rates both finalists the same 0,0 # all-zero — a CAST ballot that supports neither (an explicit zero) -,- # blank — a true ABSTENTION: no score recorded for anyone expected_winners: - Dog # file: abstentions.yaml ====================================================================== TABULATION RESULTS ====================================================================== === Abstentions — blank and abstaining ballots in STAR === Six ballots tabulated, only three of which can decide the runoff: the 5-5 Equal Support ballot, the all-zero ballot, and the truly blank ballot all express no preference between the finalists. Teaches the runoff denominator: the two-line summary (show_runoff_percent) counts ALL tabulated ballots and folds every no-preference ballot — the blank included — into one Equal Support bucket, so it reads 3 of 6 (3 Equal Support); the cast-vs-abstained split is carried separately by the abstention Note (1 of 6 ballots). Dog beats Cat 2-1 among voters WITH a preference, and the percentages never look like votes went missing. --- Runoff (Preference) Matrix --- Head-to-head / pairwise comparison Legend: For - Equal Support - Against * indicates Top 2 Finalist | * Dog | * Cat | ----------------------------------------- * Dog > | --- |2 - 3 - 1 | * Cat > | 1 - 3 - 2 | --- | [Condorcet Winner] Condorcet Winner: Dog — matches the STAR winner [Condorcet Loser] Condorcet Loser: Cat — loses every head-to-head matchup --- STAR Voting Method (single winner) --- [STAR Voting] Tabulating 6 ballots. Note: 1 of 6 ballots is marked as an abstention. Dog,Cat 5, 0 4, 0 0, 5 5, 5 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 Dog 2 1 0 0 0 2 1 | 14 2.3 2.8 Cat 2 0 0 0 0 3 1 | 10 1.7 2.0 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. Dog -- 14 -- First place Cat -- 10 -- Second place Dog and Cat advance. [STAR Voting: Automatic Runoff Round] The candidate preferred in the most head-to-head matchups wins. Dog -- 2 -- First place Cat -- 1 Equal Support -- 3 Dog wins. Runoff math: 6 ballots cast − 3 Equal Support (no preference between the two finalists) ─ 3 voters with a preference (majority = 2) Dog 2 (67%) · Cat 1 (33%) [STAR Voting: Winner — STAR Voting Method (single winner)] Dog