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SOURCE FILE:     bv2146_krk2px_ranked_robin.yaml
TABULATED FILE:  bv2146_krk2px_ranked_robin_tabulated.txt
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election_title: "Felsenthal Ex.2 after the raise — Ranked Robin: unmoved, still Ada"
scenario_description: |-
  Race 2 of 3 in the Felsenthal runoff-paradoxes election, part 2 of 2 (BV2146, bvid krk2px; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 2 (continued) — see bv2146_krk2px_irv.yaml for the setup.
  The raise (2× Cleo>Ben>Ada → Ben>Cleo>Ada) only swaps Ben and Cleo on those ballots; Ada's position against each rival is untouched, so the pairwise table barely moves: Ada still beats Ben 9–8 and Cleo 9–8 and stays the Condorcet winner. Ranked Robin elects Ada before and after — monotone where the runoff procedure (the IRV race) flips.
  Live results: https://bettervoting.com/krk2px/results
bv_test_id: BV2146
bv_election_id: krk2px
bv_results_url: https://bettervoting.com/krk2px/results
paradoxes: [non-monotonicity]
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:Ben>Cleo>Ada
expected_winners:
  - Ada

# file: bv2146_krk2px_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
     4 × Ben > Cleo > Ada
     4 × Cleo > Ada > Ben

Round-Robin — every pair, head-to-head (For – Against):
   Ada   beats Ben     9 –  8
   Ada   beats Cleo    9 –  8
   Ben   beats Cleo   11 –  6

--- 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 |    ---      |11 -  0 -  6 |
  Cleo > |  8 -  0 -  9 | 6 -  0 - 11 |    ---      |

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      +4  Cleo
    3  Cleo       0–2–0         0      -6  —

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