election_title: Weak Condorcet loser — the same five voters, on Approval ballots
scenario_description: |-
  The Approval companion to wcl_c3_b5_star.yaml. Same five voters, same
  underlying opinions, rendered onto a yes/no ballot by approving every
  candidate the voter scored 3 or higher on the 0-5 ballot:

    5,4,4 -> 1,1,1     5,4,1 -> 1,1,0     5,4,3 -> 1,1,1
    0,3,4 -> 0,1,1     0,3,4 -> 0,1,1

  Approval counts: Ben 5, Cora 4, Ada 3. Approval elects Ben — the same weak
  Condorcet loser STAR elected, and by a wide margin rather than a tiebreak.

  Two things worth separating, because they are easy to run together:

  1. WHERE THE PAIRWISE FACTS COME FROM. Ben's status as a weak Condorcet loser
     is a fact about these voters' PREFERENCES, which live on the score ballots
     (Ada beats Ben 3-2, Ada beats Cora 3-2, Ben ties Cora 2-2). It is not
     derived from the approval ballots.

  2. THE APPROVAL BALLOT CANNOT SEE IT. Run the pairwise comparison on the
     APPROVAL ballots alone and Ben beats Ada 2-0 — because three voters
     approved both, and approval records that as a tie. Coarsening 0-5 down to
     0-1 destroyed the very margins that made Ada the Condorcet winner. The
     ballot cannot represent the situation it is failing.

  That second point is the real lesson, and it is a preference-vs-support point,
  not a scoreboard point: a two-level ballot has no way to say "Ada 5, Ben 4" —
  both become "approved". So Approval does not so much CHOOSE the weak Condorcet
  loser as lose the information that would have identified one.

  The cutoff caveat applies as always: "approve everything 3 or higher" is one
  modeling choice among several, and a different threshold gives a different
  election. That is Approval's standing ambiguity, not a quirk of this case.

bv_test_id: BV2249
bv_election_id: c73pfw
bv_results_url: https://bettervoting.com/c73pfw/results
# Live on BetterVoting as BV2249 (election c73pfw) — the Approval race of a three-race
# election (STAR / Approval / Ranked Robin) on these same five voters.
# Frozen export: wcl_c3_b5_star_bv_export.json (one export covers all three races).

voting_method: Approval
num_winners: 1

ballots: |-
  Ada,Ben,Cora
  1,1,1   # scored 5,4,4 -> approves all three
  1,1,0   # scored 5,4,1 -> Cora falls below the cutoff
  1,1,1   # scored 5,4,3 -> approves all three
  0,1,1   # scored 0,3,4 -> rejects Ada
  0,1,1   # scored 0,3,4 -> rejects Ada

expected_winners:
  - Ben

# file: wcl_c3_b5_approval.yaml