====================================================================== SOURCE FILE: p3_manip_compromise_rr.yaml TABULATED FILE: p3_manip_compromise_rr_tabulated.txt ====================================================================== election_title: "P3 manipulated — the mild version: three adjacent swaps, no burial, same result" scenario_description: |- The manipulation that should worry us more than the book's. The complete reversal is a curiosity — no real voter submits their preferences backwards. But the SAME voter can achieve the SAME outcome with ordinary compromising: submit Dublin>Athens>Bergen>Cork>Edinburgh. That is three adjacent swaps. Nothing is buried, the sincere last choice Edinburgh stays last, and only the compromise candidate Dublin is lifted. Dublin goes 4-0 and wins outright. Exhaustively, 52 of the 119 alternative rankings available to this voter strictly improve their result (44 decided outright or by margin, 8 more only after the lot). Note this is COMPROMISING, not burial — Ranked Robin's documented resistance to burial is untouched and remains true, which makes this worse news rather than better, because compromising is the strategy ordinary voters actually reach for. 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:Dublin>Athens>Bergen>Cork>Edinburgh expected_winners: - Dublin # file: p3_manip_compromise_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 × Dublin > Athens > Bergen > Cork > Edinburgh Round-Robin — every pair, head-to-head (For – Against): Edinburgh beats Cork 5 – 2 Edinburgh beats Athens 5 – 2 Dublin beats Edinburgh 5 – 2 Edinburgh beats Bergen 5 – 2 Cork beats Athens 5 – 2 Dublin beats Cork 4 – 3 Bergen beats Cork 5 – 2 Dublin beats Athens 4 – 3 Athens beats Bergen 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 > | --- | 5 - 0 - 2 | 5 - 0 - 2 | 2 - 0 - 5 | 5 - 0 - 2 | Cork > | 2 - 0 - 5 | --- | 5 - 0 - 2 | 3 - 0 - 4 | 2 - 0 - 5 | Athens > | 2 - 0 - 5 | 2 - 0 - 5 | --- | 3 - 0 - 4 | 4 - 0 - 3 | Dublin > | 5 - 0 - 2 | 4 - 0 - 3 | 4 - 0 - 3 | --- | 6 - 0 - 1 | Bergen > | 2 - 0 - 5 | 5 - 0 - 2 | 3 - 0 - 4 | 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 +10 Edinburgh, Cork, Athens, Bergen 2 Edinburgh 3–1–0 3 +6 Cork, Athens, Bergen 3 Cork 1–3–0 1 -4 Athens 4 Athens 1–3–0 1 -6 Bergen 5 Bergen 1–3–0 1 -6 Cork 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