election_title: "Brams Example 6 — three counts, three winners (STAR sides with head-to-head)"

scenario_description: |-
  Example 6 of Brams & Potthoff, "The paradox of grading systems" (Public
  Choice 165, 2015): nine voters in three like-minded blocs grade three
  candidates {0..2}, and three grading aggregations crown three DIFFERENT
  winners — proven by the authors' exhaustive search to be the unique
  minimal party-structured example of this strong paradox:
    - Highest grade total (Score): Amos 11, Bree 10, Cole 10 -> AMOS.
    - Highest median grade: Bree 2 (Amos 1, Cole 1)          -> BREE.
    - Head-to-head (Condorcet): Cole beats Amos 3-2 and Bree 4-2 -> COLE.
  STAR sides with head-to-head: Bree/Cole tie at 10 for second place, the
  tie breaks to Cole (he beats Bree 4-2), and Cole wins the runoff 3-2 with
  4 Equal Support ballots. Every voter here has dichotomous preferences, so
  their natural Approval ballots elect Cole too (6-5-7) — but a uniform
  any-non-zero cut elects Amos (9-5-7). Where the 0/1 line falls decides
  the approval winner; no cut is canonical.

voting_method: STAR
num_winners: 1

ballots: |-
  Amos,Bree,Cole
  2,2,0   # bloc 1 (2 voters) — Amos and Bree top, Cole bottom
  2,2,0
  1,2,2   # bloc 2 (3 voters) — Bree and Cole top, Amos middling
  1,2,2
  1,2,2
  1,0,1   # bloc 3 (4 voters) — Amos and Cole middling, Bree bottom
  1,0,1
  1,0,1
  1,0,1

expected_winners:
  - Cole

# file: brams_ex6_three_winners_c3_b9.yaml