====================================================================== SOURCE FILE: p3_manip_reversal_rr.yaml TABULATED FILE: p3_manip_reversal_rr_tabulated.txt ====================================================================== election_title: "P3 manipulated — Zwicker's complete reversal makes Dublin a 4-0 Condorcet winner" scenario_description: |- The book's own printed manipulation. One of the two sincere Athens>Bergen>Cork>Dublin>Edinburgh voters completely REVERSES their ballot to Edinburgh>Dublin>Cork>Bergen>Athens. That single reversed ballot flips two knife-edge 4-3 contests (Athens vs Dublin and Cork vs Dublin), and Dublin goes from 2-2 to 4-0: a symmetric Copeland score of +4, the maximum possible for five candidates, and now an outright Condorcet winner. The manipulator has replaced their LAST choice (Edinburgh) with their 4th (Dublin) — a strict gain — by submitting a ballot that misrepresents every single pairwise preference they hold. IMPORTANT for this repo: Ranked Robin IS Copeland plus a tiebreak, so the book's showcase manipulation is a manipulation of a method this library advocates. voting_method: RankedRobin num_winners: 1 lot_numbers: [Athens, Bergen, Cork, Dublin, Edinburgh] ballots: |- 2:Edinburgh>Cork>Athens>Dublin>Bergen 3:Dublin>Edinburgh>Bergen>Cork>Athens 1:Athens>Bergen>Cork>Dublin>Edinburgh 1:Edinburgh>Dublin>Cork>Bergen>Athens expected_winners: - Dublin # file: p3_manip_reversal_rr.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 7 ballots (ranked ballots). Ballots: 2 × Edinburgh > Cork > Athens > Dublin > Bergen 3 × Dublin > Edinburgh > Bergen > Cork > Athens 1 × Athens > Bergen > Cork > Dublin > Edinburgh 1 × Edinburgh > Dublin > Cork > Bergen > Athens Round-Robin — every pair, head-to-head (For – Against): Edinburgh beats Cork 6 – 1 Edinburgh beats Athens 6 – 1 Dublin beats Edinburgh 4 – 3 Edinburgh beats Bergen 6 – 1 Cork beats Athens 6 – 1 Dublin beats Cork 4 – 3 Bergen beats Cork 4 – 3 Dublin beats Athens 4 – 3 Bergen beats Athens 4 – 3 Dublin beats Bergen 6 – 1 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | Edinburgh | Cork | Athens | Dublin | Bergen | --------------------------------------------------------------------------------- Edinburgh > | --- | 6 - 0 - 1 | 6 - 0 - 1 | 3 - 0 - 4 | 6 - 0 - 1 | Cork > | 1 - 0 - 6 | --- | 6 - 0 - 1 | 3 - 0 - 4 | 3 - 0 - 4 | Athens > | 1 - 0 - 6 | 1 - 0 - 6 | --- | 3 - 0 - 4 | 3 - 0 - 4 | Dublin > | 4 - 0 - 3 | 4 - 0 - 3 | 4 - 0 - 3 | --- | 6 - 0 - 1 | Bergen > | 1 - 0 - 6 | 4 - 0 - 3 | 4 - 0 - 3 | 1 - 0 - 6 | --- | Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order): # Candidate W–L–T Copeland Margin Beats 1 Dublin 4–0–0 4 +8 Edinburgh, Bergen, Cork, Athens 2 Edinburgh 3–1–0 3 +14 Bergen, Cork, Athens 3 Bergen 2–2–0 2 -8 Cork, Athens 4 Cork 1–3–0 1 -2 Athens 5 Athens 0–4–0 0 -12 — Winner — Ranked Robin (RCV-RR): Dublin beats every opponent head-to-head — the Condorcet winner. --- Smith Set (the generalized Condorcet winner) --- The smallest group whose every member beats every candidate outside it — the honest answer to "who is even in contention?". Smith set (1 of 5): Dublin Outside (4): Edinburgh, Cork, Athens, Bergen One member ⇒ Dublin is the Condorcet winner, beating every rival head-to-head. Ranked Robin (RCV-RR) winner Dublin is INSIDE the Smith set. ✓ Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of the set outscores every outsider, so the top of the win–loss table is always inside the set, however the tie among them is then broken. More: 07_Concepts/topics/smith_set.md