Large field (9 candidates) — the runoff OVERTURNS the score leader¶

Generated from 06b_c9_runoff-overturns-leader.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: Carmen

Scenario¶

STAR's headline move, in a 9-candidate field with just 3 voters. Andre has the highest score total (9 stars), so he leads the scoring round — but in the automatic runoff a 2-of-3 majority prefers Carmen, so Carmen wins 2–1.

STAR elects the majority-preferred Carmen, not the highest-scoring Andre: the runoff is the majority check that stops a high-ceiling / low-floor candidate from winning on intensity alone. (Carmen is also the Condorcet winner.)

Discussion (Larry): - "Andre got the most stars — why didn't he win?" (The runoff asks a different question: which finalist do MORE voters prefer? That's Carmen, 2–1.) - Contrast 06a_c9_b3_large-field-equal-support.yaml, where the runoff merely CONFIRMS the scoring leader. Same method, two different jobs the runoff does.

Ballots¶

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

Andre,Blake,Carmen,David,Ella,Fernando,Gabe,Helena,Ira
5,3,0,2,1,1,1,1,0   # intense Andre voter (Andre 5, Carmen 0)
2,0,3,1,0,2,0,1,1   # prefers Carmen over Andre
2,1,3,0,1,0,2,0,1   # prefers Carmen over Andre

What the engine says¶

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

[Runoff Reversal]
 - Score Round Winner(s) = (Andre)
 - Runoff Round Winner   = (Carmen)
  Candidate Andre earned the highest total score, but
  Candidate Carmen 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 3 ballots.
Andre,Blake,Carmen,David,Ella,Fernando,Gabe,Helena,Ira
    5,    3,     0,    2,   1,       1,   1,     1,  0
    2,    0,     3,    1,   0,       2,   0,     1,  1
    2,    1,     3,    0,   1,       0,   2,     0,  1

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Andre         -- 9 -- First place
   Carmen        -- 6 -- Second place
   Blake         -- 4
   David         -- 3
   Fernando      -- 3
   Gabe          -- 3
   Ella          -- 2
   Helena        -- 2
   Ira           -- 2
 Andre and Carmen advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Carmen        -- 2 -- First place
   Andre         -- 1
   Equal Support -- 0
 Carmen wins.
   Runoff math:
     3  ballots cast
   − 0  Equal Support (no preference between the two finalists)
     ─
     3  voters with a preference  (majority = 2)
           Carmen 2 (67%)  ·  Andre 1 (33%)

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

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
                 |   * Andre    |    Blake    |  * Carmen   |    David    |     Ella    |   Fernando  |     Gabe    |    Helena   |     Ira     |
-------------------------------------------------------------------------------------------------------------------------------------------------
       * Andre > |     ---      | 3 - 0 - 0   | 1 - 0 - 2   | 3 - 0 - 0   | 3 - 0 - 0   | 2 - 1 - 0   | 2 - 1 - 0   | 3 - 0 - 0   | 3 - 0 - 0   |
         Blake > |  0 - 0 - 3   |    ---      | 1 - 0 - 2   | 2 - 0 - 1   | 1 - 2 - 0   | 2 - 0 - 1   | 1 - 1 - 1   | 2 - 0 - 1   | 1 - 1 - 1   |
      * Carmen > |  2 - 0 - 1   | 2 - 0 - 1   |    ---      | 2 - 0 - 1   | 2 - 0 - 1   | 2 - 0 - 1   | 2 - 0 - 1   | 2 - 0 - 1   | 2 - 1 - 0   |
         David > |  0 - 0 - 3   | 1 - 0 - 2   | 1 - 0 - 2   |    ---      | 2 - 0 - 1   | 1 - 1 - 1   | 2 - 0 - 1   | 1 - 2 - 0   | 1 - 1 - 1   |
          Ella > |  0 - 0 - 3   | 0 - 2 - 1   | 1 - 0 - 2   | 1 - 0 - 2   |    ---      | 1 - 1 - 1   | 0 - 2 - 1   | 1 - 1 - 1   | 1 - 1 - 1   |
      Fernando > |  0 - 1 - 2   | 1 - 0 - 2   | 1 - 0 - 2   | 1 - 1 - 1   | 1 - 1 - 1   |    ---      | 1 - 1 - 1   | 1 - 2 - 0   | 2 - 0 - 1   |
          Gabe > |  0 - 1 - 2   | 1 - 1 - 1   | 1 - 0 - 2   | 1 - 0 - 2   | 1 - 2 - 0   | 1 - 1 - 1   |    ---      | 1 - 1 - 1   | 2 - 0 - 1   |
        Helena > |  0 - 0 - 3   | 1 - 0 - 2   | 1 - 0 - 2   | 0 - 2 - 1   | 1 - 1 - 1   | 0 - 2 - 1   | 1 - 1 - 1   |    ---      | 1 - 1 - 1   |
           Ira > |  0 - 0 - 3   | 1 - 1 - 1   | 0 - 1 - 2   | 1 - 1 - 1   | 1 - 1 - 1   | 1 - 0 - 2   | 1 - 0 - 2   | 1 - 1 - 1   |    ---      |

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

[Condorcet Loser]
  No strict Condorcet loser; jointly weak Condorcet losers: Ella, Helena, Ira (winless — pairwise ties)

[Score Distribution] (how many ballots gave each star rating)
                Score
Candidate  5  4  3  2  1  0  | Total   Avg
Andre      1  0  0  2  0  0  |     9   3.0
Blake      0  0  1  0  1  1  |     4   1.3
Carmen     0  0  2  0  0  1  |     6   2.0
David      0  0  0  1  1  1  |     3   1.0
Ella       0  0  0  0  2  1  |     2   0.7
Fernando   0  0  0  1  1  1  |     3   1.0
Gabe       0  0  0  1  1  1  |     3   1.0
Helena     0  0  0  0  2  1  |     2   0.7
Ira        0  0  0  0  2  1  |     2   0.7

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 01_STAR/02_Examples/cases/06b_c9_runoff-overturns-leader.yaml

Large field (9 candidates) — the runoff OVERTURNS the score leader¶

Scenario¶

Ballots¶

What the engine says¶

Full audit — preference matrix, Condorcet, and score distribution¶

See also¶