election_title: "Hamlin & Hua §4.1 — the majority bullet-votes instead: A wins, same electorate"

scenario_description: |-
  The SAME 100 voters with the SAME preferences as hh41_01_approval_as_printed.yaml.
  One thing changes: the 60-voter majority draws its approval line one candidate
  higher and approves only A. Nobody's opinion moved.

    60 voters: A          (was A + B)
    30 voters: B + C
    10 voters: C + B

  Now A wins with 60 approvals to B's 40, and the majority-criterion violation
  disappears. This is a counterfactual — the paper's assumed ballots are the
  ones in hh41_01 — and it is here to isolate what the §4.1 example actually
  turns on. Not the electorate's preferences, which are unchanged: the
  threshold. The violation exists only while the majority is generous.

  Worth reading against the paper's own §4.3, which reports 1.6 to 3.15
  approvals per ballot in real elections and surveys. Those numbers are cited
  there to answer the bullet-voting critique — but they are also the frequency
  estimate for THIS precondition. By the paper's own data, majorities usually
  do approve a second candidate, so the §4.1 configuration is the common case,
  not the exotic one.

  Compare with STAR, where the same class of failure requires the majority to
  support TWO rivals, not one — the Relaxed Majority Criterion:
  ../../../07_Concepts/topics/majority_criterion/README.md

  Claim-check page: ../../../04_Approval/01_Learn/hamlin_hua_2023.md
  Set overview: ../README.md

voting_method: Approval
num_winners: 1

ballots: |-
  Count:A,B,C
  60:1,0,0   # A > B > C — bullet-votes A
  30:0,1,1   # B > C > A — approves B and C
  10:0,1,1   # C > B > A — approves C and B

expected_winners:
  - A

# file: hh41_05_majority_bullet_votes.yaml