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SOURCE FILE:     bv2154_wq6yv7_ranked_robin.yaml
TABULATED FILE:  bv2154_wq6yv7_ranked_robin_tabulated.txt
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election_title: "Felsenthal Ex.8 — Ranked Robin: the Condorcet winner Bruce"
scenario_description: |-
  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
bv_test_id: BV2154
bv_election_id: wq6yv7
bv_results_url: https://bettervoting.com/wq6yv7/results
paradoxes: [condorcet-loser, absolute-loser]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  6:April>Bruce>Clara
  4:Bruce>Clara>April
  1:Clara>April>Bruce
  4:Clara>Bruce>April
expected_winners:
  - Bruce

# file: bv2154_wq6yv7_ranked_robin.yaml

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TABULATION RESULTS
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--- 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.

--- 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