======================================================================
SOURCE FILE:     ranked_robin_consensus_center.yaml
TABULATED FILE:  ranked_robin_consensus_center_tabulated.txt
======================================================================

election_title: "Ranked Robin (RCV-RR) — the consensus center wins the round-robin"
scenario_description: >-
  13 ranked ballots, 4 candidates. Ben beats every rival head-to-head (the Condorcet /
  Copeland winner) and wins Ranked Robin 3-0 — even though Ada and Dan each have more
  first-choices. Tabulate with STARVote_LH_tabulation_engine/tools_adam/pref_voting_tabulation_engine/ranked_robin_report.py.
voting_method: RankedRobin   # = RCV-RR / Copeland — round-robin on a ranked ballot
num_winners: 1
# Ranked Robin / Copeland worked example. 13 ranked ballots, 4 candidates
# (Ada=left, Ben=center-left, Cara=center-right, Dan=right).
# Pairwise: Ben beats Ada 9-4, Cara 7-6, Dan 9-4 -> 3-0 round-robin.
#   Copeland (wins - losses): Ben +3, Cara +1, Ada -1, Dan -3  ->  RANKED ROBIN WINNER: Ben.
# Ben is the Condorcet winner.  Note: Ada and Dan each have MORE first-choices (4) than
# Ben (3) -- Ranked Robin elects the consensus center, not the plurality leader.
# The LH engine now tabulates Ranked Robin first-class: this file prints the
# round-robin (ballots + pairwise table + win-loss record). For an independent
# Copeland cross-check, run STARVote_LH_tabulation_engine/tools_adam/pref_voting_tabulation_engine/ranked_robin_report.py.
# Lesson: 05_Ranked_Robin/01_Learn/ranked_robin.md
ballots: |-
  4:Ada>Ben>Cara>Dan
  4:Dan>Cara>Ben>Ada
  3:Ben>Cara>Ada>Dan
  2:Cara>Ben>Dan>Ada

expected_winners:
  - Ben

# file: ranked_robin_consensus_center.yaml

======================================================================
TABULATION RESULTS
======================================================================

--- Ranked Robin (RCV-RR / Copeland) Method (single winner) ---
 Tabulating 13 ballots (ranked ballots).

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

Round-Robin — every pair, head-to-head (For – Against):
   Ben   beats Ada    9 – 4
   Cara  beats Ada    9 – 4
   Ada   beats Dan    7 – 6
   Ben   beats Cara   7 – 6
   Ben   beats Dan    9 – 4
   Cara  beats Dan    9 – 4

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |    Ada    |   Ben    |  Cara    |   Dan    |
-------------------------------------------------------
   Ada > |    ---    |4 - 0 - 9 |4 - 0 - 9 |7 - 0 - 6 |
   Ben > | 9 - 0 - 4 |   ---    |7 - 0 - 6 |9 - 0 - 4 |
  Cara > | 9 - 0 - 4 |6 - 0 - 7 |   ---    |9 - 0 - 4 |
   Dan > | 6 - 0 - 7 |4 - 0 - 9 |4 - 0 - 9 |   ---    |

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        3–0–0         3     +11  Cara, Ada, Dan
    2  Cara       2–1–0         2      +9  Ada, Dan
    3  Ada        1–2–0         1      -9  Dan
    4  Dan        0–3–0         0     -11  —

Winner — Ranked Robin (RCV-RR): Ben
   beats every opponent head-to-head — the Condorcet winner.

--- 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 4): Ben
   Outside (3):        Ada, Cara, Dan
   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