Crowded field, rung 3 — 3 candidates, 65 voters, counted by Ranked Robin¶

Generated from crowded_field_c3_ranked_robin.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: Diego

Official tie-break (lot) order: Ana > Diego > Greta — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

RUNG 1, counted by Ranked Robin. Diego beats Ana 49–16 and Greta 50–15: a clean Condorcet winner and a Smith set of one. Agrees with crowded_field_c3_star.yaml and with every other method at this rung.

Same 65 voters and the same fixed candidate positions as crowded_field_c3_star.yaml; this file hands them a ranked ballot instead of a 0–5 one.

Construction: build_ladder.py in this folder. 65 voters in seven blocs at 0, 4, 8, 12, 16, 20, 24 (sizes 6, 10, 13, 9, 12, 8, 7); candidates fixed at Ana 1 · Bruno 6 · Clara 9 · Diego 11 · Elsa 14 · Felix 16 · Greta 22; utility = minus distance; scores = each bloc's own min-max scaling onto 0–5. Nothing is tuned, and no count at any rung is settled by a tie-break.

Ballots¶

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

6:Ana>Diego>Greta    # bloc at 0
10:Ana>Diego>Greta    # bloc at 4
13:Diego>Ana>Greta    # bloc at 8
9:Diego>Greta>Ana    # bloc at 12
12:Diego>Greta>Ana    # bloc at 16
8:Greta>Diego>Ana    # bloc at 20
7:Greta>Diego>Ana    # bloc at 24

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 65 ballots (ranked ballots).

Ballots:
    16 × Ana > Diego > Greta
    13 × Diego > Ana > Greta
    21 × Diego > Greta > Ana
    15 × Greta > Diego > Ana

Round-Robin — every pair, head-to-head (For – Against):
   Diego  beats Ana     49 – 16
   Greta  beats Ana     36 – 29
   Diego  beats Greta   50 – 15

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
          |     Ana      |   Diego     |   Greta     |
------------------------------------------------------
    Ana > |     ---      |16 -  0 - 49 |29 -  0 - 36 |
  Diego > | 49 -  0 - 16 |    ---      |50 -  0 - 15 |
  Greta > | 36 -  0 - 29 |15 -  0 - 50 |    ---      |

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  Diego      2–0–0         2     +68  Greta, Ana
    2  Greta      1–1–0         1     -28  Ana
    3  Ana        0–2–0         0     -40  —

Winner — Ranked Robin (RCV-RR): Diego
   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): Diego
   Outside (2):        Ana, Greta
   One member ⇒ Diego is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Diego 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/crowded_field/cases/crowded_field_c3_ranked_robin.yaml

Crowded field, rung 3 — 3 candidates, 65 voters, counted by Ranked Robin¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶