Felsenthal Ex.5 — Ranked Robin: the Condorcet winner Bert¶

Generated from bv2152_r6ctvy_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: Bert

▶ Live on BetterVoting: vote · results ↗ (election r6ctvy · test BV2152).

Scenario¶

Race 2 of 2 in the Felsenthal & Maoz Approval-paradox election (BV2152, bvid r6ctvy; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A3, Example 5, due to Felsenthal & Maoz (1988: 123, Example 2) — see bv2152_r6ctvy_approval.yaml for the setup. The same 47 voters' full rankings counted by Ranked Robin (Copeland): Bert wins both head-to-heads (Anna 27–20, Carla 32–15) — the Condorcet winner, elected directly. The approval race loses him because 18 Anna-only and 13 Carla-only voters draw their approval line above Bert even while ranking him second. Live results: https://bettervoting.com/r6ctvy/results

Ballots¶

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

18:Anna>Bert>Carla
6:Bert>Carla>Anna
8:Bert>Anna>Carla
2:Carla>Anna>Bert
13:Carla>Bert>Anna

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 47 ballots (ranked ballots).

Ballots:
    18 × Anna > Bert > Carla
     6 × Bert > Carla > Anna
     8 × Bert > Anna > Carla
     2 × Carla > Anna > Bert
    13 × Carla > Bert > Anna

Round-Robin — every pair, head-to-head (For – Against):
   Bert   beats Anna    27 – 20
   Anna   beats Carla   26 – 21
   Bert   beats Carla   32 – 15

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
          |     Anna     |    Bert     |   Carla     |
------------------------------------------------------
   Anna > |     ---      |20 -  0 - 27 |26 -  0 - 21 |
   Bert > | 27 -  0 - 20 |    ---      |32 -  0 - 15 |
  Carla > | 21 -  0 - 26 |15 -  0 - 32 |    ---      |

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  Bert       2–0–0         2     +24  Anna, Carla
    2  Anna       1–1–0         1      -2  Carla
    3  Carla      0–2–0         0     -22  —

Winner — Ranked Robin (RCV-RR): Bert
   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): Bert
   Outside (2):        Anna, Carla
   One member ⇒ Bert is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Bert 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/bv2152_r6ctvy_ranked_robin.yaml

See also¶