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SOURCE FILE:     bv2279_qywq7d_approval.yaml
TABULATED FILE:  bv2279_qywq7d_approval_tabulated.txt
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election_title: Three brothers, one fruit — Approval lands on the utilitarian winner

voting_method: Approval
num_winners: 1

bv_test_id: BV2279
bv_election_id: qywq7d
bv_results_url: https://bettervoting.com/qywq7d/results

scenario_description: |
  Race 3 of 3 in the three-brothers election (BV2279, bvid qywq7d; BV-confirmed).
  The setup, the source and the x5/11 rescale are documented in the STAR race,
  bv2279_qywq7d_star.yaml.

  The same three opinions as approvals: each brother approves every fruit he
  scored 3 or higher.

    boy 1  (1, 3, 4)  ->  Orange, Banana
    boy 2  (1, 4, 5)  ->  Orange, Banana
    boy 3  (2, 5, 0)  ->  Orange

  Orange 3, Banana 2, Apple 0. Approval elects ORANGE — the utilitarian winner,
  the same answer the STAR scoring round gives before the runoff overturns it.

  This race is the one that was missing from the prose version of this example.
  The story is usually told as Score-versus-everyone-else; running it turned up
  a second method on the utilitarian side, and the LH engine reports it directly
  as [Divergence from STAR] Approval = Orange.

  The reason is structural rather than a coincidence of this ballot set:
  Approval, like the scoring round, never takes a majority vote. It counts
  levels of support and stops. Every method here that finishes with a
  head-to-head — STAR's runoff, Ranked Robin's pairwise table — elects Banana.
  The two that don't elect Orange.

  DISCLOSURE, because it is an editorial choice and not arithmetic: the 3-or-
  higher threshold is this file's, not the source's. It is the same cut the LH
  engine uses to derive its Approval comparison, which is why the two agree.
  A 4-or-higher cut gives Orange 2, Banana 2 — a tie, decided by lot, and the
  lesson evaporates. Say which threshold a number came from.

video_script: |
  Third and last. The line that lands: "same three people, same three opinions,
  third piece of paper — and now Orange wins."

  Then the structural point, which is the durable one. Don't say "Approval is
  utilitarian"; say "Approval never holds a runoff." Point at the two methods
  that elect Banana and note what they have in common: both finish with a
  head-to-head. That's the whole split, in one sentence.

  Do disclose the 3+ threshold on camera. It's an honest example only if the
  audience knows a 4+ cut would have tied it.

ballots: |-
  Apple,Orange,Banana
  0,1,1   # Boy 1 — approves the two he scored 3 and 4
  0,1,1   # Boy 2 — approves the two he scored 4 and 5
  0,1,0   # Boy 3 — approves only Orange; Banana was a 0

expected_winners: [Orange]

# file: bv2279_qywq7d_approval.yaml

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TABULATION RESULTS
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--- Approval Voting (single winner) ---
 Tabulating 3 ballots (any non-zero score = approval).

Ballots:
   columns = Apple, Orange, Banana      (1 = approve; 0 = not approved)
     2 × 0,1,1
     1 × 0,1,0

   Orange -- 3 (100%) -- Elected
   Banana -- 2 (67%)
   Apple  -- 0 (0%)

[Approval Distribution] (how many candidates each ballot approved)
   5 approvals across 3 ballots — average 1.7 of 3 (range 1–2).
     approved 1: 1 ballot
     approved 2: 2 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
           | Orange | Banana | Apple  |
   ------------------------------------
   Orange  |   --   |  67%   |   0%   |
   Banana  |  100%  |   --   |   0%   |
   Apple   |   ·    |   ·    |   --   |

Winner — Approval Voting (single winner)
  Orange