Exercise 9 — Game night: nobody is unbeatable (a Ranked Robin ladder drill)¶

Generated from ex09_game_night_cycle.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: Azul

Official tie-break (lot) order: Azul > Boggle > Catan > Dominion — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

Ten friends rank four board games. Azul beats Boggle 7-3, Boggle beats Catan 7-3, Catan beats Azul 6-4 — a rock-paper-scissors cycle, so there is NO Condorcet winner — and everything beats Dominion 10-0. Ranked Robin walks its ladder: most pairwise wins first (Azul, Boggle, and Catan all tie at 2-1), then TOTAL WIN MARGIN: Azul +12, Boggle +10, Catan +8 — Azul wins, deterministically, no lot needed. This is an LH-only exercise on purpose: BetterVoting resolves a 3-way wins tie at RANDOM (the BV2142 caveat), so a frozen BV result cannot exist. Exercise: ex09_game_night_cycle.md. Ballots and cast are this repo's own.

Ballots¶

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

Azul>Boggle>Catan>Dominion
Azul>Boggle>Catan>Dominion
Azul>Boggle>Catan>Dominion
Azul>Boggle>Catan>Dominion
Boggle>Catan>Azul>Dominion
Boggle>Catan>Azul>Dominion
Boggle>Catan>Azul>Dominion
Catan>Azul>Boggle>Dominion
Catan>Azul>Boggle>Dominion
Catan>Azul>Boggle>Dominion

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 10 ballots (ranked ballots).

Ballots:
     4 × Azul > Boggle > Catan > Dominion
     3 × Boggle > Catan > Azul > Dominion
     3 × Catan > Azul > Boggle > Dominion

Round-Robin — every pair, head-to-head (For – Against):
   Azul      beats Boggle      7 –  3
   Catan     beats Azul        6 –  4
   Azul      beats Dominion   10 –  0
   Boggle    beats Catan       7 –  3
   Boggle    beats Dominion   10 –  0
   Catan     beats Dominion   10 –  0

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
             |     Azul     |   Boggle    |   Catan     |  Dominion   |
-----------------------------------------------------------------------
      Azul > |     ---      | 7 -  0 -  3 | 4 -  0 -  6 |10 -  0 -  0 |
    Boggle > |  3 -  0 -  7 |    ---      | 7 -  0 -  3 |10 -  0 -  0 |
     Catan > |  6 -  0 -  4 | 3 -  0 -  7 |    ---      |10 -  0 -  0 |
  Dominion > |  0 -  0 - 10 | 0 -  0 - 10 | 0 -  0 - 10 |    ---      |

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  Azul       2–1–0         2     +12  Boggle, Dominion
    2  Boggle     2–1–0         2     +10  Catan, Dominion
    3  Catan      2–1–0         2      +8  Azul, Dominion
    4  Dominion   0–3–0         0     -30  —

Winner — Ranked Robin (RCV-RR): Azul
   *** 3 candidates tie for the most wins (Azul, Boggle, Catan) — a Condorcet cycle (no candidate beats all others). Resolved by total margin, then lot order. (This is where Minimax / Ranked Pairs / Schulze differ — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.)

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 (3 of 4): Azul, Boggle, Catan
   Outside (1):        Dominion
   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.
   Ranked Robin (RCV-RR) winner Azul 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 01_STAR/05_Practice/cases/ex09_game_night_cycle.yaml

Exercise 9 — Game night: nobody is unbeatable (a Ranked Robin ladder drill)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶