Felsenthal Ex.3 District I — STAR: also Bruno¶

Generated from bv2147_9gdrqg_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: Bruno

▶ Live on BetterVoting: vote · results ↗ (election 9gdrqg · test BV2147).

Scenario¶

Race 2 of 2 in District I of the Felsenthal Reinforcement-paradox trio (BV2147, bvid 9gdrqg; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 3 — see bv2147_9gdrqg_irv.yaml for the setup. The same 17 ballots with ranks mapped to 0–5 scores (5/3/1). Scores: Alma 47, Bruno 51, Cora 55 — Cora and Bruno advance, Bruno wins the automatic runoff 10–7. Same winner as the runoff procedure in this district; the reinforcement contrast appears at the combined stage (BV2149), where STAR stays with Bruno and the runoff procedure flips to Alma. Live results: https://bettervoting.com/9gdrqg/results

Ballots¶

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

Alma,Bruno,Cora
5,3,1
5,3,1
5,3,1
5,3,1
3,5,1
1,5,3
1,5,3
1,5,3
1,5,3
1,5,3
3,1,5
3,1,5
3,1,5
3,1,5
3,1,5
3,1,5
1,3,5

What the engine says¶

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

[Divergence from STAR]
  STAR                   = Bruno
  Choose-One (Plurality) = Cora   (differs from STAR)
  Approval               = Cora   (differs from STAR)
  RCV-RR                 = Cora   (differs from STAR)
  Full round-by-round reports (generated for review):
  RCV-RR round-robin: cases_tabulated/bv2147_9gdrqg_star_RCV-RR_tabulated.txt

[Runoff Reversal]
 - Score Round Winner(s) = (Cora)
 - Runoff Round Winner   = (Bruno)
  Candidate Cora earned the highest total score, but
  Candidate Bruno 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 17 ballots.
Count × Alma,Bruno,Cora
    6 ×    3,    1,   5
    5 ×    1,    5,   3
    4 ×    5,    3,   1
    1 ×    3,    5,   1
    1 ×    1,    3,   5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Cora          -- 55 -- First place
   Bruno         -- 51 -- Second place
   Alma          -- 47
 Cora and Bruno advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Bruno         -- 10 -- First place
   Cora          --  7
   Equal Support --  0
 Bruno wins.
   Runoff math:
     17  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     17  voters with a preference  (majority = 9)
           Bruno 10 (59%)  ·  Cora 7 (41%)

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

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
                 |      Alma    |  * Bruno    |   * Cora    |
-------------------------------------------------------------
          Alma > |     ---      |10 -  0 -  7 | 5 -  0 - 12 |
       * Bruno > |  7 -  0 - 10 |    ---      |10 -  0 -  7 |
        * Cora > | 12 -  0 -  5 | 7 -  0 - 10 |    ---      |

[Condorcet Winner]
  No Condorcet winner (majority cycle: Alma > Bruno > Cora > Alma)

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Alma       4  0  7  0  6  0  |    47   2.8
Bruno      6  0  5  0  6  0  |    51   3.0
Cora       7  0  5  0  5  0  |    55   3.2

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/bv2147_9gdrqg_star.yaml

See also¶

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