======================================================================
SOURCE FILE:     resign_av_holds_c7_b5.yaml
TABULATED FILE:  resign_av_holds_c7_b5_tabulated.txt
======================================================================

election_title: Resignation monotonicity — plain Approval, before the resignation
voting_method: Approval_Multi_Winner
num_winners: 5
scenario_description: |-
  Example 3.3 of Oh & Peters (arXiv:2608.06156), counted by plain multi-winner
  Approval — the ONE rule the paper proves is resignation monotone.

  Five voters, five seats, seven candidates. Two voters share Kai and split on a
  second name (Lena, Milo); the other three all approve the same slate of four
  (Nora, Omar, Pia, Quinn).

  Approval seats the four-strong slate plus Kai. Under PAV, seq-Phragmén and the
  Method of Equal Shares the answer is the SAME committee — and that is what makes
  this example sharp: the proportional rules cannot keep it together after Kai
  resigns, and Approval can. The after half is
  `resign_av_holds_after_kai_c6_b5.yaml`.
ballots: |-
  Kai,Lena,Milo,Nora,Omar,Pia,Quinn
  1,1,0,0,0,0,0     # Kai + Lena
  1,0,1,0,0,0,0     # Kai + Milo
  0,0,0,1,1,1,1     # the slate
  0,0,0,1,1,1,1     # the slate
  0,0,0,1,1,1,1     # the slate
expected_winners: [Kai, Nora, Omar, Pia, Quinn]

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

--- Approval Voting (5 winners) ---
 Tabulating 5 ballots (any non-zero score = approval).

Ballots:
   columns = Kai, Lena, Milo, Nora, Omar, Pia, Quinn      (1 = approve; 0 = not approved)
     1 × 1,1,0,0,0,0,0
     1 × 1,0,1,0,0,0,0
     3 × 0,0,0,1,1,1,1

   Nora  -- 3 (60%) -- Elected
   Omar  -- 3 (60%) -- Elected
   Pia   -- 3 (60%) -- Elected
   Quinn -- 3 (60%) -- Elected
   Kai   -- 2 (40%) -- Elected
   Lena  -- 1 (20%)
   Milo  -- 1 (20%)

[Approval Distribution] (how many candidates each ballot approved)
   16 approvals across 5 ballots — average 3.2 of 7 (range 2–4).
     approved 2: 2 ballots
     approved 4: 3 ballots

[Co-Approval Matrix]
 Of the voters who approved the ROW candidate, the % who ALSO approved the COLUMN candidate.
          |  Nora  |  Omar  |  Pia   | Quinn  |  Kai   |  Lena  |  Milo  |
   -----------------------------------------------------------------------
   Nora   |   --   |  100%  |  100%  |  100%  |   0%   |   0%   |   0%   |
   Omar   |  100%  |   --   |  100%  |  100%  |   0%   |   0%   |   0%   |
   Pia    |  100%  |  100%  |   --   |  100%  |   0%   |   0%   |   0%   |
   Quinn  |  100%  |  100%  |  100%  |   --   |   0%   |   0%   |   0%   |
   Kai    |   0%   |   0%   |   0%   |   0%   |   --   |  50%   |  50%   |
   Lena   |   0%   |   0%   |   0%   |   0%   |  100%  |   --   |   0%   |
   Milo   |   0%   |   0%   |   0%   |   0%   |  100%  |   0%   |   --   |

Winners — Approval Voting (5 winners)
  Nora, Omar, Pia, Quinn, Kai