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SOURCE FILE:     bv2170_pp2q4q_ranked_robin.yaml
TABULATED FILE:  bv2170_pp2q4q_ranked_robin_tabulated.txt
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election_title: "Symmetric centrist (47/47/3/3) — Ranked Robin: elects Casey, beats everyone head-to-head"
scenario_description: |-
  One of four races in the Symmetric Centrist election (BV2170, bvid pp2q4q; BV-confirmed). 100 voters, three candidates, ONE electorate tabulated four ways. Avery is the left pole, Blake the right pole, Casey the centrist. Ranked Robin (Copeland) compares every pair head-to-head: Casey beats Avery 53–47 and Casey beats Blake 53–47, while Avery ties Blake 50–50. Casey wins both matchups (2–0) — the Condorcet winner — so Ranked Robin elects Casey directly and deterministically (no cycle, no tiebreak), agreeing with STAR and disagreeing with the center-squeeze methods IRV and Choose-One.

  Live results: https://bettervoting.com/pp2q4q/results
  Companion races: bv2170_pp2q4q_star.yaml, bv2170_pp2q4q_irv.yaml, bv2170_pp2q4q_plurality.yaml.
  Overview page: bv2170_pp2q4q_symmetric_centrist.md
bv_test_id: BV2170
bv_election_id: pp2q4q
bv_results_url: https://bettervoting.com/pp2q4q/results
paradoxes: [condorcet-winner]
voting_method: RankedRobin
num_winners: 1
lot_numbers: [Avery, Casey, Blake]
ballots: |-
  47:Avery>Casey>Blake
  47:Blake>Casey>Avery
  3:Casey>Avery>Blake
  3:Casey>Blake>Avery
expected_winners:
  - Casey

# file: bv2170_pp2q4q_ranked_robin.yaml

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TABULATION RESULTS
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--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 100 ballots (ranked ballots).

Ballots:
    47 × Avery > Casey > Blake
    47 × Blake > Casey > Avery
     3 × Casey > Avery > Blake
     3 × Casey > Blake > Avery

Round-Robin — every pair, head-to-head (For – Against):
   Casey  beats Avery   53 – 47
   Avery  ties  Blake   50 – 50
   Casey  beats Blake   53 – 47

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
          |    Avery     |   Casey     |   Blake     |
------------------------------------------------------
  Avery > |     ---      |47 -  0 - 53 |50 -  0 - 50 |
  Casey > | 53 -  0 - 47 |    ---      |53 -  0 - 47 |
  Blake > | 50 -  0 - 50 |47 -  0 - 53 |    ---      |

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  Casey      2–0–0         2     +12  Avery, Blake
    2  Avery      0–1–1       0.5      -6  —
    3  Blake      0–1–1       0.5      -6  —

Winner — Ranked Robin (RCV-RR): Casey
   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): Casey
   Outside (2):        Avery, Blake
   One member ⇒ Casey is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Casey 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