Ranked Robin (RCV-RR) — the smallest round-robin that shows the report¶

Generated from ranked_robin_intro_c3_b7.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: Ben

Scenario¶

The three-candidate, seven-ballot election the Ranked Robin lesson opens with — small enough that every pairwise comparison fits on one screen.

Ada leads on first choices (3 of 7) and finishes LAST. Ben never leads the first count, yet beats Ada 4-3 and Cara 5-2, so he takes the round-robin 2-0 and is the Condorcet winner. Cara beats Ada 4-3 and loses to Ben: 1-1.

Copeland scores (wins + 1/2*ties): Ben 2, Cara 1, Ada 0.

This case exists so the lesson can EMBED the report instead of pasting it — the page shows exactly what the engine prints today, and the test suite notices if that ever stops being true.

Ballots¶

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

3:Ada>Ben>Cara
2:Ben>Cara>Ada
2:Cara>Ben>Ada

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 7 ballots (ranked ballots).

Ballots:
     3 × Ada > Ben > Cara
     2 × Ben > Cara > Ada
     2 × Cara > Ben > Ada

Round-Robin — every pair, head-to-head (For – Against):
   Ben   beats Ada    4 – 3
   Cara  beats Ada    4 – 3
   Ben   beats Cara   5 – 2

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |    Ada    |   Ben    |  Cara    |
--------------------------------------------
   Ada > |    ---    |3 - 0 - 4 |3 - 0 - 4 |
   Ben > | 4 - 0 - 3 |   ---    |5 - 0 - 2 |
  Cara > | 4 - 0 - 3 |2 - 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  Ben        2–0–0         2      +4  Cara, Ada
    2  Cara       1–1–0         1      -2  Ada
    3  Ada        0–2–0         0      -2  —

Winner — Ranked Robin (RCV-RR): Ben
   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): Ben
   Outside (2):        Ada, Cara
   One member ⇒ Ben is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Ben 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 05_Ranked_Robin/02_Examples/cases/ranked_robin_intro_c3_b7.yaml

Ranked Robin (RCV-RR) — the smallest round-robin that shows the report¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶