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SOURCE FILE:     rr_combined.yaml
TABULATED FILE:  rr_combined_tabulated.txt
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election_title: "Summability demo — Combined (A+B), counted by Ranked Robin"
scenario_description: |-
  The two districts merged, counted by Ranked Robin. These are the SAME ranked
  ballots IRV could not combine (under IRV, B wins both districts yet is
  eliminated when merged — see irv_combined). Ranked Robin's pairwise matrix is
  summable: District A's matrix + District B's matrix EQUALS this combined matrix
  cell-by-cell, and from it B beats A (11–9) and C (11–9) → B is the Condorcet
  winner. The candidate who won both districts wins the merge, reached by adding
  precinct tables, never pooling ballots.
voting_method: RankedRobin
num_winners: 1
ballots: |-
  6:A
  4:B
  3:C>B>A
  6:C
  4:B
  3:A>B>C
expected_winners:
  - B

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TABULATION RESULTS
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--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 26 ballots (ranked ballots).

Ballots:
     6 × A
     8 × B
     3 × C > B > A
     6 × C
     3 × A > B > C

Round-Robin — every pair, head-to-head (For – Against):
   B  beats A   11 –  9
   A  ties  C    9 –  9
   B  beats C   11 –  9

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
      |      A       |     B       |     C       |
--------------------------------------------------
  A > |     ---      | 9 -  6 - 11 | 9 -  8 -  9 |
  B > | 11 -  6 -  9 |    ---      |11 -  6 -  9 |
  C > |  9 -  8 -  9 | 9 -  6 - 11 |    ---      |

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  B          2–0–0         2      +4  A, C
    2  A          0–1–1       0.5      -2  —
    3  C          0–1–1       0.5      -2  —

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