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

scenario_description: |-
  A rotated companion to reinf_south_c3_b3_rr.yaml, built to complete the case
  analysis in Zwicker's proof of Proposition 2.5 ("all Condorcet extension SCFs
  for three or more alternatives violate reinforcement").

  North (reinf_north_c3_b6_rr.yaml) is the perfectly symmetric 6-voter cycle, so
  an anonymous, neutral rule can only call it a three-way tie: every candidate is
  a co-winner. But a RESOLUTE engine — like the LH tabulator, which spends
  neutrality on a published lot order — must name exactly one of them. Which one
  it names decides which South district is needed to spring the contradiction.

  North is invariant under the rotation Ada→Ben→Cara→Ada, so rotating the
  original South gives the branch for each possible North winner. This file is the
  BEN branch: Ben beats both rivals head-to-head here —

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

  so every method elects Ben. Ben is also a co-winner of North's dead heat, so
  reinforcement demands Ben win the merged 9-voter election. He doesn't — ADA does
  (see reinf_combined_ben_c3_b9_rr.yaml). The contradiction fires no matter which
  way the cycle is resolved; that is the whole content of the proposition.

  Branch companions: reinf_south_c3_b3_rr.yaml (Ada branch → combined elects Cara),
  reinf_south_cara_c3_b3_rr.yaml (Cara branch → combined elects Ben).

paradoxes: [multiple-districts]

voting_method: RankedRobin
num_winners: 1

lot_numbers: [Ada, Ben, Cara]

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

expected_winners:
  - Ben