====================================================================== SOURCE FILE: bv2145_6fj2kg_irv.yaml TABULATED FILE: bv2145_6fj2kg_irv_tabulated.txt ====================================================================== election_title: "Felsenthal Ex.2 — Runoff/IRV: the Condorcet winner is eliminated first" scenario_description: |- Race 1 of 3 in the Felsenthal runoff-paradoxes election, part 1 of 2 (BV2145, bvid 6fj2kg; BV-confirmed). Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A2, Example 2 (plurality with runoff). 17 voters, three candidates. Ada is the Condorcet winner (beats Ben 9–8 and Cleo 9–8; social ordering Ada>Ben>Cleo) but has the FEWEST first choices (Ada 5, Ben 6, Cleo 6). Plurality-with-runoff — run here as IRV, which is identical for three candidates — eliminates Ada first, and Ben beats Cleo 9–8. The Condorcet winner paradox, plus Felsenthal's SCC note: had Cleo withdrawn, Ada would have won the first round outright (9 of 17). The non-monotonicity half of the lesson is the paired election BV2146. Live results: https://bettervoting.com/6fj2kg/results bv_test_id: BV2145 bv_election_id: 6fj2kg bv_results_url: https://bettervoting.com/6fj2kg/results paradoxes: [condorcet-winner, spoiler-scc, non-monotonicity] voting_method: IRV num_winners: 1 ballots: |- 3:Ada>Ben>Cleo 2:Ada>Cleo>Ben 4:Ben>Ada>Cleo 2:Ben>Cleo>Ada 4:Cleo>Ada>Ben 2:Cleo>Ben>Ada expected_winners: - Ben # file: bv2145_6fj2kg_irv.yaml ====================================================================== TABULATION RESULTS ====================================================================== --- RCV / Instant-Runoff Voting (single winner) --- Felsenthal Ex.2 — Runoff/IRV: the Condorcet winner is eliminated first Tabulating 17 ballots (ranked ballots). ROUND 1 Candidate Votes Status ----------- ------- -------- Ben 6 Hopeful Cleo 6 Hopeful Ada 5 Rejected FINAL RESULT Candidate Votes Status ----------- ------- -------- Ben 9 Elected Cleo 8 Rejected Ada 0 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 3): Ada Outside (2): Ben, Cleo One member ⇒ Ada is the Condorcet winner, beating every rival head-to-head. RCV-IRV winner Ben is OUTSIDE the Smith set. ✗ Every member of the set (Ada) 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