election_title: Three brothers, one fruit — the majoritarian winner is not the utilitarian one

voting_method: STAR
num_winners: 1

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

scenario_description: |
  Race 1 of 3 in the three-brothers election (BV2279, bvid qywq7d; BV-confirmed).
  Live results: https://bettervoting.com/qywq7d/results
  Companion races: bv2279_qywq7d_ranked_robin.yaml (also elects Banana) and
  bv2279_qywq7d_approval.yaml (elects Orange).

  The smallest election in which the two deepest ideals of a "good winner"
  name different candidates.

  The construction is Warren Smith's "three brothers split one fruit"
  (rangevoting.org), quoted for years in this repo as a prose table of
  happiness numbers on an arbitrary 0-11 scale. This file is that table
  made runnable: the utilities are rescaled x5/11 onto a real 0-5 STAR
  ballot, which preserves every relation the example turns on — the
  ordering of the totals, and every head-to-head.

    original utility   Apple  Orange  Banana        this ballot   Apple  Orange  Banana
    boy 1                  2       7       8        boy 1             1       3       4
    boy 2                  3       9      10        boy 2             1       4       5
    boy 3                  4      11       0        boy 3             2       5       0
    average                3       9       6        total             4      12       9

  Two answers, both defensible:

  UTILITARIAN — Orange maximizes total satisfaction (12 points to
  Banana's 9). Banana is the favorite of two brothers but is worth
  literally nothing to the third, and that zero is the whole story.
  Orange is everyone's good-enough fruit.

  MAJORITARIAN — Banana is the Condorcet winner. It beats Orange 2-1
  head-to-head and Apple 2-1, so it wins every one-on-one matchup. A
  majority prefers it, and majority preference does not care that boy 3's
  loss is far larger than boys 1 and 2's gain.

  What the engine shows is which ideal each stage of STAR is chasing.
  The SCORING ROUND is a utilitarian count and Orange leads it. The
  AUTOMATIC RUNOFF is a majoritarian check and it overturns that result:
  Banana 2, Orange 1. STAR elects Banana.

  So this is a case where STAR does NOT elect the utilitarian winner —
  by design. The runoff exists precisely to make the score leader survive
  a majority vote, and here it doesn't. Score voting and Approval elect
  Orange; STAR, Ranked Robin, IRV and Plurality all elect Banana. Only
  the two methods that never take a majority vote reach the utilitarian
  answer.

  Apple is the Condorcet LOSER and finishes last everywhere. It is in the
  file to keep the pairwise matrix from being a two-candidate echo of the
  runoff — with only Orange and Banana there is no "beats everyone"
  ideal to distinguish, because head-to-head and majority rule coincide.

  Neither winner is wrong. They optimize different things, which is the
  point of the page this case backs.

video_script: |
  Read the scoring round out loud first — Orange 12, Banana 9 — and say
  "Orange makes everyone happiest." Then the runoff line, and say "and a
  majority still prefers Banana." That pause is the lesson: STAR shows
  you both answers and tells you which one it acted on. Ranked methods
  can only ever compute the second, because the ballot never recorded
  boy 3's zero.

  Don't sell this as a STAR win. It's an honest limit — the utilitarian
  optimum is on screen and STAR walks past it. The sales point is that
  you can SEE it walk past.

ballots: |-
  Apple,Orange,Banana
  1,3,4   # Boy 1 — banana by a nose, orange close behind
  1,4,5   # Boy 2 — banana best, orange nearly as good
  2,5,0   # Boy 3 — orange is everything, banana is worthless

expected_winners: [Banana]

# file: bv2279_qywq7d_star.yaml