The smallest spoiler, fixed — the same seven friends, scoring¶

Generated from 08b_smallest_spoiler_star.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: Milk Chocolate

▶ Live on BetterVoting: vote · results ↗ (election 9cff2d · test BV2296).

Scenario¶

The identical seven friends from 08a, scoring each flavour 0-5 instead of marking one. Nothing about their opinions changed; the ballot simply records what the single mark could not — that a chocolate lover likes BOTH chocolates and does not want vanilla.

Scoring Round: Milk Chocolate 20, Dark Chocolate 18, Vanilla 15 — and note where Vanilla lands. The Choose-One winner finishes LAST of three and is shut out of the runoff entirely; the two chocolates take BOTH finalist slots, which is the split disappearing in the most visible way it can. The Automatic Runoff is therefore Milk Chocolate 4, Dark Chocolate 2, with one voter at Equal Support.

Read the runoff line carefully, because it is easy to narrate wrongly: the 4 is NOT "the four chocolate lovers reunited". Those four split 2-2 between the two chocolates, exactly as they should — they disagree about chocolate. The margin comes from two of the vanilla voters leaning mildly toward milk. What the score ballot fixed was not the chocolate lovers' disagreement; it was that their disagreement no longer costs them the election.

Head-to-head, either chocolate beats Vanilla 4-3. (The permanent BetterVoting description for the SUPERSEDED BV2294 said "the runoff goes to Milk Chocolate 4-3" — that 4-3 is this Milk-versus-Vanilla head-to-head, not the Automatic Runoff, which is Milk versus Dark. BV descriptions cannot be edited, so BV2296 was minted to replace it and states the runoff correctly.)

This is the whole argument in seven ballots. Choose-One did not count the chocolate votes wrongly. It never asked the question whose answer would have changed the result. Live results: https://bettervoting.com/9cff2d/results

Parameters (from the YAML)¶

blocs:
  Chocolate: [Milk Chocolate, Dark Chocolate]

Ballots¶

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

Milk Chocolate,Dark Chocolate,Vanilla
5,4,0   # milk first, dark is a close second, vanilla no thanks
5,3,0   # milk first, dark is fine, vanilla no thanks
4,5,0   # dark first, milk is a close second
3,5,0   # dark first, milk is fine
0,0,5   # vanilla only
1,0,5   # vanilla, and milk chocolate at a pinch
2,1,5   # vanilla, but not fussy

What the engine says¶

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

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

[Vote-splitting check]
  Choose-One first choices: Vanilla 3, Milk Chocolate 2, Dark Chocolate 2
  Plurality winner: Vanilla (3, 42.9%)
  Bloc 'Chocolate' = Milk Chocolate, Dark Chocolate: combined 4 (57.1%); winner Vanilla is OUTSIDE it.
  => VOTE SPLITTING: the 'Chocolate' bloc is an outright majority (4 vs
     Vanilla's 3) but split across 2 candidates, so Vanilla won Choose-One.
     STAR elected Milk Chocolate.

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

[STAR Voting]
 Tabulating 7 ballots.
Milk Chocolate,Dark Chocolate,Vanilla
             5,             4,      0
             5,             3,      0
             4,             5,      0
             3,             5,      0
             0,             0,      5
             1,             0,      5
             2,             1,      5

[STAR Voting: Scoring Round]
 The two highest-scoring candidates advance to the next round.
   Milk Chocolate -- 20 -- First place
   Dark Chocolate -- 18 -- Second place
   Vanilla        -- 15
 Milk Chocolate and Dark Chocolate advance.

[STAR Voting: Automatic Runoff Round]
 The candidate preferred in the most head-to-head matchups wins.
   Milk Chocolate -- 4 -- First place
   Dark Chocolate -- 2
   Equal Support  -- 1
 Milk Chocolate wins.
   Runoff math:
     7  ballots cast
   − 1  Equal Support (no preference between the two finalists)
     ─
     6  voters with a preference  (majority = 4)
           Milk Chocolate 4 (67%)  ·  Dark Chocolate 2 (33%)

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

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
                       |  * Milk Chocolate  | * Dark Chocolate  |      Vanilla      |
-------------------------------------------------------------------------------------
    * Milk Chocolate > |        ---         |    4 - 1 - 2      |    4 - 0 - 3      |
    * Dark Chocolate > |     2 - 1 - 4      |       ---         |    4 - 0 - 3      |
             Vanilla > |     3 - 0 - 4      |    3 - 0 - 4      |       ---         |

[Condorcet Winner]
  Condorcet Winner: Milk Chocolate — 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
Milk Chocolate  2  1  1  1  1  1  |    20   2.9
Dark Chocolate  2  1  1  0  1  2  |    18   2.6
Vanilla         3  0  0  0  0  4  |    15   2.1

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 method_comparisons/split_voting/_main/08b_smallest_spoiler_star.yaml