election_title: "Reinforcement — South district, Cara branch (3 voters, Cara is the clear Condorcet winner)"

scenario_description: |-
  The third and last branch of the case analysis in Zwicker's proof of
  Proposition 2.5 ("all Condorcet extension SCFs for three or more alternatives
  violate reinforcement"), completing reinf_south_c3_b3_rr.yaml (Ada branch) and
  reinf_south_ben_c3_b3_rr.yaml (Ben branch).

  North (reinf_north_c3_b6_rr.yaml) is the perfectly symmetric 6-voter cycle: an
  anonymous, neutral rule can only call it a three-way tie, but a RESOLUTE engine
  must name one winner. North is invariant under the rotation Ada→Ben→Cara→Ada, so
  rotating South twice gives the branch for a North winner of Cara. Here —

      Cara beats Ben 2–1 · Cara beats Ada 3–0 · Ben beats Ada 3–0

  so Cara is the Condorcet winner and every method elects her. Cara is also a
  co-winner of North's dead heat, so reinforcement demands Cara win the merged
  9-voter election. She doesn't — BEN does (reinf_combined_cara_c3_b9_rr.yaml).

  With all three branches built, the demonstration no longer depends on which
  candidate the cycle happens to resolve to: whichever one it is, there is a South
  district that agrees with it and a merged electorate that overturns it.

paradoxes: [multiple-districts]

voting_method: RankedRobin
num_winners: 1

lot_numbers: [Ada, Ben, Cara]

ballots: |-
  2:Cara>Ben>Ada
  1:Ben>Cara>Ada

expected_winners:
  - Cara