====================================================================== SOURCE FILE: ballot_expressiveness_c9_irv_top5.yaml TABULATED FILE: ballot_expressiveness_c9_irv_top5_tabulated.txt ====================================================================== election_title: "Nine candidates, 25 voters — ranking only five, counted by RCV-IRV" scenario_description: |- BOTH LIMITS AT ONCE, and the winner does not move again. Five ranks out of nine, counted by instant runoff: Ben, exactly as in bv2280_37yf8x_irv_full.yaml. This file is the honest control on the rest of the folder, and it is the one that stops the lesson from overreaching. Ranked Robin's winner DID change when the ballot was capped (Finn → Gus). IRV's did not — because IRV had already lost Finn on the uncapped ballot, for a completely different reason: too few first choices. Truncation and elimination are separate failures, and here stacking them changes nothing. So "the cap costs you the answer" is a claim about the COUNT as much as the paper. It bites a method that reads the whole ballot, and glances off one that only reads the top of it. Convention, stated: an unranked candidate is beaten by everyone the voter ranked. A ballot whose five names have all been eliminated is EXHAUSTED — it leaves the count and the majority denominator, which is what a rank cap really does to an instant runoff. 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: RCV-IRV num_winners: 1 # Not on BetterVoting: this is the control leg that changes nothing. # The other four papers are BV2280 (37yf8x). lot_numbers: [Ada, Ben, Cleo, Dev, Emma, Finn, Gus, Hugo, Iris] ballots: |- Ben>Cleo>Dev>Ada>Emma # voter at -0.43 Gus>Hugo>Iris>Finn>Emma # voter at +0.60 Ada>Ben>Cleo>Dev>Emma # voter at -0.67 Iris>Hugo>Gus>Finn>Emma # voter at +0.89 Finn>Gus>Emma>Dev>Cleo # voter at +0.18 Emma>Dev>Cleo>Ben>Finn # voter at -0.13 Gus>Hugo>Iris>Finn>Emma # voter at +0.59 Hugo>Iris>Gus>Finn>Emma # voter at +0.72 Gus>Finn>Emma>Hugo>Iris # voter at +0.34 Hugo>Iris>Gus>Finn>Emma # voter at +0.69 Finn>Gus>Emma>Dev>Cleo # voter at +0.23 Ben>Cleo>Dev>Emma>Ada # voter at -0.30 Ben>Ada>Cleo>Dev>Emma # voter at -0.51 Iris>Hugo>Gus>Finn>Emma # voter at +0.89 Emma>Dev>Cleo>Finn>Ben # voter at -0.05 Gus>Hugo>Iris>Finn>Emma # voter at +0.60 Finn>Gus>Emma>Dev>Cleo # voter at +0.28 Ben>Cleo>Dev>Emma>Ada # voter at -0.40 Hugo>Gus>Iris>Finn>Emma # voter at +0.62 Ada>Ben>Cleo>Dev>Emma # voter at -0.63 Finn>Gus>Emma>Dev>Cleo # voter at +0.27 Ada>Ben>Cleo>Dev>Emma # voter at -0.61 Ada>Ben>Cleo>Dev>Emma # voter at -1.33 Cleo>Dev>Emma>Ben>Finn # voter at -0.23 Ada>Ben>Cleo>Dev>Emma # voter at -1.82 expected_winners: - Ben # file: ballot_expressiveness_c9_irv_top5.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- RCV / Instant-Runoff Voting (single winner) --- Nine candidates, 25 voters — ranking only five, counted by RCV-IRV Tabulating 25 ballots (ranked ballots). ROUND 1 Candidate Votes Status ----------- ------- -------- Ada 5 Hopeful Gus 4 Hopeful Ben 4 Hopeful Finn 4 Hopeful Hugo 3 Hopeful Iris 2 Hopeful Emma 2 Hopeful Cleo 1 Rejected Dev 0 Rejected ROUND 2 Candidate Votes Status ----------- ------- -------- Ada 5 Hopeful Ben 4 Hopeful Gus 4 Hopeful Finn 4 Hopeful Hugo 3 Hopeful Emma 3 Hopeful Iris 2 Rejected Cleo 0 Rejected Dev 0 Rejected ROUND 3 Candidate Votes Status ----------- ------- -------- Hugo 5 Hopeful Ada 5 Hopeful Gus 4 Hopeful Ben 4 Hopeful Finn 4 Hopeful Emma 3 Rejected Iris 0 Rejected Cleo 0 Rejected Dev 0 Rejected ROUND 4 Candidate Votes Status ----------- ------- -------- Ben 6 Hopeful Ada 5 Hopeful Finn 5 Hopeful Hugo 5 Hopeful Gus 4 Rejected Emma 0 Rejected Iris 0 Rejected Cleo 0 Rejected Dev 0 Rejected ROUND 5 Candidate Votes Status ----------- ------- -------- Hugo 8 Hopeful Finn 6 Hopeful Ben 6 Hopeful Ada 5 Rejected Gus 0 Rejected Emma 0 Rejected Iris 0 Rejected Cleo 0 Rejected Dev 0 Rejected ROUND 6 Candidate Votes Status ----------- ------- -------- Ben 11 Hopeful Hugo 8 Hopeful Finn 6 Rejected Ada 0 Rejected Gus 0 Rejected Emma 0 Rejected Iris 0 Rejected Cleo 0 Rejected Dev 0 Rejected FINAL RESULT Candidate Votes Status ----------- ------- -------- Ben 12 Elected Hugo 9 Rejected Finn 0 Rejected Ada 0 Rejected Gus 0 Rejected Emma 0 Rejected Iris 0 Rejected Cleo 0 Rejected Dev 0 Rejected Blank Votes 4 Rejected Winner(s) — RCV / Instant-Runoff Voting (single winner) Ben --- 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): Gus Outside (8): Ben, Cleo, Dev, Ada, Emma, Hugo, Iris, Finn One member ⇒ Gus is the Condorcet winner, beating every rival head-to-head. RCV-IRV winner Ben is OUTSIDE the Smith set. ✗ Every member of the set (Gus) beats Ben head-to-head, yet RCV-IRV elected Ben 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