Large field (9 candidates) — STAR scales, and Equal Support decides¶

Generated from 06a_c9_b3_large-field-equal-support.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¶

The ballot-visual election: 9 candidates, scored 0–5. STAR handles a big field with no extra machinery — the scoring round is just addition (no elimination rounds, unlike IRV, which would need up to 8).

Carmen (15) and David (14) are the two highest totals, so they're the finalists. In the automatic runoff, 2 of the 3 voters scored BOTH finalists equally (Equal Support); the one voter who preferred Carmen decides it. Carmen wins.

Discussion (Larry): - 9 candidates, one screen — why no rounds? (Scoring is addition.) - Most of the runoff is "Equal Support" — were those votes wasted? (No: they picked the finalists; neutral only on the Carmen-vs-David tie they declared.) - Helena and Gabe got plenty of stars — why aren't they in the runoff? (Only the top two by score are finalists.) - Did the runoff change the result or confirm it? (Confirms here; see 06b_c9_runoff-overturns-leader.yaml for a case where it OVERTURNS the leader.)

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
4,0,5,5,1,3,5,4,0
4,3,5,5,1,3,5,4,1
1,0,5,4,1,3,1,4,0

What the engine says¶

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

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

[STAR Voting]
 Tabulating 3 ballots.
Andre,Blake,Carmen,David,Ella,Fernando,Gabe,Helena,Ira
    4,    0,     5,    5,   1,       3,   5,     4,  0
    4,    3,     5,    5,   1,       3,   5,     4,  1
    1,    0,     5,    4,   1,       3,   1,     4,  0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Carmen        -- 15 -- First place
   David         -- 14 -- Second place
   Helena        -- 12
   Gabe          -- 11
   Andre         --  9
   Fernando      --  9
   Blake         --  3
   Ella          --  3
   Ira           --  1
 Carmen and David advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Carmen        -- 1 -- First place
   David         -- 0
   Equal Support -- 2
 Carmen wins.
   Runoff math:
     3  ballots cast
   − 2  Equal Support (no preference between the two finalists)
     ─
     1  voters with a preference  (majority = 1)
           Carmen 1 (100%)  ·  David 0 (0%)

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

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

[Condorcet Loser]
  Condorcet Loser: Ira — 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
Andre      0  2  0  0  1  0  |     9   3.0
Blake      0  0  1  0  0  2  |     3   1.0
Carmen     3  0  0  0  0  0  |    15   5.0
David      2  1  0  0  0  0  |    14   4.7
Ella       0  0  0  0  3  0  |     3   1.0
Fernando   0  0  3  0  0  0  |     9   3.0
Gabe       2  0  0  0  1  0  |    11   3.7
Helena     0  3  0  0  0  0  |    12   4.0
Ira        0  0  0  0  1  2  |     1   0.3

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/06a_c9_b3_large-field-equal-support.yaml

Large field (9 candidates) — STAR scales, and Equal Support decides¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶