Vote splitting — two chocolates split the majority¶

Generated from vote_splitting2.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. 360 voters.

220 of the 360 are chocolate lovers — a clear 61% majority. But there are TWO chocolates on the menu, DarkChoco and MilkChoco, and 140 voters prefer Vanilla.

Under Choose-One Plurality each voter may name only one flavor, so the chocolate majority splits its vote — 120 for DarkChoco, 100 for MilkChoco — and Vanilla wins with just 140 of 360 (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.

Parameters (from the YAML)¶

blocs:
  Chocolate: [DarkChoco, MilkChoco]

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
120:5,4,0   # love dark, like milk, no vanilla
100:4,5,0   # love milk, like dark, no vanilla
140:2,1,5   # 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)

[Vote-splitting check]
  Choose-One first choices: Vanilla 140, DarkChoco 120, MilkChoco 100
  Plurality winner: Vanilla (140, 38.9%)
  Bloc 'Chocolate' = DarkChoco, MilkChoco: combined 220 (61.1%); winner Vanilla is OUTSIDE it.
  => VOTE SPLITTING: the 'Chocolate' bloc is an outright majority (220 vs
     Vanilla's 140) but split across 2 candidates, so Vanilla won Choose-
     One. STAR elected DarkChoco.

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

[STAR Voting]
 Tabulating 360 ballots.
Count × DarkChoco,MilkChoco,Vanilla
  140 ×         2,        1,      5
  120 ×         5,        4,      0
  100 ×         4,        5,      0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   DarkChoco     -- 1280 -- First place
   MilkChoco     -- 1120 -- Second place
   Vanilla       --  700
 DarkChoco and MilkChoco advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   DarkChoco     -- 260 -- First place
   MilkChoco     -- 100
   Equal Support --   0
 DarkChoco wins.
   Runoff math:
     360  ballots cast
   −   0  Equal Support (no preference between the two finalists)
     ───
     360  voters with a preference  (majority = 181)
           DarkChoco 260 (72%)  ·  MilkChoco 100 (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 > |       ---       |260 -   0 - 100 |220 -   0 - 140 |
      * MilkChoco > | 100 -   0 - 260 |      ---       |220 -   0 - 140 |
          Vanilla > | 140 -   0 - 220 |140 -   0 - 220 |      ---       |

[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  120  100    0  140    0    0  |  1280   3.6
MilkChoco  100  120    0    0  140    0  |  1120   3.1
Vanilla    140    0    0    0    0  220  |   700   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_splitting2.yaml