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SOURCE FILE:     bv2147_9gdrqg_irv.yaml
TABULATED FILE:  bv2147_9gdrqg_irv_tabulated.txt
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election_title: "Felsenthal Ex.3 District I — Runoff/IRV: Bruno wins the runoff"
scenario_description: |-
  Race 1 of 2 in District I of the Felsenthal Reinforcement-paradox trio (BV2147, bvid 9gdrqg; BV-confirmed; the trio is BV2147/48/49). 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 3 (the Reinforcement paradox).
  District I: 17 voters. No first-round majority (Alma 4, Bruno 6, Cora 7), so plurality-with-runoff — run as IRV, identical for three candidates — deletes Alma, and Bruno beats Cora 10–7. Note the district's pairwise preferences form a Condorcet CYCLE (Alma>Bruno 10–7, Bruno>Cora 10–7, Cora>Alma 12–5): no Condorcet winner exists here. Bruno also wins District II (BV2148) outright — yet the amalgamated electorate (BV2149) elects Alma under the same procedure.
  Live results: https://bettervoting.com/9gdrqg/results
bv_test_id: BV2147
bv_election_id: 9gdrqg
bv_results_url: https://bettervoting.com/9gdrqg/results
paradoxes: [multiple-districts, condorcet-cycle]
voting_method: IRV
num_winners: 1
ballots: |-
  4:Alma>Bruno>Cora
  1:Bruno>Alma>Cora
  5:Bruno>Cora>Alma
  6:Cora>Alma>Bruno
  1:Cora>Bruno>Alma
expected_winners:
  - Bruno

# file: bv2147_9gdrqg_irv.yaml

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TABULATION RESULTS
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--- RCV / Instant-Runoff Voting (single winner) ---
  Felsenthal Ex.3 District I — Runoff/IRV: Bruno wins the runoff
 Tabulating 17 ballots (ranked ballots).

ROUND 1
Candidate      Votes  Status
-----------  -------  --------
Cora               7  Hopeful
Bruno              6  Hopeful
Alma               4  Rejected

FINAL RESULT
Candidate      Votes  Status
-----------  -------  --------
Bruno             10  Elected
Cora               7  Rejected
Alma               0  Rejected


Winner(s) — RCV / Instant-Runoff Voting (single winner)
  Bruno

--- 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 (3 of 3): Alma, Bruno, Cora
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   RCV-IRV winner Bruno is INSIDE the Smith set. ✓
      Not guaranteed — RCV-IRV is not Smith-efficient — but it holds here.
   More: 07_Concepts/topics/smith_set.md