Vote splitting — scenario 1 of 3 — the spoiler strikes¶

Generated from vote_splitting_scenario1_spoiler.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¶

A bloc that is a MAJORITY can still LOSE under Choose-One when it splits.

90 voters. 55 are chocolate lovers (a 61% majority), but they split across two chocolates — 30 for DarkChoco, 25 for MilkChoco. The other 35 prefer Vanilla.

Choose-One first choices: Vanilla 35, DarkChoco 30, MilkChoco 25. Vanilla wins with 38.9% even though 61% wanted chocolate — that is the spoiler effect.

STAR lets chocolate lovers score BOTH chocolates, so the bloc is not split and DarkChoco wins. Watch the [Vote-splitting check] confirm it.

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
30:5,4,0   # love dark, like milk, no vanilla
25:4,5,0   # love milk, like dark, no vanilla
35:2,1,5   # 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 35, DarkChoco 30, MilkChoco 25
  Plurality winner: Vanilla (35, 38.9%)
  Bloc 'Chocolate' = DarkChoco, MilkChoco: combined 55 (61.1%); winner Vanilla is OUTSIDE it.
  => VOTE SPLITTING: the 'Chocolate' bloc is an outright majority (55 vs
     Vanilla's 35) but split across 2 candidates, so Vanilla won Choose-One.
     STAR elected DarkChoco.

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

[STAR Voting]
 Tabulating 90 ballots.
Count × DarkChoco,MilkChoco,Vanilla
   35 ×         2,        1,      5
   30 ×         5,        4,      0
   25 ×         4,        5,      0

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   DarkChoco     -- 320 -- First place
   MilkChoco     -- 280 -- Second place
   Vanilla       -- 175
 DarkChoco and MilkChoco advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   DarkChoco     -- 65 -- First place
   MilkChoco     -- 25
   Equal Support --  0
 DarkChoco wins.
   Runoff math:
     90  ballots cast
   −  0  Equal Support (no preference between the two finalists)
     ──
     90  voters with a preference  (majority = 46)
           DarkChoco 65 (72%)  ·  MilkChoco 25 (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 > |      ---      |65 -  0 - 25  |55 -  0 - 35  |
    * MilkChoco > | 25 -  0 - 65  |     ---      |55 -  0 - 35  |
        Vanilla > | 35 -  0 - 55  |35 -  0 - 55  |     ---      |

[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  30  25   0  35   0   0  |   320   3.6
MilkChoco  25  30   0   0  35   0  |   280   3.1
Vanilla    35   0   0   0   0  55  |   175   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_scenario1_spoiler.yaml