Felsenthal Ex.2 — Ranked Robin: the Condorcet winner survives¶

Generated from bv2145_6fj2kg_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: Ada

▶ Live on BetterVoting: vote · results ↗ (election 6fj2kg · test BV2145).

Scenario¶

Race 2 of 3 in the Felsenthal runoff-paradoxes election, part 1 of 2 (BV2145, bvid 6fj2kg; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 2 — see bv2145_6fj2kg_irv.yaml for the full citation and setup. The same 17 ranked ballots counted by Ranked Robin (Copeland): Ada wins both her head-to-heads (Ben 9–8, Cleo 9–8) — 2 pairwise wins, the Condorcet winner, elected directly. What the runoff procedure's elimination order threw away, the round-robin count keeps. Live results: https://bettervoting.com/6fj2kg/results

Ballots¶

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

3:Ada>Ben>Cleo
2:Ada>Cleo>Ben
4:Ben>Ada>Cleo
2:Ben>Cleo>Ada
4:Cleo>Ada>Ben
2:Cleo>Ben>Ada

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 17 ballots (ranked ballots).

Ballots:
     3 × Ada > Ben > Cleo
     2 × Ada > Cleo > Ben
     4 × Ben > Ada > Cleo
     2 × Ben > Cleo > Ada
     4 × Cleo > Ada > Ben
     2 × Cleo > Ben > Ada

Round-Robin — every pair, head-to-head (For – Against):
   Ada   beats Ben    9 – 8
   Ada   beats Cleo   9 – 8
   Ben   beats Cleo   9 – 8

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |    Ada    |   Ben    |  Cleo    |
--------------------------------------------
   Ada > |    ---    |9 - 0 - 8 |9 - 0 - 8 |
   Ben > | 8 - 0 - 9 |   ---    |9 - 0 - 8 |
  Cleo > | 8 - 0 - 9 |8 - 0 - 9 |   ---    |

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  Ada        2–0–0         2      +2  Ben, Cleo
    2  Ben        1–1–0         1      +0  Cleo
    3  Cleo       0–2–0         0      -2  —

Winner — Ranked Robin (RCV-RR): Ada
   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 3): Ada
   Outside (2):        Ben, Cleo
   One member ⇒ Ada is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Ada 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/bv2145_6fj2kg_ranked_robin.yaml

See also¶