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SOURCE FILE:     bv2152_r6ctvy_ranked_robin.yaml
TABULATED FILE:  bv2152_r6ctvy_ranked_robin_tabulated.txt
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election_title: "Felsenthal Ex.5 — Ranked Robin: the Condorcet winner Bert"
scenario_description: |-
  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
bv_test_id: BV2152
bv_election_id: r6ctvy
bv_results_url: https://bettervoting.com/r6ctvy/results
paradoxes: [condorcet-winner]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  18:Anna>Bert>Carla
  6:Bert>Carla>Anna
  8:Bert>Anna>Carla
  2:Carla>Anna>Bert
  13:Carla>Bert>Anna
expected_winners:
  - Bert

# file: bv2152_r6ctvy_ranked_robin.yaml

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TABULATION RESULTS
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--- 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.

--- 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