Margins matter — Ranked Robin (Copeland) ties all three¶

Generated from margins_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: Berry

▶ Live on BetterVoting: vote · results ↗ (election kdjjkq · test BV2251).

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

Scenario¶

Twelve gelato voters, three flavours, a rock-paper-scissors cycle: Almond beats Berry 7-5, Berry beats Cocoa 8-4, Cocoa beats Almond 7-5. Copeland counts WINS and throws the margins away, so every flavour goes 1-1-0 and the Copeland winning set is all three. That is the whole point of the profile: the same tournament, WEIGHTED by those margins, is the Borda count — and Borda separates them (Berry +2, Almond 0, Cocoa -2). LH breaks the Copeland tie by total margin (Berry +2) and elects Berry, which is exactly the margin-weighted answer; BetterVoting falls past its head-to-head rung on a 3-way tie and picks at RANDOM, so BV's crowned winner is a coin flip and only its pairwise matrix is freezable. Structural twin of the 304-ballot textbook profile in margins_paper_exact_304.yaml.

Ballots¶

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

Almond>Berry>Cocoa
Almond>Berry>Cocoa
Almond>Berry>Cocoa
Almond>Berry>Cocoa
Almond>Berry>Cocoa
Berry>Cocoa>Almond
Berry>Cocoa>Almond
Berry>Cocoa>Almond
Cocoa>Almond>Berry
Cocoa>Almond>Berry
Cocoa>Berry>Almond
Cocoa>Berry>Almond

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 12 ballots (ranked ballots).

Ballots:
     5 × Almond > Berry > Cocoa
     3 × Berry > Cocoa > Almond
     2 × Cocoa > Almond > Berry
     2 × Cocoa > Berry > Almond

Round-Robin — every pair, head-to-head (For – Against):
   Almond  beats Berry    7 – 5
   Cocoa   beats Almond   7 – 5
   Berry   beats Cocoa    8 – 4

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
           |  Almond   |  Berry   |  Cocoa   |
----------------------------------------------
  Almond > |    ---    |7 - 0 - 5 |5 - 0 - 7 |
   Berry > | 5 - 0 - 7 |   ---    |8 - 0 - 4 |
   Cocoa > | 7 - 0 - 5 |4 - 0 - 8 |   ---    |

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  Berry      1–1–0         1      +2  Cocoa
    2  Almond     1–1–0         1      +0  Berry
    3  Cocoa      1–1–0         1      -2  Almond

Winner — Ranked Robin (RCV-RR): Berry
   *** 3 candidates tie for the most wins (Almond, Berry, Cocoa) — a Condorcet cycle (no candidate beats all others). Resolved by total margin, then lot order. (This is where Minimax / Ranked Pairs / Schulze differ — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.)

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 (3 of 3): Almond, Berry, Cocoa
   Outside (0):        —
   More than one member ⇒ NO Condorcet winner: the top of the tournament is a
   cycle, so the strongest "candidate" is a set, not a person. Which member of
   the set should win is exactly what Minimax / Ranked Pairs / Schulze disagree
   about — see 05_Ranked_Robin/01_Learn/cycle_resolution.md.
   Ranked Robin (RCV-RR) winner Berry 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/copeland_vs_borda_margins/cases/margins_ranked_robin.yaml

Margins matter — Ranked Robin (Copeland) ties all three¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶