Coombs Ex.17 — Ranked Robin: the Condorcet winner Arlo¶

Generated from bv2164_xbqq8t_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: Arlo

▶ Live on BetterVoting: vote · results ↗ (election xbqq8t · test BV2164).

Scenario¶

Race 3 of 3 in the Coombs Condorcet-failure election (BV2164, bvid xbqq8t; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A7, Example 17 — see bv2164_xbqq8t_star.yaml for the setup. The same 33 rankings counted by Ranked Robin (Copeland): Arlo wins every head-to-head (Bree 19–14, Cole 17–16, Dana 17–16) — the Condorcet winner, elected directly. The irony this case teaches: Coombs deletes candidates for being ranked LAST by many, and Arlo — everyone's pairwise favorite — is also the most-frequent last choice (12 ballots), so Coombs deletes the Condorcet winner FIRST. Felsenthal conjectures four candidates are the minimum for this failure. Live results: https://bettervoting.com/xbqq8t/results

Ballots¶

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

11:Arlo>Bree>Cole>Dana
12:Bree>Cole>Dana>Arlo
2:Bree>Arlo>Dana>Cole
4:Cole>Arlo>Dana>Bree
4:Dana>Arlo>Bree>Cole

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 33 ballots (ranked ballots).

Ballots:
    11 × Arlo > Bree > Cole > Dana
    12 × Bree > Cole > Dana > Arlo
     2 × Bree > Arlo > Dana > Cole
     4 × Cole > Arlo > Dana > Bree
     4 × Dana > Arlo > Bree > Cole

Round-Robin — every pair, head-to-head (For – Against):
   Arlo  beats Bree   19 – 14
   Arlo  beats Cole   17 – 16
   Arlo  beats Dana   17 – 16
   Bree  beats Cole   29 –  4
   Bree  beats Dana   25 –  8
   Cole  beats Dana   27 –  6

--- Pairwise (Round-Robin) Matrix ---
Head-to-head / pairwise comparison — the Ranked Robin tally
Legend: For - Equal Support - Against   (row vs column)
         |     Arlo     |    Bree     |    Cole     |    Dana     |
-------------------------------------------------------------------
  Arlo > |     ---      |19 -  0 - 14 |17 -  0 - 16 |17 -  0 - 16 |
  Bree > | 14 -  0 - 19 |    ---      |29 -  0 -  4 |25 -  0 -  8 |
  Cole > | 16 -  0 - 17 | 4 -  0 - 29 |    ---      |27 -  0 -  6 |
  Dana > | 16 -  0 - 17 | 8 -  0 - 25 | 6 -  0 - 27 |    ---      |

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  Arlo       3–0–0         3      +7  Bree, Cole, Dana
    2  Bree       2–1–0         2     +37  Cole, Dana
    3  Cole       1–2–0         1      -5  Dana
    4  Dana       0–3–0         0     -39  —

Winner — Ranked Robin (RCV-RR): Arlo
   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 4): Arlo
   Outside (3):        Bree, Cole, Dana
   One member ⇒ Arlo is the Condorcet winner, beating every rival head-to-head.
   Ranked Robin (RCV-RR) winner Arlo 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/felsenthal_paradoxes/cases/bv2164_xbqq8t_ranked_robin.yaml

Coombs Ex.17 — Ranked Robin: the Condorcet winner Arlo¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶