Felsenthal Ex.2 after the raise — STAR: unmoved, still Ada¶

Generated from bv2146_krk2px_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: Ada

▶ Live on BetterVoting: vote · results ↗ (election krk2px · test BV2146).

Scenario¶

Race 3 of 3 in the Felsenthal runoff-paradoxes election, part 2 of 2 (BV2146, bvid krk2px; BV-confirmed). Source: Dan S. Felsenthal (2010), Appendix A2, Example 2 (continued) — see bv2146_krk2px_irv.yaml for the setup. The same 17 voters after the raise, ranks mapped 5/3/1. Ben's two raised ballots move him 51 → 55 and Cleo 49 → 45; Ada stays 53. Finalists are now Ben and Ada — and Ada still wins the automatic runoff 9–8, exactly as in BV2145. Giving Ben more support changed STAR's finalist pair but not its winner: no more-is-less here, while the same raise flips the IRV race. Live results: https://bettervoting.com/krk2px/results

Ballots¶

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

Ada,Ben,Cleo
5,3,1
5,3,1
5,3,1
5,1,3
5,1,3
3,5,1
3,5,1
3,5,1
3,5,1
1,5,3
1,5,3
3,1,5
3,1,5
3,1,5
3,1,5
1,5,3
1,5,3

What the engine says¶

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

[Divergence from STAR]
  STAR                   = Ada
  Choose-One (Plurality) = Ben   (differs from STAR)

[Runoff Reversal]
 - Score Round Winner(s) = (Ben)
 - Runoff Round Winner   = (Ada)
  Candidate Ben earned the highest total score, but
  Candidate Ada 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 × Ada,Ben,Cleo
    4 ×   3,  5,   1
    4 ×   1,  5,   3
    4 ×   3,  1,   5
    3 ×   5,  3,   1
    2 ×   5,  1,   3

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Ben           -- 55 -- First place
   Ada           -- 53 -- Second place
   Cleo          -- 45
 Ben and Ada advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Ada           -- 9 -- First place
   Ben           -- 8
   Equal Support -- 0
 Ada wins.
   Runoff math:
     17  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     17  voters with a preference  (majority = 9)
           Ada 9 (53%)  ·  Ben 8 (47%)

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

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
                 |    * Ada     |   * Ben     |     Cleo    |
-------------------------------------------------------------
         * Ada > |     ---      | 9 -  0 -  8 | 9 -  0 -  8 |
         * Ben > |  8 -  0 -  9 |    ---      |11 -  0 -  6 |
          Cleo > |  8 -  0 -  9 | 6 -  0 - 11 |    ---      |

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

[Condorcet Loser]
  Condorcet Loser: Cleo — 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
Ada        5  0  8  0  4  0  |    53   3.1
Ben        8  0  3  0  6  0  |    55   3.2
Cleo       4  0  6  0  7  0  |    45   2.6

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/bv2146_krk2px_star.yaml

See also¶