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SOURCE FILE:     bv2153_pcttmr_ranked_robin.yaml
TABULATED FILE:  bv2153_pcttmr_ranked_robin_tabulated.txt
======================================================================

election_title: "Felsenthal Ex.7 — Ranked Robin: the Condorcet winner Amos"
scenario_description: |-
  Race 3 of 3 in the Absolute-Majority-paradox election (BV2153, bvid pcttmr; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A3, Example 7 — see bv2153_pcttmr_approval.yaml for the setup.
  The same 100 voters' full rankings counted by Ranked Robin (Copeland): Amos wins both head-to-heads (Bella 51–49, Chad 51–49) — the Condorcet winner, elected. A majority's first choice survives any pairwise count; it is the approval cutoff, not the ballots, that loses him.
  Live results: https://bettervoting.com/pcttmr/results
bv_test_id: BV2153
bv_election_id: pcttmr
bv_results_url: https://bettervoting.com/pcttmr/results
paradoxes: [majority-failure]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  51:Amos>Bella>Chad
  48:Bella>Chad>Amos
  1:Chad>Bella>Amos
expected_winners:
  - Amos

# file: bv2153_pcttmr_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:
    51 × Amos > Bella > Chad
    48 × Bella > Chad > Amos
     1 × Chad > Bella > Amos

Round-Robin — every pair, head-to-head (For – Against):
   Amos   beats Bella   51 – 49
   Amos   beats Chad    51 – 49
   Bella  beats Chad    99 –  1

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
          |     Amos     |   Bella     |    Chad     |
------------------------------------------------------
   Amos > |     ---      |51 -  0 - 49 |51 -  0 - 49 |
  Bella > | 49 -  0 - 51 |    ---      |99 -  0 -  1 |
   Chad > | 49 -  0 - 51 | 1 -  0 - 99 |    ---      |

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  Amos       2–0–0         2      +4  Bella, Chad
    2  Bella      1–1–0         1     +96  Chad
    3  Chad       0–2–0         0    -100  —

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