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SOURCE FILE:     bv2145_6fj2kg_ranked_robin.yaml
TABULATED FILE:  bv2145_6fj2kg_ranked_robin_tabulated.txt
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election_title: "Felsenthal Ex.2 — Ranked Robin: the Condorcet winner survives"
scenario_description: |-
  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
bv_test_id: BV2145
bv_election_id: 6fj2kg
bv_results_url: https://bettervoting.com/6fj2kg/results
paradoxes: [condorcet-winner]
voting_method: RankedRobin
num_winners: 1
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
expected_winners:
  - Ada

# file: bv2145_6fj2kg_ranked_robin.yaml

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TABULATION RESULTS
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--- 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.

--- 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