======================================================================
SOURCE FILE:     ex13_opinions.yaml
TABULATED FILE:  ex13_opinions_tabulated.txt
======================================================================

election_title: "Exercise 13 — Where do you draw the line? The honest opinions (STAR)"
bv_test_id: BV2200
bv_election_id: qdtqf2
bv_results_url: https://bettervoting.com/qdtqf2/results

scenario_description: |-
  The reference election for the approval-threshold exercise: nine voters'
  honest 0-5 opinions about Ash, Beck, and Cora — 3×(Ash 5, Beck 4),
  2×(Beck 5, Cora 3), 4×(Cora 5, Ash 3). On the full scores, STAR
  advances Ash (27) and Cora (26) and Cora wins the runoff 6-3; plain
  Score voting would say Ash. The exercise then converts these SAME
  opinions to Approval ballots under three defensible thresholds — and
  gets three different Approval winners: approve 3+ elects Ash (7 of 9),
  approve 4+ elects Beck (5), approve only 5s elects Cora (4). The
  instructions, not the opinions, pick the winner. Companion files:
  ex13_approve3.yaml / ex13_approve4.yaml / ex13_bullet.yaml. Exercise:
  ex13_draw_the_line.md. Ballots and cast are this repo's own.
  Live on BetterVoting (Test ID BV2200): https://bettervoting.com/qdtqf2/results
  — one election, four races (STAR + the three approval thresholds); BV
  agrees on all four winners.
voting_method: STAR
num_winners: 1
ballots: |-
  Ash,Beck,Cora
  5,4,0 # 3 voters: Ash first, Beck a strong second
  5,4,0
  5,4,0
  0,5,3 # 2 voters: Beck first, Cora mild
  0,5,3
  3,0,5 # 4 voters: Cora first, Ash tolerable
  3,0,5
  3,0,5
  3,0,5
expected_winners:
  - Cora

# file: ex13_opinions.yaml

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

=== Exercise 13 — Where do you draw the line? The honest opinions (STAR) ===
  The reference election for the approval-threshold exercise: nine voters'
  honest 0-5 opinions about Ash, Beck, and Cora — 3×(Ash 5, Beck 4),
  2×(Beck 5, Cora 3), 4×(Cora 5, Ash 3). On the full scores, STAR
  advances Ash (27) and Cora (26) and Cora wins the runoff 6-3; plain
  Score voting would say Ash. The exercise then converts these SAME
  opinions to Approval ballots under three defensible thresholds — and
  gets three different Approval winners: approve 3+ elects Ash (7 of 9),
  approve 4+ elects Beck (5), approve only 5s elects Cora (4). The
  instructions, not the opinions, pick the winner. Companion files:
  ex13_approve3.yaml / ex13_approve4.yaml / ex13_bullet.yaml. Exercise:
  ex13_draw_the_line.md. Ballots and cast are this repo's own.
  Live on BetterVoting (Test ID BV2200): https://bettervoting.com/qdtqf2/results
  — one election, four races (STAR + the three approval thresholds); BV
  agrees on all four winners.

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
               |   * Ash    |    Beck   |  * Cora   |
-----------------------------------------------------
       * Ash > |    ---     |7 - 0 - 2  |3 - 0 - 6  |
        Beck > | 2 - 0 - 7  |   ---     |5 - 0 - 4  |
      * Cora > | 6 - 0 - 3  |4 - 0 - 5  |   ---     |

[Condorcet Winner]
  No Condorcet winner (majority cycle: Ash > Beck > Cora > Ash)

[Divergence from STAR]
  STAR     = Cora
  Approval = Ash   (differs from STAR)
  RCV-RR   = Ash   (differs from STAR)
  Full round-by-round reports (generated for review):
  RCV-RR round-robin: cases_tabulated/ex13_opinions_RCV-RR_tabulated.txt

[Runoff Reversal]
 - Score Round Winner(s) = (Ash)
 - Runoff Round Winner   = (Cora)
  Candidate Ash earned the highest total score, but
  Candidate Cora won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).


--- STAR Voting Method (single winner) ---
[STAR Voting]
 Tabulating 9 ballots.
Count × Ash,Beck,Cora
    4 ×   3,   0,   5
    3 ×   5,   4,   0
    2 ×   0,   5,   3

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Ash        3  0  4  0  0  2  |    27   3.0
Beck       2  3  0  0  0  4  |    22   2.4
Cora       4  0  2  0  0  3  |    26   2.9

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Ash           -- 27 -- First place
   Cora          -- 26 -- Second place
   Beck          -- 22
 Ash and Cora advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Cora          -- 6 -- First place
   Ash           -- 3
   Equal Support -- 0
 Cora wins.
   Runoff math:
     9  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     9  voters with a preference  (majority = 5)
           Cora 6 (67%)  ·  Ash 3 (33%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Cora