Nurmi Ex.16 sincere — STAR: elects the Condorcet winner B¶

Generated from bv2162_4htk44_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 4htk44 · test BV2162).

Scenario¶

Race 1 of 3 in the RCV-IRV truncation pair, part 1 of 2 (BV2162, bvid 4htk44; BV-confirmed; the pair is BV2162/63). 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 A6 (instant-runoff — Felsenthal's "Alternative Vote" is the British name for RCV-IRV), Example 16, due to Nurmi (1999: 63). 103 voters, four candidates, everyone ranking all four: 33×(A>B>C>D), 29×(B>A>C>D), 24×(C>B>A>D), 17×(D>C>B>A). B is the Condorcet winner (beats A 70–33, C 62–41, D 86–17). This STAR race (ranks mapped 5/4/2/1) scores A 346, B 407, C 312, D 171 — B wins the automatic runoff 70–33. The IRV race elects A instead (a Condorcet winner failure); part 2 (BV2163) shows 17 voters improving their result by TRUNCATING. Live results: https://bettervoting.com/4htk44/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
33: 5,4,2,1
29: 4,5,2,1
24: 2,4,5,1
17: 1,2,4,5

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) = A   (differs from STAR)
  RCV-IRV                = 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.
  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/bv2162_4htk44_star_RCV-IRV_tabulated.txt

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

[STAR Voting]
 Tabulating 103 ballots.
Count × A,B,C,D
   33 × 5,4,2,1
   29 × 4,5,2,1
   24 × 2,4,5,1
   17 × 1,2,4,5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   B             -- 407 -- First place
   A             -- 346 -- Second place
   C             -- 312
   D             -- 171
 B and A advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   B             -- 70 -- First place
   A             -- 33
   Equal Support --  0
 B wins.
   Runoff math:
     103  ballots cast
   −   0  Equal Support (no preference between the two finalists)
     ───
     103  voters with a preference  (majority = 52)
           B 70 (68%)  ·  A 33 (32%)

[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 > |     ---      |33 -  0 - 70 |62 -  0 - 41 |86 -  0 - 17 |
           * B > | 70 -  0 - 33 |    ---      |62 -  0 - 41 |86 -  0 - 17 |
             C > | 41 -  0 - 62 |41 -  0 - 62 |    ---      |86 -  0 - 17 |
             D > | 17 -  0 - 86 |17 -  0 - 86 |17 -  0 - 86 |    ---      |

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

[Condorcet Loser]
  Condorcet Loser: D — 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
A          33  29   0  24  17   0  |   346   3.4
B          29  57   0  17   0   0  |   407   4.0
C          24  17   0  62   0   0  |   312   3.0
D          17   0   0   0  86   0  |   171   1.7

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/bv2162_4htk44_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