Felsenthal Ex.4 full electorate — STAR: elects the Condorcet winner Beth¶

Generated from bv2150_dxg8pb_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: Beth

▶ Live on BetterVoting: vote · results ↗ (election dxg8pb · test BV2150).

Scenario¶

Race 3 of 3 in the No-Show-paradox pair, part 1 of 2 (BV2150, bvid dxg8pb; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 4 — see bv2150_dxg8pb_irv.yaml for the setup. The same 11 voters with ranks mapped to 0–5 scores (5/3/1). Scores: Andy 29, Beth 37, Carl 33 — Beth and Carl advance, Beth wins the automatic runoff 7–4. STAR elects the Condorcet winner that the runoff procedure (the IRV race) deleted in round one. Live results: https://bettervoting.com/dxg8pb/results

Ballots¶

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

Andy,Beth,Carl
5,3,1
5,3,1
5,3,1
5,3,1
1,5,3
1,5,3
1,5,3
3,1,5
1,3,5
1,3,5
1,3,5

What the engine says¶

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

[Divergence from STAR]
  STAR                   = Beth
  Choose-One (Plurality) = Andy   (differs from STAR)
  RCV-IRV                = Carl   (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.
  Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
        outlier — the classic center-squeeze signature.
  Full round-by-round reports (generated for review):
  RCV-IRV rounds: cases_tabulated/bv2150_dxg8pb_star_RCV-IRV_tabulated.txt

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

[STAR Voting]
 Tabulating 11 ballots.
Count × Andy,Beth,Carl
    4 ×    5,   3,   1
    3 ×    1,   5,   3
    3 ×    1,   3,   5
    1 ×    3,   1,   5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Beth          -- 37 -- First place
   Carl          -- 33 -- Second place
   Andy          -- 29
 Beth and Carl advance.

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

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

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
               |     Andy   |  * Beth   |  * Carl   |
-----------------------------------------------------
        Andy > |    ---     |5 - 0 - 6  |4 - 0 - 7  |
      * Beth > | 6 - 0 - 5  |   ---     |7 - 0 - 4  |
      * Carl > | 7 - 0 - 4  |4 - 0 - 7  |   ---     |

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

[Condorcet Loser]
  Condorcet Loser: Andy — 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
Andy       4  0  1  0  6  0  |    29   2.6
Beth       3  0  7  0  1  0  |    37   3.4
Carl       4  0  3  0  4  0  |    33   3.0

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/bv2150_dxg8pb_star.yaml

See also¶

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