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SOURCE FILE:     chicken_approval_both_defect.yaml
TABULATED FILE:  chicken_approval_both_defect_tabulated.txt
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election_title: "Chicken / Burr dilemma — Approval, both sides defect: C wins on 40%"
scenario_description: |-
  The third horn of the Burr dilemma, and the one the set previously only
  described in prose. Same 100 voters as chicken_approval and chicken_star: 60
  prefer either ally to C, 40 want C.

  In chicken_approval the 60 cooperate honestly and A and B tie 60-60 — the
  1800 Jefferson-Burr outcome, and the reason each side is tempted to defect.
  Here both sides give in to that temptation. The 35 A-first voters approve only
  A; the 25 B-first voters approve only B. Neither is voting dishonestly about
  who they prefer; each is simply withholding approval from an ally to win the
  intra-faction contest.

  A 35, B 25, C 40. C wins with 40 of 100 while SIXTY voters preferred either
  ally. The faction did not lose because the ballot forced it to split — Approval
  never forces that. It lost because its two halves each declined to support the
  other.

  This is Approval's exact counterpart to STAR's residual split
  (method_comparisons/split_voting/_main/05a_residual_split_bullet-voting.yaml,
  where a 60% side loses to a 40% opponent the same way). Both are SELF-inflicted:
  the ballot offered a remedy and the voters declined it. That is a real and
  meaningful difference from Choose-One, where no remedy is on offer at all — but
  it is not immunity, and neither method should be sold as immune.

  Where the avalanche starts: with a of the 35 A-first voters and b of the 25
  B-first voters bullet-voting, A holds 60 - b approvals and B holds 60 - a. C
  takes the lead only once BOTH a > 20 and b > 20 — so it is not one defector
  who does the damage, it is defection becoming general. That threshold is what
  makes the Approval slope slippery, and it is exactly what STAR's runoff
  removes: see chicken_star.yaml, where supporting both allies honestly costs
  nothing.

paradoxes: [spoiler-scc]
voting_method: Approval
num_winners: 1

ballots: |-
  Count:A,B,C
  35:1,0,0   # A-first voters bullet-vote — no approval for ally B
  25:0,1,0   # B-first voters bullet-vote — no approval for ally A
  40:0,0,1   # the C bloc, unchanged and undivided

expected_winners:
  - C

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TABULATION RESULTS
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--- Approval Voting (single winner) ---
 Tabulating 100 ballots (any non-zero score = approval).

Ballots:
   columns = A, B, C      (1 = approve; 0 = not approved)
    35 × 1,0,0
    25 × 0,1,0
    40 × 0,0,1

   C -- 40 (40%) -- Elected
   A -- 35 (35%)
   B -- 25 (25%)

[Approval Distribution] (how many candidates each ballot approved)
   100 approvals across 100 ballots — average 1.0 of 3 (range 1–1).
     approved 1: 100 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
      |   C    |   A    |   B    |
   -------------------------------
   C  |   --   |   0%   |   0%   |
   A  |   0%   |   --   |   0%   |
   B  |   0%   |   0%   |   --   |

Winner — Approval Voting (single winner)
  C