Coombs Ex.17 — STAR: Bree tops the scores, the Condorcet winner Arlo wins the runoff¶

Generated from bv2164_xbqq8t_star.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.

Method: STAR (single winner) · 1 seat · Expected winner: Arlo

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

Scenario¶

Race 1 of 3 in the Coombs Condorcet-failure election (BV2164, bvid xbqq8t; BV-confirmed). Source: Dan S. Felsenthal, "Review of Paradoxes Afflicting Various Voting Procedures Where One Out of m Candidates (m ≥ 2) Must Be Elected", University of Haifa / LSE, revised 26 May 2010; Appendix A7 (Coombs' procedure: eliminate whoever is ranked LAST by the most voters), Example 17. 33 voters, four candidates: 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). Arlo is the Condorcet winner (beats Bree 19–14, Cole 17–16, Dana 17–16). Coombs — worked on the case page; no tabulator on BetterVoting or in the LH engine — deletes ARLO first (ranked last by 12, the most) and elects Bree. This STAR race (ranks mapped 5/4/2/1): Arlo 107, Bree 126, Cole 96, Dana 67 — Bree tops the scoring round, but Arlo wins the automatic runoff 19–14. No IRV race: its first elimination is a random Cole/Dana 4–4 tie on BV. Live results: https://bettervoting.com/xbqq8t/results

Ballots¶

Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).

Arlo,Bree,Cole,Dana
11: 5,4,2,1
12: 1,5,4,2
# 2× Bree>Arlo>Dana>Cole and 4× Cole>Arlo>Dana>Bree and 4× Dana>Arlo>Bree>Cole:
4,5,1,2
4,5,1,2
4,1,5,2
4,1,5,2
4,1,5,2
4,1,5,2
4,2,1,5
4,2,1,5
4,2,1,5
4,2,1,5

What the engine says¶

The count, step by step — the rounds and how the winner is reached:

[Divergence from STAR]
  STAR                   = Arlo
  Choose-One (Plurality) = Bree   (differs from STAR)
  Approval               = Bree   (differs from STAR)

[Runoff Reversal]
 - Score Round Winner(s) = (Bree)
 - Runoff Round Winner   = (Arlo)
  Candidate Bree earned the highest total score, but
  Candidate Arlo won the automatic runoff — not a malfunction,
  STAR working as designed: the runoff elects the finalist preferred
  by the majority (of voters with a preference).

--- STAR Voting Method (single winner) ---

[STAR Voting]
 Tabulating 33 ballots.
Count × Arlo,Bree,Cole,Dana
   12 ×    1,   5,   4,   2
   11 ×    5,   4,   2,   1
    4 ×    4,   1,   5,   2
    4 ×    4,   2,   1,   5
    2 ×    4,   5,   1,   2

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Bree          -- 126 -- First place
   Arlo          -- 107 -- Second place
   Cole          --  96
   Dana          --  67
 Bree and Arlo advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Arlo          -- 19 -- First place
   Bree          -- 14
   Equal Support --  0
 Arlo wins.
   Runoff math:
     33  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     33  voters with a preference  (majority = 17)
           Arlo 19 (58%)  ·  Bree 14 (42%)

[STAR Voting: Winner — STAR Voting Method (single winner)]
 Arlo

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

--- Runoff (Preference) Matrix ---
Head-to-head / pairwise comparison
Legend: For - Equal Support - Against
        * indicates Top 2 Finalist
                 |    * 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 |    ---      |

[Condorcet Winner]
  Condorcet Winner: Arlo — matches the STAR winner

[Condorcet Loser]
  Condorcet Loser: Dana — loses every head-to-head matchup

[Score Distribution] (how many ballots gave each star rating)
                   Score
Candidate   5   4   3   2   1   0  | Total   Avg
Arlo       11  10   0   0  12   0  |   107   3.2
Bree       14  11   0   4   4   0  |   126   3.8
Cole        4  12   0  11   6   0  |    96   2.9
Dana        4   0   0  18  11   0  |    67   2.0

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_star.yaml

See also¶

Methods disagree on this election — its entry in the divergence review ledger
Condorcet efficiency (topic hub)
Ties & tie-breaking (topic hub)
Runoff reversal (worked set)
Glossary · all cases by method