Summability demo — District A, counted by Ranked Robin¶

Generated from rr_district_A.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¶

District A of the two-district summability demo, counted by Ranked Robin (RCV-RR / Copeland) instead of IRV. Same ranked ballots as irv_district_A. The summable artifact is the pairwise (For–Against–Equal) matrix: B beats both A and C, so B is the Condorcet winner here. Combine with rr_district_B by ADDING the matrices cell-by-cell (see rr_combined) — the sum recovers the true winner without pooling ballots, the summability property IRV's count lacks.

Ballots¶

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

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

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 13 ballots (ranked ballots).

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

Round-Robin — every pair, head-to-head (For – Against):
   B  beats A   7 – 6
   A  beats C   6 – 3
   B  beats C   4 – 3

--- 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 > |    ---    |6 - 0 - 7 |6 - 4 - 3 |
  B > | 7 - 0 - 6 |   ---    |4 - 6 - 3 |
  C > | 3 - 4 - 6 |3 - 6 - 4 |   ---    |

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

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_district_A.yaml

Summability demo — District A, counted by Ranked Robin¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶