election_title: "A candidate nobody prefers still flips the winner — Schulze's spoiler, and Split Cycle's immunity"

scenario_description: |-
  A runnable counterexample for Holliday & Pacuit's central claim in "Split Cycle"
  (arXiv:2004.02350; Public Choice 197, 2023): that Schulze/beat-path is NOT immune
  to spoilers, and Split Cycle is. Reproduced independently — this is not the
  paper's own profile — with pref_voting, on the smallest electorate a search
  turned up. 40 hikers rank five national parks.

  Cascade beats Bryce 40-0: NOT ONE VOTER prefers Bryce to Cascade. Bryce wins
  under no method, in any field. And yet:

      Schulze WITHOUT Bryce on the ballot  ->  Cascade
      Schulze WITH    Bryce on the ballot  ->  Everglade

  Bryce's mere presence takes the win away from a park she is unanimously behind,
  and hands it to a third party. That is exactly the paper's Definition 4.1: Bryce
  spoils the election for Cascade — Cascade wins without Bryce, a majority (here,
  everyone) prefers Cascade to Bryce, and with Bryce present neither of them wins.

  Split Cycle does not do this. It returns {Cascade, Everglade} with Bryce present
  and {Cascade} without — Cascade is never dropped, so no spoiler effect occurs.
  That is the paper's "stability for winners" in action, and the reason the authors
  argue the criterion is worth the cost (Split Cycle sometimes declines to break a
  tie that Schulze and Ranked Pairs break by convention).

  Read the honest fine print on the lesson page: this is a five-candidate profile
  with no Condorcet winner and a Smith set of ALL FIVE parks — a genuinely knotted
  election, not an everyday one. Ranked Pairs happens to elect Cascade here too, so
  this profile does not exhibit its (separately proven) spoiler failure. Nothing
  here is evidence about STAR or Ranked Robin, neither of which is a C2 method.

  Verified with pref_voting, both fields:
    uv run STARVote_LH_tabulation_engine/tools_adam/pref_voting_tabulation_engine/cycle_resolution_report.py \
      method_comparisons/split_cycle/cases/split_cycle_schulze_spoiler_c5_b40.yaml
    uv run …/cycle_resolution_report.py …/split_cycle_schulze_spoiler_c5_b40.yaml --drop Bryce

  LH-only (no BetterVoting election): neither BV nor the LH engine implements
  Schulze or Split Cycle, and the LH Copeland result here is a tie. Lesson page:
  07_Concepts/topics/condorcet/split_cycle.md

paradoxes: [condorcet-cycle]

voting_method: RankedRobin
num_winners: 1

lot_numbers: [Arches, Bryce, Cascade, Denali, Everglade]

ballots: |-
  11:Everglade>Denali>Cascade>Bryce>Arches
  11:Arches>Denali>Cascade>Everglade>Bryce
  8:Everglade>Cascade>Bryce>Arches>Denali
  10:Cascade>Bryce>Arches>Denali>Everglade

expected_winners:
  - Cascade