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SOURCE FILE:     minimax_ex30_noshow_after.yaml
TABULATED FILE:  minimax_ex30_noshow_after_tabulated.txt
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election_title: "Minimax Ex.30 — after: three C>A>B>D voters stay home, Minimax elects A"
scenario_description: |-
  The AFTER half of Felsenthal's Minimax no-show pair. Source: Dan S. Felsenthal (2010), Appendix A10, Example 30 (credited to Hannu Nurmi, private communication 22.2.2010) — see minimax_ex30_noshow_before.yaml for the setup.
  The same electorate with three of the four C>A>B>D voters ABSENT: 16 voters now. Worst pairwise losses become A 10, B 11, C 12, D 11, so the smallest belongs to A and Minimax elects A. Those three voters ranked A second and B third, so by staying home they got a result they PREFER to the one their own ballots produced — the no-show paradox in its sharpest form. Read forward instead of backward it is the twin paradox: with one such voter A wins, and when the three "twin brothers" join, B does.
  Nothing about the ballots changed. The only edit is which voters showed up, which is what makes this a conditional paradox in Felsenthal's sense rather than a surprising-but-static result.
  Labels are Felsenthal's own A/B/C/D so the case can be read side by side with the paper's table.
  Tabulated here as Ranked Robin for the pairwise matrix Minimax reads; Ranked Robin elects D on these ballots, disagreeing with Minimax's A. For the Minimax count run tools_adam/pref_voting_tabulation_engine/minimax_report.py, which is cross-checked against pref_voting.
paradoxes: [no-show, twin, condorcet-cycle]
voting_method: RankedRobin
num_winners: 1
ballots: |-
  5:D>B>C>A
  4:B>C>A>D
  3:A>D>C>B
  3:A>D>B>C
  1:C>A>B>D
expected_winners:
  - D

# file: minimax_ex30_noshow_after.yaml

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TABULATION RESULTS
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--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 16 ballots (ranked ballots).

Ballots:
     5 × D > B > C > A
     4 × B > C > A > D
     3 × A > D > C > B
     3 × A > D > B > C
     1 × C > A > B > D

Round-Robin — every pair, head-to-head (For – Against):
   D  beats B   11 –  5
   D  beats C   11 –  5
   A  beats D   11 –  5
   B  beats C   12 –  4
   B  beats A    9 –  7
   C  beats A   10 –  6

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
      |      D       |     B       |     C       |     A       |
----------------------------------------------------------------
  D > |     ---      |11 -  0 -  5 |11 -  0 -  5 | 5 -  0 - 11 |
  B > |  5 -  0 - 11 |    ---      |12 -  0 -  4 | 9 -  0 -  7 |
  C > |  5 -  0 - 11 | 4 -  0 - 12 |    ---      |10 -  0 -  6 |
  A > | 11 -  0 -  5 | 7 -  0 -  9 | 6 -  0 - 10 |    ---      |

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  D          2–1–0         2      +6  B, C
    2  B          2–1–0         2      +4  A, C
    3  A          1–2–0         1      +0  D
    4  C          1–2–0         1     -10  A

Winner — Ranked Robin (RCV-RR): D
   *** 2 candidates tie for the most wins (D, B) — tied on the tally, not a cycle (some of them beat others head-to-head, but no loop closes). Resolved by total margin, then lot order.

--- 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 (4 of 4): D, B, C, A
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   Note: the Copeland leaders (D, B) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   Ranked Robin (RCV-RR) winner D 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