====================================================================== SOURCE FILE: crowded_field_c5_irv.yaml TABULATED FILE: crowded_field_c5_irv_tabulated.txt ====================================================================== election_title: "Crowded field, rung 5 — 5 candidates, 65 voters, counted by RCV-IRV" scenario_description: |- RUNG 2 — the same voters, two more candidates, and both choose-one methods lose the Condorcet winner. Diego still beats all four rivals head-to-head (crowded_field_c5_ranked_robin.yaml proves it). But first choices are what these methods count, and Bruno at 6 and Elsa at 14 now stand between Diego and the voters who previously had nobody closer. Diego drops from 34 first choices to 9, is eliminated early, and the seat goes to Elsa. Round 1 is also the Choose-One count, and it elects Bruno on 23 of 65 — a candidate Diego beats head-to-head. Note what caused all of this: not one voter changing their mind, only two more names on the ballot. Same 65 voters and the same fixed candidate positions as crowded_field_c5_star.yaml, on a ranked ballot — the same ballots as crowded_field_c5_ranked_robin.yaml, counted by elimination instead of head-to-head. Construction: build_ladder.py in this folder. 65 voters in seven blocs at 0, 4, 8, 12, 16, 20, 24 (sizes 6, 10, 13, 9, 12, 8, 7); candidates fixed at Ana 1 · Bruno 6 · Clara 9 · Diego 11 · Elsa 14 · Felix 16 · Greta 22; utility = minus distance; scores = each bloc's own min-max scaling onto 0–5. Nothing is tuned, and no count at any rung is settled by a tie-break. voting_method: RCV_IRV num_winners: 1 lot_numbers: [Ana, Bruno, Diego, Elsa, Greta] ballots: |- 6:Ana>Bruno>Diego>Elsa>Greta # bloc at 0 10:Bruno>Ana>Diego>Elsa>Greta # bloc at 4 13:Bruno>Diego>Elsa>Ana>Greta # bloc at 8 9:Diego>Elsa>Bruno>Greta>Ana # bloc at 12 12:Elsa>Diego>Greta>Bruno>Ana # bloc at 16 8:Greta>Elsa>Diego>Bruno>Ana # bloc at 20 7:Greta>Elsa>Diego>Bruno>Ana # bloc at 24 expected_winners: - Elsa ====================================================================== TABULATION RESULTS ====================================================================== --- RCV / Instant-Runoff Voting (single winner) --- Crowded field, rung 5 — 5 candidates, 65 voters, counted by RCV-IRV Tabulating 65 ballots (ranked ballots). ROUND 1 Candidate Votes Status ----------- ------- -------- Bruno 23 Hopeful Greta 15 Hopeful Elsa 12 Hopeful Diego 9 Hopeful Ana 6 Rejected ROUND 2 Candidate Votes Status ----------- ------- -------- Bruno 29 Hopeful Greta 15 Hopeful Elsa 12 Hopeful Diego 9 Rejected Ana 0 Rejected ROUND 3 Candidate Votes Status ----------- ------- -------- Bruno 29 Hopeful Elsa 21 Hopeful Greta 15 Rejected Diego 0 Rejected Ana 0 Rejected FINAL RESULT Candidate Votes Status ----------- ------- -------- Elsa 36 Elected Bruno 29 Rejected Greta 0 Rejected Diego 0 Rejected Ana 0 Rejected Winner(s) — RCV / Instant-Runoff Voting (single winner) Elsa --- 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): Diego Outside (4): Ana, Bruno, Elsa, Greta One member ⇒ Diego is the Condorcet winner, beating every rival head-to-head. RCV-IRV winner Elsa is OUTSIDE the Smith set. ✗ Every member of the set (Diego) beats Elsa head-to-head, yet RCV-IRV elected Elsa anyway. RCV-IRV is not Smith-efficient (nor Condorcet-efficient) — this is the shape a center squeeze leaves behind. More: 07_Concepts/topics/smith_set.md