======================================================================
SOURCE FILE:     ex13_approve4.yaml
TABULATED FILE:  ex13_approve4_tabulated.txt
======================================================================

election_title: "Exercise 13 — Where do you draw the line? Approve 4 and up"
bv_test_id: BV2200
bv_election_id: qdtqf2
bv_results_url: https://bettervoting.com/qdtqf2/results

scenario_description: |-
  The nine honest opinions of ex13_opinions.yaml converted to Approval
  ballots under the STRICTER reading: approve only what you scored 4 or
  higher. Approvals: Beck 5 of 9, Cora 4, Ash 3 — BECK wins. The 4-point
  Becks on the Ash-first ballots survive the cut while the 3-point
  tolerances (Ash from Cora's fans, Cora from Beck's) all vanish, so the
  quiet middle candidate tops the count. Compare ex13_approve3.yaml
  (generous line: Ash) and ex13_bullet.yaml (favorites only: Cora).
  Exercise: ex13_draw_the_line.md.
  Live on BetterVoting (Test ID BV2200): https://bettervoting.com/qdtqf2/results
  — this is the "approve 4 and up" race; BV agrees: Beck 5.
voting_method: Approval
num_winners: 1
ballots: |-
  Ash,Beck,Cora
  1,1,0 # 3 voters: Ash 5 and Beck 4 both clear the 4+ line
  1,1,0
  1,1,0
  0,1,0 # 2 voters: only Beck (5) clears it — the Cora 3 vanishes
  0,1,0
  0,0,1 # 4 voters: only Cora (5) clears it — the Ash 3 vanishes
  0,0,1
  0,0,1
  0,0,1
expected_winners:
  - Beck

# file: ex13_approve4.yaml

======================================================================
TABULATION RESULTS
======================================================================

--- Approval Voting (single winner) ---
 Tabulating 9 ballots (any non-zero score = approval).

Ballots:
   columns = Ash, Beck, Cora      (1 = approve; 0 = not approved)
     3 × 1,1,0
     2 × 0,1,0
     4 × 0,0,1

   Beck -- 5 (56%) -- Elected
   Cora -- 4 (44%)
   Ash  -- 3 (33%)

[Approval Distribution] (how many candidates each ballot approved)
   12 approvals across 9 ballots — average 1.3 of 3 (range 1–2).
     approved 1: 6 ballots
     approved 2: 3 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
         |  Beck  |  Cora  |  Ash   |
   ----------------------------------
   Beck  |   --   |   0%   |  60%   |
   Cora  |   0%   |   --   |   0%   |
   Ash   |  100%  |   0%   |   --   |

Winner — Approval Voting (single winner)
  Beck