election_title: "Best Cycle-Breaking Rule — a society votes on how to break a cycle, and cycles" scenario_description: |- Reproduced from the "Best Cycle-Breaking Rule" sample election published by RCV Lab (rcv-lab.org), converted from its downloadable cast vote record so this library counts it independently rather than quoting it. 999 ballots, five candidates — and the candidates ARE the rules for resolving a Condorcet cycle: Ranked Pairs, the Schulze Method, Minimax, Copeland's Rule, and Flip a Coin. It is synthetic, and says so: the source config is stamped "RCV Lab synthetic", dated 2026-07-30, from "The Condorcet Paradox Society". It is a built demonstration, not an election anyone held. The ballots are real data in the sense that matters here — a fixed CVR anyone can download and re-count — but nobody's actual preferences are in them. The joke is that the ballots cycle. The society convened to choose a completion rule and produced exactly the situation a completion rule exists to resolve. Companion file cycle_vote_on_the_rule_rr_c5_b999.yaml counts the same ballots as Ranked Robin and shows the cycle head-on; this file is the RCV-IRV count, and exists to prove the reproduction is faithful. WHY IT EARNS 999 BALLOTS. This library keeps examples small on purpose, and a hand-built cycle needs 21 voters, not a thousand. This one is not hand-built: it is an outside engine's published sample, and the whole point is that our count and theirs agree ballot-for-ballot. Shrinking it would forfeit that. THREE THINGS IT TEACHES: 1. A MAJORITY OF THE SURVIVORS IS NOT A MAJORITY OF THE VOTERS. Ranked Pairs wins the final round 492 to 394. That is a comfortable majority of the 886 ballots still live — and 49.2% of the 999 people who voted. 113 ballots ranked nobody still standing and stopped counting. 2. THE CYCLE IS INVISIBLE IN THE ROUNDS. Nothing in the elimination report hints that majority preference is knotted. You have to run the pairwise table (the companion RR file) to find out there is no Condorcet winner at all. An IRV report is not silent about the cycle because anything is being hidden — it simply never asks the question. 3. ROUND COUNT IS A REPORTING CHOICE, NOT A RESULT. RCV Lab reports FOUR rounds, eliminating Flip a Coin and then Copeland's Rule one at a time. This engine reports THREE, because 52 + 61 = 113 is less than Minimax's 258 and neither candidate can catch up — so it clears both in one step. Every tally that appears in both reports is identical. Two engines, two round numberings, one election. Verified against the source's own published report: first choices 315 / 313 / 258 / 61 / 52, the three-way round at 324 / 321 / 262 with 92 exhausted, and the final 492 / 394 with 113 exhausted, all match. Our independently computed pairwise matrix also reproduces theirs cell for cell. voting_method: RCV_IRV num_winners: 1 # 65 distinct rankings across 999 ballots — the full CVR, collapsed to weighted # blocs. The source data is clean: no overvotes, no skipped ranks, no equal # rankings, no blank ballots. Counts below 6 are kept as they came; the house # "Count >= 6" rule guards against collision with 0-5 SCORES, which ranked # ballots do not have. 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: - Ranked Pairs # Source: https://rcv-lab.org/sample-data/best-cycle-breaking-rule/best-cycle-breaking-rule_cvr.csv # file: cycle_vote_on_the_rule_irv_c5_b999.yaml