======================================================================
SOURCE FILE:     bv2152_r6ctvy_approval.yaml
TABULATED FILE:  bv2152_r6ctvy_approval_tabulated.txt
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election_title: "Felsenthal Ex.5 — Approval: the Condorcet winner loses the approval count"
scenario_description: |-
  Race 1 of 2 in the Felsenthal & Maoz Approval-paradox election (BV2152, bvid r6ctvy; 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 A3, Example 5 — due to Felsenthal & Maoz (1988: 123, Example 2).
  47 voters, rankings 18×(Anna>Bert>Carla), 6×(Bert>Carla>Anna), 8×(Bert>Anna>Carla), 2×(Carla>Anna>Bert), 13×(Carla>Bert>Anna). Bert is the Condorcet winner (beats Anna 27–20, Carla 32–15; social ordering Bert>Anna>Carla). But each voter approves only the candidates the text marks in parentheses — 18×{Anna}, 6×{Bert,Carla}, 8×{Bert,Anna}, 2×{Carla,Anna}, 13×{Carla} — and the approval totals are Anna 28, Bert 14, Carla 21: APPROVAL ELECTS ANNA. The Condorcet winner paradox under Approval: where a voter draws the approval cutoff decides the election, and the pairwise favorite can fall below it.
  Live results: https://bettervoting.com/r6ctvy/results
bv_test_id: BV2152
bv_election_id: r6ctvy
bv_results_url: https://bettervoting.com/r6ctvy/results
paradoxes: [condorcet-winner]
voting_method: Approval
num_winners: 1
ballots: |-
  Anna,Bert,Carla
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  1,0,0
  0,1,1
  0,1,1
  0,1,1
  0,1,1
  0,1,1
  0,1,1
  1,1,0
  1,1,0
  1,1,0
  1,1,0
  1,1,0
  1,1,0
  1,1,0
  1,1,0
  1,0,1
  1,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
  0,0,1
expected_winners:
  - Anna

# file: bv2152_r6ctvy_approval.yaml

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TABULATION RESULTS
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--- Approval Voting (single winner) ---
 Tabulating 47 ballots (any non-zero score = approval).

Ballots:
   columns = Anna, Bert, Carla      (1 = approve; 0 = not approved)
    18 × 1,0,0
     6 × 0,1,1
     8 × 1,1,0
     2 × 1,0,1
    13 × 0,0,1

   Anna  -- 28 (60%) -- Elected
   Carla -- 21 (45%)
   Bert  -- 14 (30%)

[Approval Distribution] (how many candidates each ballot approved)
   63 approvals across 47 ballots — average 1.3 of 3 (range 1–2).
     approved 1: 31 ballots
     approved 2: 16 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
          |  Anna  | Carla  |  Bert  |
   -----------------------------------
   Anna   |   --   |   7%   |  29%   |
   Carla  |  10%   |   --   |  29%   |
   Bert   |  57%   |  43%   |   --   |

Winner — Approval Voting (single winner)
  Anna