Summability demo — Combined (A+B), counted by Ranked Robin¶

Generated from rr_combined.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: Ranked Robin (RCV-RR / Copeland) · 1 seat · Expected winner: B

Scenario¶

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.

Ballots¶

Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).

6:A
4:B
3:C>B>A
6:C
4:B
3:A>B>C

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

--- 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.

Full audit — preference matrix, Condorcet, and score distribution¶

--- 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

Everything in one file: the _tabulated mirror (regenerated on every run; every analysis forced on).

Run it yourself:

python STARVote_LH_tabulation_engine/starvote_larry_hastings.py method_comparisons/summability_demo/cases/rr_combined.yaml

Summability demo — Combined (A+B), counted by Ranked Robin¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶