Reinforcement — South district alone (3 voters, Ada is the clear Condorcet winner)¶

Generated from reinf_south_c3_b3_rr.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: Ada

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

Scenario¶

District 2 of the reinforcement-paradox pair from Brandt, Dong & Peters, "Condorcet-Consistent Choice Among Three Candidates" (2024), Theorem 2 (the profile P2). Three voters, and Ada beats both rivals head-to-head:

Ada beats Cara 2–1 · Ada beats Ben 3–0 · Cara beats Ben 3–0

So Ada is the Condorcet winner and every method elects her here. Combined with North (a dead tie in which Ada is also a co-winner), reinforcement/consistency demands that Ada win the merged 9-voter election too — but she doesn't. See the folder README.

Companion cases: reinf_north_c3_b6_rr.yaml (a 3-way tie), reinf_combined_c3_b9_rr.yaml and reinf_combined_c3_b9_star.yaml (Cara wins).

Ballots¶

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

2:Ada>Cara>Ben
1:Cara>Ada>Ben

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 3 ballots (ranked ballots).

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

Round-Robin — every pair, head-to-head (For – Against):
   Ada   beats Cara   2 – 1
   Ada   beats Ben    3 – 0
   Cara  beats Ben    3 – 0

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

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  Ada        2–0–0         2      +4  Cara, Ben
    2  Cara       1–1–0         1      +2  Ben
    3  Ben        0–2–0         0      -6  —

Winner — Ranked Robin (RCV-RR): Ada
   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): Ada
   Outside (2):        Cara, Ben
   One member ⇒ Ada is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Ada 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/reinforcement_paradox/cases/reinf_south_c3_b3_rr.yaml

Reinforcement — South district alone (3 voters, Ada is the clear Condorcet winner)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶