Minimax Ex.29 — STAR: elects B, a top-cycle member, not the universal loser¶

Generated from bv2167_f3dxq9_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: B

▶ Live on BetterVoting: vote · results ↗ (election f3dxq9 · test BV2167).

Scenario¶

Race 1 of 2 in the Minimax-elects-the-absolute-loser election (BV2167, bvid f3dxq9; 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 A10 (the Condorcet / Minimax / Simpson-Kramer procedure), Example 29. 11 voters, four candidates: 2×(D>A>C>B), 3×(D>B>A>C), 3×(C>B>A>D), 1×(B>A>C>D), 2×(A>C>B>D). A, B, C form a top cycle (B>A 7–4, A>C 8–3, C>B 7–4); D loses every matchup 5–6 — the Condorcet loser AND absolute loser (6 of 11 rank D last). Minimax — worked on the case page; no tabulator on BV or in LH — elects D, whose worst loss (6) is the smallest (A/B/C: 7/7/8). This STAR race (ranks mapped 5/4/2/1): A 34, B 35, C 32, D 31 — B and A advance, B wins the automatic runoff 7–4. No RR race (the A/B/C Copeland tie → BV random) and no IRV race (random transfer tie). Live results: https://bettervoting.com/f3dxq9/results

Ballots¶

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

A,B,C,D
4,1,2,5
4,1,2,5
2,4,1,5
2,4,1,5
2,4,1,5
2,4,5,1
2,4,5,1
2,4,5,1
4,5,2,1
5,2,4,1
5,2,4,1

What the engine says¶

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

[Divergence from STAR]
  STAR                   = B
  Choose-One (Plurality) = D   (differs from STAR)
  RCV-IRV                = C   (differs from STAR)
  RCV-RR                 = A   (differs from STAR)
  Note: no ballots had tied scores, so RCV-IRV vs STAR here is a genuine
        method difference, not a tie-breaking artifact.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/bv2167_f3dxq9_star_RCV-IRV_tabulated.txt
  RCV-RR round-robin: cases_tabulated/bv2167_f3dxq9_star_RCV-RR_tabulated.txt

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

[STAR Voting]
 Tabulating 11 ballots.
Count × A,B,C,D
    3 × 2,4,1,5
    3 × 2,4,5,1
    2 × 4,1,2,5
    2 × 5,2,4,1
    1 × 4,5,2,1

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   B             -- 35 -- First place
   A             -- 34 -- Second place
   C             -- 32
   D             -- 31
 B and A advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   B             -- 7 -- First place
   A             -- 4
   Equal Support -- 0
 B wins.
   Runoff math:
     11  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     11  voters with a preference  (majority = 6)
           B 7 (64%)  ·  A 4 (36%)

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

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
               |    * A     |   * B     |     C     |     D     |
-----------------------------------------------------------------
         * A > |    ---     |4 - 0 - 7  |8 - 0 - 3  |6 - 0 - 5  |
         * B > | 7 - 0 - 4  |   ---     |4 - 0 - 7  |6 - 0 - 5  |
           C > | 3 - 0 - 8  |7 - 0 - 4  |   ---     |6 - 0 - 5  |
           D > | 5 - 0 - 6  |5 - 0 - 6  |5 - 0 - 6  |   ---     |

[Condorcet Winner]
  No Condorcet winner (majority cycle: A > C > B > A)

[Condorcet Loser]
  Condorcet Loser: D — loses every head-to-head matchup — elected by Choose-One (Plurality)!

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
A          2  3  0  6  0  0  |    34   3.1
B          1  6  0  2  2  0  |    35   3.2
C          3  2  0  3  3  0  |    32   2.9
D          5  0  0  0  6  0  |    31   2.8

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/bv2167_f3dxq9_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