Vote splitting — two chocolates split the majority¶

Generated from vote_splitting.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: DarkChoco

Scenario¶

Election: pick ONE dessert for the party. 36 voters.

Twenty-two of the thirty-six are chocolate lovers — a clear 61% majority. But there are TWO chocolates on the menu, DarkChoco and MilkChoco, and only fourteen voters prefer Vanilla.

Under Choose-One Plurality each voter may name only one flavor, so the chocolate majority splits its vote — 12 for DarkChoco, 10 for MilkChoco — and Vanilla wins with just 14 of 36 (38.9%), a dessert a 61% majority actively dislikes. That is vote splitting / the spoiler effect.

STAR fixes it without asking chocolate to drop a flavor: every voter scores all three 0–5, so a chocolate lover can give BOTH chocolates a high score instead of choosing between them. The two highest totals advance to an automatic runoff, and the winner has majority support head-to-head.

Ballots¶

The ballots as marked — the filled bubble is the score given, and the score is the number in its column:

#	DarkChoco	MilkChoco	Vanilla
1	5	4	0
2	4	5	0
3	2	1	5

The same ballots as the file records them:

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

Count:DarkChoco,MilkChoco,Vanilla
12:5,4,0   # love dark, like milk, no vanilla
10:4,5,0   # love milk, like dark, no vanilla
14:2,1,5   # love vanilla, mild on chocolate

What the engine says¶

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

[Divergence from STAR]
  STAR                   = DarkChoco
  Choose-One (Plurality) = Vanilla   (differs from STAR)

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

[STAR Voting]
 Tabulating 36 ballots.
Count × DarkChoco,MilkChoco,Vanilla
   14 ×         2,        1,      5
   12 ×         5,        4,      0
   10 ×         4,        5,      0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   DarkChoco     -- 128 -- First place
   MilkChoco     -- 112 -- Second place
   Vanilla       --  70
 DarkChoco and MilkChoco advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   DarkChoco     -- 26 -- First place
   MilkChoco     -- 10
   Equal Support --  0
 DarkChoco wins.
   Runoff math:
     36  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     36  voters with a preference  (majority = 19)
           DarkChoco 26 (72%)  ·  MilkChoco 10 (28%)

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

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
                  |  * DarkChoco  | * MilkChoco  |    Vanilla   |
-----------------------------------------------------------------
    * DarkChoco > |      ---      |26 -  0 - 10  |22 -  0 - 14  |
    * MilkChoco > | 10 -  0 - 26  |     ---      |22 -  0 - 14  |
        Vanilla > | 14 -  0 - 22  |14 -  0 - 22  |     ---      |

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

[Condorcet Loser]
  Condorcet Loser: Vanilla — loses every head-to-head matchup — elected by Choose-One (Plurality)!

[Score Distribution] (how many ballots gave each star rating)
                   Score
Candidate   5   4   3   2   1   0  | Total   Avg
DarkChoco  12  10   0  14   0   0  |   128   3.6
MilkChoco  10  12   0   0  14   0  |   112   3.1
Vanilla    14   0   0   0   0  22  |    70   1.9

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/vote_splitting.yaml

Vote splitting — two chocolates split the majority¶

Scenario¶

Ballots¶

What the engine says¶

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

See also¶