election_title: "Best Cycle-Breaking Rule — the cycle itself, and who each rule crowns"

scenario_description: |-
  The same 999 ballots as cycle_vote_on_the_rule_irv_c5_b999.yaml, counted as
  Ranked Robin so the pairwise table is on screen. Reproduced from the "Best
  Cycle-Breaking Rule" sample election published by RCV Lab (rcv-lab.org),
  converted from its downloadable cast vote record. Synthetic — the source
  config is stamped "RCV Lab synthetic", from "The Condorcet Paradox Society" —
  and built to make exactly this point.

  The candidates are the cycle-breaking rules themselves, and the ballots cycle:

      Ranked Pairs   beats  Schulze Method   492-394   (margin  98)
      Schulze Method beats  Minimax          542-341   (margin 201)
      Minimax        beats  Ranked Pairs     466-413   (margin  53)

  No Condorcet winner. Smith set = those same three. Copeland's Rule and Flip a
  Coin lose to all three and to nobody but each other.

  SO WHICH RULE WINS THE VOTE ABOUT RULES? Run the whole family and the answer
  is less chaotic than the setup promises, which is the actual lesson:

      Copeland (= Ranked Robin)   Minimax, Ranked Pairs, Schulze  (3-way tie)
      Minimax                     Ranked Pairs
      Ranked Pairs                Ranked Pairs
      Schulze (beat path)         Ranked Pairs
      Split Cycle                 Ranked Pairs
      Stable Voting               Ranked Pairs
      RCV-IRV                     Ranked Pairs

  Every refined rule elects RANKED PAIRS, including Schulze and Minimax — each
  voting for a rival over itself. The lone rule that cannot decide is
  COPELAND'S RULE, which counts wins and losses only: all three cycle members
  go 3-1, so it returns a three-way tie. It is also the candidate that finished
  fourth, on 61 first choices.

  AND THAT IS WHERE THIS ENGINE PARTS COMPANY. LH's Ranked Robin IS Copeland,
  so it hits that same three-way tie and breaks it by TOTAL MARGIN — where
  Schulze Method leads on +1327 to Ranked Pairs' +1264. So the report below
  elects SCHULZE METHOD while every margin-reading rule above elects Ranked
  Pairs. Not a bug in either: Copeland-plus-a-tiebreak is a different rule from
  Minimax or Ranked Pairs, and a cycle is precisely where different rules are
  allowed to differ. It is the cleanest demonstration in this folder of why the
  refined rules were invented at all.

  The tiebreak here is decided by margin, not by lot — the three totals are far
  apart — so the result is reproducible from the file. lot_numbers is published
  anyway, per house practice.

voting_method: RankedRobin
num_winners: 1

lot_numbers: [Ranked Pairs, Schulze Method, Minimax, Copeland's Rule, Flip a Coin]

# The full 999-ballot CVR collapsed to 65 weighted blocs — identical to the
# companion IRV file. Clean data: no overvotes, skipped ranks, or equal
# rankings.
ballots: |-
  82:Ranked Pairs>Schulze Method
  70:Schulze Method>Minimax
  65:Minimax>Ranked Pairs
  56:Ranked Pairs>Schulze Method>Minimax>Copeland's Rule
  49:Schulze Method>Minimax>Ranked Pairs>Copeland's Rule
  45:Schulze Method>Minimax>Ranked Pairs
  44:Copeland's Rule>Flip a Coin
  44:Minimax>Ranked Pairs>Schulze Method>Copeland's Rule
  42:Ranked Pairs>Schulze Method>Minimax
  41:Flip a Coin>Copeland's Rule
  39:Schulze Method>Ranked Pairs
  34:Ranked Pairs>Minimax
  30:Minimax>Schulze Method>Ranked Pairs>Copeland's Rule
  27:Minimax>Ranked Pairs>Schulze Method
  23:Schulze Method>Ranked Pairs>Minimax>Copeland's Rule
  21:Minimax>Schulze Method
  20:Ranked Pairs>Minimax>Schulze Method
  19:Schulze Method
  18:Ranked Pairs>Minimax>Schulze Method>Copeland's Rule
  18:Schulze Method>Ranked Pairs>Minimax
  16:Minimax>Schulze Method>Ranked Pairs
  16:Ranked Pairs
  14:Minimax
  12:Ranked Pairs>Schulze Method>Copeland's Rule>Minimax
  12:Schulze Method>Minimax>Copeland's Rule>Ranked Pairs
  11:Minimax>Ranked Pairs>Copeland's Rule>Schulze Method
  11:Ranked Pairs>Schulze Method>Minimax>Copeland's Rule>Flip a Coin
  9:Minimax>Ranked Pairs>Schulze Method>Copeland's Rule>Flip a Coin
  9:Schulze Method>Minimax>Copeland's Rule
  9:Schulze Method>Minimax>Ranked Pairs>Copeland's Rule>Flip a Coin
  8:Ranked Pairs>Schulze Method>Copeland's Rule
  7:Minimax>Ranked Pairs>Copeland's Rule
  6:Schulze Method>Ranked Pairs>Minimax>Copeland's Rule>Flip a Coin
  5:Minimax>Schulze Method>Ranked Pairs>Copeland's Rule>Flip a Coin
  5:Ranked Pairs>Minimax>Schulze Method>Copeland's Rule>Flip a Coin
  4:Copeland's Rule
  4:Flip a Coin>Copeland's Rule>Ranked Pairs
  4:Ranked Pairs>Copeland's Rule>Schulze Method
  4:Schulze Method>Copeland's Rule>Minimax>Ranked Pairs
  3:Copeland's Rule>Flip a Coin>Ranked Pairs
  3:Copeland's Rule>Flip a Coin>Schulze Method
  3:Flip a Coin
  3:Minimax>Copeland's Rule
  3:Schulze Method>Copeland's Rule
  2:Copeland's Rule>Schulze Method>Minimax>Ranked Pairs
  2:Flip a Coin>Copeland's Rule>Minimax
  2:Flip a Coin>Copeland's Rule>Schulze Method
  2:Minimax>Copeland's Rule>Ranked Pairs>Schulze Method
  2:Minimax>Ranked Pairs>Copeland's Rule>Schulze Method>Flip a Coin
  2:Ranked Pairs>Copeland's Rule>Schulze Method>Minimax
  2:Ranked Pairs>Schulze Method>Copeland's Rule>Minimax>Flip a Coin
  2:Schulze Method>Copeland's Rule>Minimax
  2:Schulze Method>Minimax>Copeland's Rule>Ranked Pairs>Flip a Coin
  2:Schulze Method>Ranked Pairs>Copeland's Rule
  1:Copeland's Rule>Flip a Coin>Minimax
  1:Copeland's Rule>Minimax
  1:Copeland's Rule>Ranked Pairs>Schulze Method
  1:Copeland's Rule>Ranked Pairs>Schulze Method>Minimax
  1:Copeland's Rule>Schulze Method
  1:Minimax>Copeland's Rule>Ranked Pairs>Schulze Method>Flip a Coin
  1:Minimax>Schulze Method>Copeland's Rule
  1:Ranked Pairs>Copeland's Rule
  1:Ranked Pairs>Minimax>Copeland's Rule
  1:Ranked Pairs>Minimax>Copeland's Rule>Schulze Method>Flip a Coin
  1:Schulze Method>Ranked Pairs>Copeland's Rule>Minimax

expected_winners:
  - Schulze Method

# Source: https://rcv-lab.org/sample-data/best-cycle-breaking-rule/best-cycle-breaking-rule_cvr.csv
# file: cycle_vote_on_the_rule_rr_c5_b999.yaml