Felsenthal Ex.6 — Ranked Robin: the Pareto-dominant Condorcet winner Aria (LH-only)¶

Generated from felsenthal_ex6_ranked_robin.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: Aria

Scenario¶

LH-only companion to felsenthal_ex6_pareto_approval.yaml (no BetterVoting election — see that file for why). Source: Dan S. Felsenthal (2010), Appendix A3, Example 6, due to Felsenthal & Maoz (1988: 123, Example 4). The same 3 voters' full rankings counted by Ranked Robin (Copeland): Aria wins every head-to-head — Beau 3–0 (every single voter prefers Aria to Beau: Pareto dominance), Cole 2–1, Dean 2–1 — the Condorcet winner, elected outright. The approval count in the companion file loses this information because the top-three approval cutoff puts Aria and Beau in the same bucket on every ballot.

Ballots¶

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

1:Aria>Beau>Cole>Dean
1:Cole>Aria>Beau>Dean
1:Dean>Aria>Beau>Cole

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 3 ballots (ranked ballots).

Ballots:
     1 × Aria > Beau > Cole > Dean
     1 × Cole > Aria > Beau > Dean
     1 × Dean > Aria > Beau > Cole

Round-Robin — every pair, head-to-head (For – Against):
   Aria  beats Beau   3 – 0
   Aria  beats Cole   2 – 1
   Aria  beats Dean   2 – 1
   Beau  beats Cole   2 – 1
   Beau  beats Dean   2 – 1
   Cole  beats Dean   2 – 1

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |   Aria    |  Beau    |  Cole    |  Dean    |
-------------------------------------------------------
  Aria > |    ---    |3 - 0 - 0 |2 - 0 - 1 |2 - 0 - 1 |
  Beau > | 0 - 0 - 3 |   ---    |2 - 0 - 1 |2 - 0 - 1 |
  Cole > | 1 - 0 - 2 |1 - 0 - 2 |   ---    |2 - 0 - 1 |
  Dean > | 1 - 0 - 2 |1 - 0 - 2 |1 - 0 - 2 |   ---    |

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  Aria       3–0–0         3      +5  Beau, Cole, Dean
    2  Beau       2–1–0         2      -1  Cole, Dean
    3  Cole       1–2–0         1      -1  Dean
    4  Dean       0–3–0         0      -3  —

Winner — Ranked Robin (RCV-RR): Aria
   beats every opponent head-to-head — the Condorcet winner.

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 (1 of 4): Aria
   Outside (3):        Beau, Cole, Dean
   One member ⇒ Aria is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Aria 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/felsenthal_paradoxes/cases/felsenthal_ex6_ranked_robin.yaml

See also¶