====================================================================== SOURCE FILE: bv2280_37yf8x_rr_full.yaml TABULATED FILE: bv2280_37yf8x_rr_full_tabulated.txt ====================================================================== election_title: "Nine candidates, 25 voters — ranking all nine, counted by Ranked Robin" scenario_description: |- THE CONTROL. Every voter ranks all nine candidates, nothing truncated and nothing rounded, and Ranked Robin returns Finn — the candidate who beats each of the other eight head-to-head. This is the full-resolution ranked ballot that Condorcet-efficiency simulations normally hand to ranked methods. It is also an idealization: no large-field jurisdiction issues it. bv2280_37yf8x_rr_top5.yaml cuts it down to five ranks, which is what a real ranked ballot looks like, and the winner changes. Compare with bv2280_37yf8x_star.yaml: the 0–5 score ballot agrees with this one. Compare with bv2280_37yf8x_irv_full.yaml: the SAME ballots, counted by instant runoff, do not — which is the cleanest evidence in this folder that the paper and the count are separate things. Construction: build_cases.py in this folder. 25 voters and 9 candidates at frozen positions on one spectrum — Ada −0.73 · Ben −0.37 · Cleo −0.18 · Dev −0.17 · Emma −0.11 · Finn +0.24 · Gus +0.41 · Hugo +0.80 · Iris +0.84; utility = minus the distance; scores = each voter's own min-max scaling onto 0–5; rankings = those same utilities in order. Nothing is tuned to the result, and **no count in this folder is settled by a tie-break** — that was a search constraint, so every winner here survives any lot rule. voting_method: RankedRobin num_winners: 1 bv_test_id: BV2280 bv_election_id: 37yf8x bv_results_url: https://bettervoting.com/37yf8x/results lot_numbers: [Ada, Ben, Cleo, Dev, Emma, Finn, Gus, Hugo, Iris] ballots: |- Ben>Cleo>Dev>Ada>Emma>Finn>Gus>Hugo>Iris # voter at -0.43 Gus>Hugo>Iris>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.60 Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris # voter at -0.67 Iris>Hugo>Gus>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.89 Finn>Gus>Emma>Dev>Cleo>Ben>Hugo>Iris>Ada # voter at +0.18 Emma>Dev>Cleo>Ben>Finn>Gus>Ada>Hugo>Iris # voter at -0.13 Gus>Hugo>Iris>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.59 Hugo>Iris>Gus>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.72 Gus>Finn>Emma>Hugo>Iris>Dev>Cleo>Ben>Ada # voter at +0.34 Hugo>Iris>Gus>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.69 Finn>Gus>Emma>Dev>Cleo>Hugo>Iris>Ben>Ada # voter at +0.23 Ben>Cleo>Dev>Emma>Ada>Finn>Gus>Hugo>Iris # voter at -0.30 Ben>Ada>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris # voter at -0.51 Iris>Hugo>Gus>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.89 Emma>Dev>Cleo>Finn>Ben>Gus>Ada>Hugo>Iris # voter at -0.05 Gus>Hugo>Iris>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.60 Finn>Gus>Emma>Dev>Cleo>Hugo>Iris>Ben>Ada # voter at +0.28 Ben>Cleo>Dev>Emma>Ada>Finn>Gus>Hugo>Iris # voter at -0.40 Hugo>Gus>Iris>Finn>Emma>Dev>Cleo>Ben>Ada # voter at +0.62 Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris # voter at -0.63 Finn>Gus>Emma>Dev>Cleo>Hugo>Iris>Ben>Ada # voter at +0.27 Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris # voter at -0.61 Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris # voter at -1.33 Cleo>Dev>Emma>Ben>Finn>Ada>Gus>Hugo>Iris # voter at -0.23 Ada>Ben>Cleo>Dev>Emma>Finn>Gus>Hugo>Iris # voter at -1.82 expected_winners: - Finn # file: bv2280_37yf8x_rr_full.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- Ranked Robin (RCV-RR / Copeland) Method (single winner) --- Tabulating 25 ballots (ranked ballots). Ballots: 1 × Ben > Cleo > Dev > Ada > Emma > Finn > Gus > Hugo > Iris 3 × Gus > Hugo > Iris > Finn > Emma > Dev > Cleo > Ben > Ada 5 × Ada > Ben > Cleo > Dev > Emma > Finn > Gus > Hugo > Iris 2 × Iris > Hugo > Gus > Finn > Emma > Dev > Cleo > Ben > Ada 1 × Finn > Gus > Emma > Dev > Cleo > Ben > Hugo > Iris > Ada 1 × Emma > Dev > Cleo > Ben > Finn > Gus > Ada > Hugo > Iris 2 × Hugo > Iris > Gus > Finn > Emma > Dev > Cleo > Ben > Ada 1 × Gus > Finn > Emma > Hugo > Iris > Dev > Cleo > Ben > Ada 3 × Finn > Gus > Emma > Dev > Cleo > Hugo > Iris > Ben > Ada 2 × Ben > Cleo > Dev > Emma > Ada > Finn > Gus > Hugo > Iris 1 × Ben > Ada > Cleo > Dev > Emma > Finn > Gus > Hugo > Iris 1 × Emma > Dev > Cleo > Finn > Ben > Gus > Ada > Hugo > Iris 1 × Hugo > Gus > Iris > Finn > Emma > Dev > Cleo > Ben > Ada 1 × Cleo > Dev > Emma > Ben > Finn > Ada > Gus > Hugo > Iris Round-Robin — every pair, head-to-head (For – Against): Cleo beats Ben 16 – 9 Dev beats Ben 16 – 9 Ben beats Ada 20 – 5 Emma beats Ben 16 – 9 Finn beats Ben 14 – 11 Gus beats Ben 13 – 12 Ben beats Hugo 13 – 12 Ben beats Iris 13 – 12 Dev beats Cleo 15 – 10 Cleo beats Ada 19 – 6 Emma beats Cleo 15 – 10 Finn beats Cleo 13 – 12 Gus beats Cleo 13 – 12 Cleo beats Hugo 16 – 9 Cleo beats Iris 16 – 9 Dev beats Ada 19 – 6 Emma beats Dev 15 – 10 Finn beats Dev 13 – 12 Gus beats Dev 13 – 12 Dev beats Hugo 16 – 9 Dev beats Iris 16 – 9 Emma beats Ada 18 – 7 Finn beats Ada 16 – 9 Gus beats Ada 15 – 10 Hugo beats Ada 13 – 12 Iris beats Ada 13 – 12 Finn beats Emma 13 – 12 Gus beats Emma 13 – 12 Emma beats Hugo 17 – 8 Emma beats Iris 17 – 8 Finn beats Gus 16 – 9 Finn beats Hugo 17 – 8 Finn beats Iris 17 – 8 Gus beats Hugo 20 – 5 Gus beats Iris 21 – 4 Hugo beats Iris 23 – 2 --- Pairwise (Round-Robin) Matrix --- Head-to-head / pairwise comparison — the Ranked Robin tally Legend: For - Equal Support - Against (row vs column) | Ben | Cleo | Dev | Ada | Emma | Finn | Gus | Hugo | Iris | ----------------------------------------------------------------------------------------------------------------------------------------- Ben > | --- | 9 - 0 - 16 | 9 - 0 - 16 |20 - 0 - 5 | 9 - 0 - 16 |11 - 0 - 14 |12 - 0 - 13 |13 - 0 - 12 |13 - 0 - 12 | Cleo > | 16 - 0 - 9 | --- |10 - 0 - 15 |19 - 0 - 6 |10 - 0 - 15 |12 - 0 - 13 |12 - 0 - 13 |16 - 0 - 9 |16 - 0 - 9 | Dev > | 16 - 0 - 9 |15 - 0 - 10 | --- |19 - 0 - 6 |10 - 0 - 15 |12 - 0 - 13 |12 - 0 - 13 |16 - 0 - 9 |16 - 0 - 9 | Ada > | 5 - 0 - 20 | 6 - 0 - 19 | 6 - 0 - 19 | --- | 7 - 0 - 18 | 9 - 0 - 16 |10 - 0 - 15 |12 - 0 - 13 |12 - 0 - 13 | Emma > | 16 - 0 - 9 |15 - 0 - 10 |15 - 0 - 10 |18 - 0 - 7 | --- |12 - 0 - 13 |12 - 0 - 13 |17 - 0 - 8 |17 - 0 - 8 | Finn > | 14 - 0 - 11 |13 - 0 - 12 |13 - 0 - 12 |16 - 0 - 9 |13 - 0 - 12 | --- |16 - 0 - 9 |17 - 0 - 8 |17 - 0 - 8 | Gus > | 13 - 0 - 12 |13 - 0 - 12 |13 - 0 - 12 |15 - 0 - 10 |13 - 0 - 12 | 9 - 0 - 16 | --- |20 - 0 - 5 |21 - 0 - 4 | Hugo > | 12 - 0 - 13 | 9 - 0 - 16 | 9 - 0 - 16 |13 - 0 - 12 | 8 - 0 - 17 | 8 - 0 - 17 | 5 - 0 - 20 | --- |23 - 0 - 2 | Iris > | 12 - 0 - 13 | 9 - 0 - 16 | 9 - 0 - 16 |13 - 0 - 12 | 8 - 0 - 17 | 8 - 0 - 17 | 4 - 0 - 21 | 2 - 0 - 23 | --- | 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 Finn 8–0–0 8 +38 Gus, Emma, Dev, Cleo, Ben, Hugo, Iris, Ada 2 Gus 7–1–0 7 +34 Emma, Dev, Cleo, Ben, Hugo, Iris, Ada 3 Emma 6–2–0 6 +44 Dev, Cleo, Ben, Hugo, Iris, Ada 4 Dev 5–3–0 5 +32 Cleo, Ben, Hugo, Iris, Ada 5 Cleo 4–4–0 4 +22 Ben, Hugo, Iris, Ada 6 Ben 3–5–0 3 -8 Hugo, Iris, Ada 7 Hugo 2–6–0 2 -26 Iris, Ada 8 Iris 1–7–0 1 -70 Ada 9 Ada 0–8–0 0 -66 — Winner — Ranked Robin (RCV-RR): Finn 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 9): Finn Outside (8): Ben, Cleo, Dev, Ada, Emma, Gus, Hugo, Iris One member ⇒ Finn is the Condorcet winner, beating every rival head-to-head. Ranked Robin (RCV-RR) winner Finn 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