election_title: "Brams' grading paradox — the grade leader loses the runoff"

scenario_description: |-
  Steven Brams' three-voter grading example (Brams & Potthoff, "The paradox
  of grading systems," Public Choice 165, 2015), offered as a critique of
  grading systems: the candidate with the best grade total (Adams, 6-5-4) is
  not the head-to-head champion (Baker beats both rivals — the Condorcet
  winner). Run under STAR, the example vindicates the automatic runoff
  instead of indicting it: finalists Adams & Baker, and Baker takes the seat
  2-1. Pure score summation (Score voting) elects Adams. The Approval reading
  depends entirely on where the 0/1 line is drawn: the engine's any-non-zero
  cut elects Adams, Brams' own top-grades cut elects Baker, and two other
  reasonable cuts produce ties. Grades {0..3} as in the original slide.
  LH-only for now (no BetterVoting election).

voting_method: STAR
num_winners: 1

ballots: |-
  Adams,Baker,Chen
  3,0,0   # voter 1 — Adams gets the top grade, zeros for the rest
  2,3,3   # voter 2 — Baker and Chen top grades, Adams a friendly 2
  1,2,1   # voter 3 — Baker best, mild on Adams and Chen

expected_winners:
  - Baker

# file: brams_grading_paradox_c3_b3.yaml