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SOURCE FILE:     bv2151_97hbpw_ranked_robin.yaml
TABULATED FILE:  bv2151_97hbpw_ranked_robin_tabulated.txt
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election_title: "Felsenthal Ex.4 after two no-shows — Ranked Robin: unmoved, still Beth"
scenario_description: |-
  Race 2 of 3 in the No-Show-paradox pair, part 2 of 2 (BV2151, bvid 97hbpw; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 4 — see bv2151_97hbpw_irv.yaml for the setup.
  The same 9 ranked ballots counted by Ranked Robin (Copeland): Beth still wins both head-to-heads (Andy 6–3, Carl 5–4) — the Condorcet winner, elected directly. Ranked Robin elects Beth with 11 voters (BV2150) and with 9: in this pair, showing up never hurt the Andy voters under a pairwise count. (Condorcet methods are not participation-proof in general — Moulin's theorem — but this electorate doesn't trigger it.)
  Live results: https://bettervoting.com/97hbpw/results
bv_test_id: BV2151
bv_election_id: 97hbpw
bv_results_url: https://bettervoting.com/97hbpw/results
paradoxes: [no-show]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  2:Andy>Beth>Carl
  3:Beth>Carl>Andy
  1:Carl>Andy>Beth
  3:Carl>Beth>Andy
expected_winners:
  - Beth

# file: bv2151_97hbpw_ranked_robin.yaml

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TABULATION RESULTS
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--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 9 ballots (ranked ballots).

Ballots:
     2 × Andy > Beth > Carl
     3 × Beth > Carl > Andy
     1 × Carl > Andy > Beth
     3 × Carl > Beth > Andy

Round-Robin — every pair, head-to-head (For – Against):
   Beth  beats Andy   6 – 3
   Carl  beats Andy   7 – 2
   Beth  beats Carl   5 – 4

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |   Andy    |  Beth    |  Carl    |
--------------------------------------------
  Andy > |    ---    |3 - 0 - 6 |2 - 0 - 7 |
  Beth > | 6 - 0 - 3 |   ---    |5 - 0 - 4 |
  Carl > | 7 - 0 - 2 |4 - 0 - 5 |   ---    |

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  Beth       2–0–0         2      +4  Carl, Andy
    2  Carl       1–1–0         1      +4  Andy
    3  Andy       0–2–0         0      -8  —

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