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SOURCE FILE:     bv2162_4htk44_ranked_robin.yaml
TABULATED FILE:  bv2162_4htk44_ranked_robin_tabulated.txt
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election_title: "Nurmi Ex.16 sincere — Ranked Robin: the Condorcet winner B"
scenario_description: |-
  Race 3 of 3 in the RCV-IRV truncation pair, part 1 of 2 (BV2162, bvid 4htk44; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A6, Example 16, due to Nurmi (1999: 63) — see bv2162_4htk44_star.yaml for the setup.
  The same 103 full rankings counted by Ranked Robin (Copeland): B wins every head-to-head (A 70–33, C 62–41, D 86–17) — the Condorcet winner, elected directly, agreeing with STAR and disagreeing with the IRV race's A.
  Live results: https://bettervoting.com/4htk44/results
bv_test_id: BV2162
bv_election_id: 4htk44
bv_results_url: https://bettervoting.com/4htk44/results
paradoxes: [condorcet-winner]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  33:A>B>C>D
  29:B>A>C>D
  24:C>B>A>D
  17:D>C>B>A
expected_winners:
  - B

# file: bv2162_4htk44_ranked_robin.yaml

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TABULATION RESULTS
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--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 103 ballots (ranked ballots).

Ballots:
    33 × A > B > C > D
    29 × B > A > C > D
    24 × C > B > A > D
    17 × D > C > B > A

Round-Robin — every pair, head-to-head (For – Against):
   B  beats A   70 – 33
   A  beats C   62 – 41
   A  beats D   86 – 17
   B  beats C   62 – 41
   B  beats D   86 – 17
   C  beats D   86 – 17

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
      |      A       |     B       |     C       |     D       |
----------------------------------------------------------------
  A > |     ---      |33 -  0 - 70 |62 -  0 - 41 |86 -  0 - 17 |
  B > | 70 -  0 - 33 |    ---      |62 -  0 - 41 |86 -  0 - 17 |
  C > | 41 -  0 - 62 |41 -  0 - 62 |    ---      |86 -  0 - 17 |
  D > | 17 -  0 - 86 |17 -  0 - 86 |17 -  0 - 86 |    ---      |

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  B          3–0–0         3    +127  A, C, D
    2  A          2–1–0         2     +53  C, D
    3  C          1–2–0         1     +27  D
    4  D          0–3–0         0    -207  —

Winner — Ranked Robin (RCV-RR): B
   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 4): B
   Outside (3):        A, C, D
   One member ⇒ B is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner B 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