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SOURCE FILE:     bv2164_xbqq8t_ranked_robin.yaml
TABULATED FILE:  bv2164_xbqq8t_ranked_robin_tabulated.txt
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election_title: "Coombs Ex.17 — Ranked Robin: the Condorcet winner Arlo"
scenario_description: |-
  Race 3 of 3 in the Coombs Condorcet-failure election (BV2164, bvid xbqq8t; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A7, Example 17 — see bv2164_xbqq8t_star.yaml for the setup.
  The same 33 rankings counted by Ranked Robin (Copeland): Arlo wins every head-to-head (Bree 19–14, Cole 17–16, Dana 17–16) — the Condorcet winner, elected directly. The irony this case teaches: Coombs deletes candidates for being ranked LAST by many, and Arlo — everyone's pairwise favorite — is also the most-frequent last choice (12 ballots), so Coombs deletes the Condorcet winner FIRST. Felsenthal conjectures four candidates are the minimum for this failure.
  Live results: https://bettervoting.com/xbqq8t/results
bv_test_id: BV2164
bv_election_id: xbqq8t
bv_results_url: https://bettervoting.com/xbqq8t/results
paradoxes: [condorcet-winner]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  11:Arlo>Bree>Cole>Dana
  12:Bree>Cole>Dana>Arlo
  2:Bree>Arlo>Dana>Cole
  4:Cole>Arlo>Dana>Bree
  4:Dana>Arlo>Bree>Cole
expected_winners:
  - Arlo

# file: bv2164_xbqq8t_ranked_robin.yaml

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TABULATION RESULTS
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--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 33 ballots (ranked ballots).

Ballots:
    11 × Arlo > Bree > Cole > Dana
    12 × Bree > Cole > Dana > Arlo
     2 × Bree > Arlo > Dana > Cole
     4 × Cole > Arlo > Dana > Bree
     4 × Dana > Arlo > Bree > Cole

Round-Robin — every pair, head-to-head (For – Against):
   Arlo  beats Bree   19 – 14
   Arlo  beats Cole   17 – 16
   Arlo  beats Dana   17 – 16
   Bree  beats Cole   29 –  4
   Bree  beats Dana   25 –  8
   Cole  beats Dana   27 –  6

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |     Arlo     |    Bree     |    Cole     |    Dana     |
-------------------------------------------------------------------
  Arlo > |     ---      |19 -  0 - 14 |17 -  0 - 16 |17 -  0 - 16 |
  Bree > | 14 -  0 - 19 |    ---      |29 -  0 -  4 |25 -  0 -  8 |
  Cole > | 16 -  0 - 17 | 4 -  0 - 29 |    ---      |27 -  0 -  6 |
  Dana > | 16 -  0 - 17 | 8 -  0 - 25 | 6 -  0 - 27 |    ---      |

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  Arlo       3–0–0         3      +7  Bree, Cole, Dana
    2  Bree       2–1–0         2     +37  Cole, Dana
    3  Cole       1–2–0         1      -5  Dana
    4  Dana       0–3–0         0     -39  —

Winner — Ranked Robin (RCV-RR): Arlo
   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): Arlo
   Outside (3):        Bree, Cole, Dana
   One member ⇒ Arlo is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Arlo 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