======================================================================
SOURCE FILE:     crowded_field_c3_approval.yaml
TABULATED FILE:  crowded_field_c3_approval_tabulated.txt
======================================================================

election_title: "Crowded field, rung 3 — 3 candidates, 65 voters, counted by Approval"

scenario_description: |-
  RUNG 1, counted by Approval — each bloc approves everyone it would have scored 4 or
  5 on the STAR ballot for this rung. Diego wins with 44 approvals of 65. Every method at
  this rung agrees.

  Same 65 voters and the same fixed candidate positions as crowded_field_c3_star.yaml;
  the approval ballot is that file's 0–5 ballot thresholded at 4 (approve everyone you
  would score 4 or 5). Change the cutoff in build_ladder.py and this file changes with it.

  Construction: build_ladder.py in this folder. 65 voters in seven blocs at 0, 4, 8, 12,
  16, 20, 24 (sizes 6, 10, 13, 9, 12, 8, 7); candidates fixed at Ana 1 · Bruno 6 ·
  Clara 9 · Diego 11 · Elsa 14 · Felix 16 · Greta 22; utility = minus distance; scores =
  each bloc's own min-max scaling onto 0–5. Nothing is tuned, and no count at any rung is
  settled by a tie-break.

voting_method: Approval
num_winners: 1

lot_numbers: [Ana, Diego, Greta]

ballots: |-
  Count:Ana,Diego,Greta
  6:1,0,0    # bloc at 0
  10:1,1,0    # bloc at 4
  13:0,1,0    # bloc at 8
  9:0,1,0    # bloc at 12
  12:0,1,1    # bloc at 16
  8:0,0,1    # bloc at 20
  7:0,0,1    # bloc at 24

expected_winners:
  - Diego

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

--- Approval Voting (single winner) ---
 Tabulating 65 ballots (any non-zero score = approval).

Ballots:
   columns = Ana, Diego, Greta      (1 = approve; 0 = not approved)
     6 × 1,0,0
    10 × 1,1,0
    22 × 0,1,0
    12 × 0,1,1
    15 × 0,0,1

   Diego -- 44 (68%) -- Elected
   Greta -- 27 (42%)
   Ana   -- 16 (25%)

[Approval Distribution] (how many candidates each ballot approved)
   87 approvals across 65 ballots — average 1.3 of 3 (range 1–2).
     approved 1: 43 ballots
     approved 2: 22 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
          | Diego  | Greta  |  Ana   |
   -----------------------------------
   Diego  |   --   |  27%   |  23%   |
   Greta  |  44%   |   --   |   0%   |
   Ana    |  62%   |   0%   |   --   |

Winner — Approval Voting (single winner)
  Diego