Felsenthal Ex.8 — Ranked Robin: the Condorcet winner Bruce¶

Generated from bv2154_wq6yv7_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: Bruce

▶ Live on BetterVoting: vote · results ↗ (election wq6yv7 · test BV2154).

Scenario¶

Race 3 of 3 in the three-winners election (BV2154, bvid wq6yv7; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A3, Example 8 — see bv2154_wq6yv7_approval.yaml for the setup. The same 15 voters' full rankings counted by Ranked Robin (Copeland): Bruce wins both head-to-heads (April 8–7, Clara 10–5) — the Condorcet winner, elected. The three races of this election return three different winners (Approval → April, IRV → Clara, Ranked Robin → Bruce): the tabulation, not the ballot, decides. Live results: https://bettervoting.com/wq6yv7/results

Ballots¶

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

6:April>Bruce>Clara
4:Bruce>Clara>April
1:Clara>April>Bruce
4:Clara>Bruce>April

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 15 ballots (ranked ballots).

Ballots:
     6 × April > Bruce > Clara
     4 × Bruce > Clara > April
     1 × Clara > April > Bruce
     4 × Clara > Bruce > April

Round-Robin — every pair, head-to-head (For – Against):
   Bruce  beats April    8 –  7
   Clara  beats April    9 –  6
   Bruce  beats Clara   10 –  5

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
          |    April     |   Bruce     |   Clara     |
------------------------------------------------------
  April > |     ---      | 7 -  0 -  8 | 6 -  0 -  9 |
  Bruce > |  8 -  0 -  7 |    ---      |10 -  0 -  5 |
  Clara > |  9 -  0 -  6 | 5 -  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  Bruce      2–0–0         2      +6  Clara, April
    2  Clara      1–1–0         1      -2  April
    3  April      0–2–0         0      -4  —

Winner — Ranked Robin (RCV-RR): Bruce
   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): Bruce
   Outside (2):        April, Clara
   One member ⇒ Bruce is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Bruce 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/bv2154_wq6yv7_ranked_robin.yaml

See also¶