P3 sincere — Ranked Robin elects Edinburgh (the baseline every manipulation attacks)¶

Generated from p3_sincere_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: Edinburgh

▶ Live on BetterVoting: vote · results ↗ (election 4w96tr · test BV2253).

Official tie-break (lot) order: Athens > Bergen > Cork > Dublin > Edinburgh — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

Zwicker's profile P3 (Handbook of Computational Social Choice ch. 2, Definition 2.3), 7 voters and 5 candidates, cast SINCERELY. Edinburgh goes 3-1 head-to-head and is the Copeland/Ranked Robin winner with a symmetric Copeland score of +2; Bergen is -2 and the rest are 0, exactly the numbers the book prints. There is NO Condorcet winner (Dublin beats Edinburgh 5-2, so nobody beats everybody). This is the baseline: the two Athens-first voters are about to see their LAST choice, Edinburgh, win — which is precisely the pressure the book uses to define single-voter manipulability. The manipulated counterparts are p3_manip_reversal_rr.yaml and p3_manip_compromise_rr.yaml.

Ballots¶

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

2:Edinburgh>Cork>Athens>Dublin>Bergen
3:Dublin>Edinburgh>Bergen>Cork>Athens
2:Athens>Bergen>Cork>Dublin>Edinburgh

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:
     2 × Edinburgh > Cork > Athens > Dublin > Bergen
     3 × Dublin > Edinburgh > Bergen > Cork > Athens
     2 × Athens > Bergen > Cork > Dublin > Edinburgh

Round-Robin — every pair, head-to-head (For – Against):
   Edinburgh  beats Cork        5 – 2
   Edinburgh  beats Athens      5 – 2
   Dublin     beats Edinburgh   5 – 2
   Edinburgh  beats Bergen      5 – 2
   Cork       beats Athens      5 – 2
   Cork       beats Dublin      4 – 3
   Bergen     beats Cork        5 – 2
   Athens     beats Dublin      4 – 3
   Athens     beats Bergen      4 – 3
   Dublin     beats Bergen      5 – 2

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
              |  Edinburgh  |   Cork     |  Athens    |  Dublin    |  Bergen    |
---------------------------------------------------------------------------------
  Edinburgh > |     ---     | 5 - 0 - 2  | 5 - 0 - 2  | 2 - 0 - 5  | 5 - 0 - 2  |
       Cork > |  2 - 0 - 5  |    ---     | 5 - 0 - 2  | 4 - 0 - 3  | 2 - 0 - 5  |
     Athens > |  2 - 0 - 5  | 2 - 0 - 5  |    ---     | 4 - 0 - 3  | 4 - 0 - 3  |
     Dublin > |  5 - 0 - 2  | 3 - 0 - 4  | 3 - 0 - 4  |    ---     | 5 - 0 - 2  |
     Bergen > |  2 - 0 - 5  | 5 - 0 - 2  | 3 - 0 - 4  | 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  Edinburgh  3–1–0         3      +6  Cork, Athens, Bergen
    2  Dublin     2–2–0         2      +4  Edinburgh, Bergen
    3  Cork       2–2–0         2      -2  Dublin, Athens
    4  Athens     2–2–0         2      -4  Dublin, Bergen
    5  Bergen     1–3–0         1      -4  Cork

Winner — Ranked Robin (RCV-RR): Edinburgh
   the most head-to-head wins (3).

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 (5 of 5): Edinburgh, Cork, Athens, Dublin, Bergen
   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.
   Note: the Copeland leaders (Edinburgh) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   Ranked Robin (RCV-RR) winner Edinburgh 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/manipulability_p3/cases/p3_sincere_ranked_robin.yaml

P3 sincere — Ranked Robin elects Edinburgh (the baseline every manipulation attacks)¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶