The Post-it RCV example (20 voters) — Ranked Robin: a cycle, a 2-1 tie, and two ladders¶

Generated from bv2176_p8dp28_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: Blue

▶ Live on BetterVoting: vote · results ↗ (election p8dp28 · test BV2176).

Official tie-break (lot) order: Purple > Green > Blue > Pink — consulted only if every deterministic tiebreaker stays tied (how the ladder works).

Scenario¶

One of three races in the Post-it RCV example (BV2176, bvid p8dp28; BV-confirmed). The same 20 ranked ballots as the RCV-IRV race, compared every-pair head-to-head. The pairwise picture is a genuine Condorcet cycle — Purple beats Green 9-8, Green beats Blue 7-4, Blue beats Purple 10-9 (and Pink beats Purple 12-8) — so no candidate beats all others, and Green and Blue tie on record at 2-1 (Copeland 2). This is the documented spot where the two engines' tiebreak ladders part ways (05_Ranked_Robin/01_Learn/rr_tiebreak_lh_vs_bv.md), and BOTH stay deterministic here: BetterVoting's ladder (exactly 2 tied -> their own head-to-head) elects GREEN, who beats Blue 7-4 — BV-confirmed, freezable; the LH ladder below (total margin, then lot) elects BLUE (+5 vs Green's +4). Same ballots, same 2-1 tie, two defensible winners — the first live BetterVoting election to exhibit the ladder divergence. expected_winners records the LH result (Blue); the frozen BV export records Green.

Live results: https://bettervoting.com/p8dp28/results Companion races: bv2176_p8dp28_star.yaml, bv2176_p8dp28_irv.yaml. Overview page: bv2176_p8dp28_postit_rcv_example.md

Ballots¶

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

Purple
Purple
Purple
Purple
Purple
Purple
Purple
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Green>Blue>Pink
Blue>Pink
Blue>Pink
Blue>Green>Pink
Blue>Purple
Pink>Green>Purple
Pink>Purple
Pink

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 20 ballots (ranked ballots).

Ballots:
     7 × Purple
     6 × Green > Blue > Pink
     2 × Blue > Pink
     1 × Blue > Green > Pink
     1 × Blue > Purple
     1 × Pink > Green > Purple
     1 × Pink > Purple
     1 × Pink

Round-Robin — every pair, head-to-head (For – Against):
   Purple  beats Green     9 –  8
   Blue    beats Purple   10 –  9
   Pink    beats Purple   12 –  8
   Green   beats Blue      7 –  4
   Green   beats Pink      7 –  5
   Blue    beats Pink     10 –  3

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
           |    Purple    |   Green     |    Blue     |    Pink     |
---------------------------------------------------------------------
  Purple > |     ---      | 9 -  3 -  8 | 9 -  1 - 10 | 8 -  0 - 12 |
   Green > |  8 -  3 -  9 |    ---      | 7 -  9 -  4 | 7 -  8 -  5 |
    Blue > | 10 -  1 -  9 | 4 -  9 -  7 |    ---      |10 -  7 -  3 |
    Pink > | 12 -  0 -  8 | 5 -  8 -  7 | 3 -  7 - 10 |    ---      |

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  Blue       2–1–0         2      +5  Purple, Pink
    2  Green      2–1–0         2      +4  Blue, Pink
    3  Purple     1–2–0         1      -4  Green
    4  Pink       1–2–0         1      -5  Purple

Winner — Ranked Robin (RCV-RR): Blue
   *** 2 candidates tie for the most wins (Green, Blue) — tied on the tally, not a cycle (some of them beat others head-to-head, but no loop closes). Resolved by total margin, then lot order.

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 (4 of 4): Green, Blue, Purple, Pink
   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 (Green, Blue) are only part of the set — the
   win–loss table's top block understates how wide the contention is.
   Ranked Robin (RCV-RR) winner Blue 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/postit_rcv_example/cases/bv2176_p8dp28_ranked_robin.yaml

The Post-it RCV example (20 voters) — Ranked Robin: a cycle, a 2-1 tie, and two ladders¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶