====================================================================== SOURCE FILE: irv_district_B.yaml TABULATED FILE: irv_district_B_tabulated.txt ====================================================================== election_title: "Summability demo — RCV-IRV district B (B wins)" scenario_description: |- District B of the RCV-IRV summability trio: B wins here too — both districts independently elect B. Yet the combined electorate does NOT elect B (see irv_combined.yaml: B is eliminated first there). District winners, and even full district round-by-round tallies, cannot be summed into the combined result — the non-summability this trio demonstrates. voting_method: RCV_IRV num_winners: 1 # Summability demo (IRV), district B (A/C roles swapped). IRV winner: B. ballots: |- 6:C 4:B 3:A>B>C expected_winners: - B # file: irv_district_B.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- RCV / Instant-Runoff Voting (single winner) --- Summability demo — RCV-IRV district B (B wins) Tabulating 13 ballots (ranked ballots). ROUND 1 Candidate Votes Status ----------- ------- -------- C 6 Hopeful B 4 Hopeful A 3 Rejected FINAL RESULT Candidate Votes Status ----------- ------- -------- B 7 Elected C 6 Rejected A 0 Rejected Winner(s) — RCV / Instant-Runoff Voting (single winner) B --- 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 3): B Outside (2): C, A One member ⇒ B is the Condorcet winner, beating every rival head-to-head. RCV-IRV winner B is INSIDE the Smith set. ✓ Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here. More: 07_Concepts/topics/smith_set.md