The whole Condorcet family splits — Minimax & Schulze pick Ava, Ranked Pairs picks Ben, on one set of ballots¶

Generated from cycle_family_splits_c5_b77.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Ranked Robin (RCV-RR / Copeland) · 1 seat · Expected winner: Ava

Official tie-break (lot) order: Ava > Ben > Cole > Dana > Ezra — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

The five-candidate profile behind the "…but they don't always agree" table in 05_Ranked_Robin/01_Learn/cycle_resolution.md. 77 members of a program committee rank five finalists, and majority preference is knotted about as badly as it can be: there is no Condorcet winner and the Smith set is ALL FIVE candidates — every finalist is in a beat-cycle with the rest.

On these identical ballots the Condorcet family gives four different answers:

Copeland (Ranked Robin)  Ava, Ben   (tie — both go 2-2; LH breaks it by margin)
Minimax                  Ava
Schulze (beat path)      Ava
Ranked Pairs             Ben
Split Cycle              Ava, Ben

Minimax and Schulze land on Ava (her worst defeat is the mildest); Ranked Pairs locks the biggest margins first and they carry Ben; Copeland can't separate the two, and Split Cycle deliberately returns both. That is the entire lesson of the cycle-resolution page in one election: "Condorcet method" names a FAMILY, and inside a cycle the family stops agreeing.

The LH engine tabulates the Copeland column (= Ranked Robin) and breaks the Ava/Ben tie by total margin, then lot. The other four rules are printed by: uv run STARVote_LH_tabulation_engine/tools_adam/pref_voting_tabulation_engine/cycle_resolution_report.py \ method_comparisons/cycle_resolution/cases/cycle_family_splits_c5_b77.yaml

LH-only (no BetterVoting election): the result is a Copeland tie, and BV breaks Copeland ties at random, so this can't be frozen on BV. Constructed by search and verified with pref_voting (it is NOT a profile from the literature — an earlier draft mis-attributed a 100-voter version to Heitzig; this replaces it with a real, reproducible one). Companion: cycle_schulze_vs_ranked_pairs_c4_b40.yaml.

Ballots¶

Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).

12:Ezra>Ava>Dana>Ben>Cole
7:Ezra>Cole>Ava>Dana>Ben
14:Ben>Ava>Ezra>Cole>Dana
8:Dana>Ben>Ava>Ezra>Cole
5:Cole>Ava>Dana>Ezra>Ben
11:Dana>Ben>Ava>Cole>Ezra
13:Ezra>Cole>Ava>Ben>Dana
7:Ben>Ava>Cole>Ezra>Dana

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 77 ballots (ranked ballots).

Ballots:
    12 × Ezra > Ava > Dana > Ben > Cole
     7 × Ezra > Cole > Ava > Dana > Ben
    14 × Ben > Ava > Ezra > Cole > Dana
     8 × Dana > Ben > Ava > Ezra > Cole
     5 × Cole > Ava > Dana > Ezra > Ben
    11 × Dana > Ben > Ava > Cole > Ezra
    13 × Ezra > Cole > Ava > Ben > Dana
     7 × Ben > Ava > Cole > Ezra > Dana

Round-Robin — every pair, head-to-head (For – Against):
   Ava   beats Ezra   45 – 32
   Ezra  beats Dana   53 – 24
   Ben   beats Ezra   40 – 37
   Ezra  beats Cole   54 – 23
   Ava   beats Dana   58 – 19
   Ben   beats Ava    40 – 37
   Ava   beats Cole   52 – 25
   Dana  beats Ben    43 – 34
   Cole  beats Dana   46 – 31
   Ben   beats Cole   52 – 25

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |     Ezra     |    Ava      |    Dana     |    Ben      |    Cole     |
---------------------------------------------------------------------------------
  Ezra > |     ---      |32 -  0 - 45 |53 -  0 - 24 |37 -  0 - 40 |54 -  0 - 23 |
   Ava > | 45 -  0 - 32 |    ---      |58 -  0 - 19 |37 -  0 - 40 |52 -  0 - 25 |
  Dana > | 24 -  0 - 53 |19 -  0 - 58 |    ---      |43 -  0 - 34 |31 -  0 - 46 |
   Ben > | 40 -  0 - 37 |40 -  0 - 37 |34 -  0 - 43 |    ---      |52 -  0 - 25 |
  Cole > | 23 -  0 - 54 |25 -  0 - 52 |46 -  0 - 31 |25 -  0 - 52 |    ---      |

Win–loss record — Copeland score = wins + ½·ties (highest score wins; ties broken by total margin, then lot order):
    #  Candidate  W–L–T  Copeland  Margin  Beats
    1  Ava        3–1–0         3     +76  Ezra, Cole, Dana
    2  Ben        3–1–0         3     +24  Ava, Ezra, Cole
    3  Ezra       2–2–0         2     +44  Cole, Dana
    4  Cole       1–3–0         1     -70  Dana
    5  Dana       1–3–0         1     -74  Ben

Winner — Ranked Robin (RCV-RR): Ava
   *** 2 candidates tie for the most wins (Ava, Ben) — tied on the tally, not a cycle (some of them beat others head-to-head, but no loop closes). Resolved by total margin, then lot order.

Full audit — preference matrix, Condorcet, and score distribution¶

--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
   Smith set (5 of 5): Ava, Ben, Ezra, Dana, Cole
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   Note: the Copeland leaders (Ava, Ben) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   Ranked Robin (RCV-RR) winner Ava is INSIDE the Smith set. ✓
      Guaranteed: Ranked Robin (Copeland) is Smith-efficient — every member of
      the set outscores every outsider, so the top of the win–loss table is
      always inside the set, however the tie among them is then broken.
   More: 07_Concepts/topics/smith_set.md

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/cycle_resolution/cases/cycle_family_splits_c5_b77.yaml

The whole Condorcet family splits — Minimax & Schulze pick Ava, Ranked Pairs picks Ben, on one set of ballots¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶