Nine candidates, 25 voters — the 0–5 score ballot¶
Generated from bv2280_37yf8x_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: Finn
▶ Live on BetterVoting: vote · results ↗ (election 37yf8x · test BV2280).
Official tie-break (lot) order: Ada > Ben > Cleo > Dev > Emma > Finn > Gus > Hugo > Iris — consulted only if every deterministic tiebreaker stays tied (how the ladder works).
Scenario¶
THE COARSE BALLOT GETS IT RIGHT. Finn beats all eight rivals head-to-head, and STAR elects them from a ballot that cannot even rank the field.
Nine candidates will not fit on six rungs — 0, 1, 2, 3, 4 and 5 hold six distinct places, so every voter here must give at least two candidates the same score. They actually tie far more than that minimum: about 16% of all candidate pairs go equal on this paper, against a pigeonhole floor of 8%. Most of the flattening is rounding, not the hard limit.
And it does not matter. The preference that decides this election — Finn over everyone — survives the rounding, so STAR returns the Condorcet winner anyway.
Read this file against bv2280_37yf8x_rr_top5.yaml, where the same 25 voters fill in a RANKED ballot capped at five names, the cap New York City and Maine actually use, and the count elects Gus instead. The ballot usually called "more expressive" loses the answer that these six rungs kept.
Construction: build_cases.py in this folder. 25 voters and 9 candidates at frozen positions on one spectrum — Ada −0.73 · Ben −0.37 · Cleo −0.18 · Dev −0.17 · Emma −0.11 · Finn +0.24 · Gus +0.41 · Hugo +0.80 · Iris +0.84; utility = minus the distance; scores = each voter's own min-max scaling onto 0–5; rankings = those same utilities in order. Nothing is tuned to the result, and no count in this folder is settled by a tie-break — that was a search constraint, so every winner here survives any lot rule.
Ballots¶
Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).
Ada,Ben,Cleo,Dev,Emma,Finn,Gus,Hugo,Iris
4,5,4,4,4,2,2,0,0 # voter at -0.43
0,2,2,2,3,4,5,5,5 # voter at +0.60
5,4,4,3,3,2,1,0,0 # voter at -0.67
0,1,2,2,2,3,4,5,5 # voter at +0.89
0,2,3,3,4,5,4,2,1 # voter at +0.18
2,4,5,5,5,3,2,0,0 # voter at -0.13
0,2,2,2,3,4,5,5,5 # voter at +0.59
0,1,2,2,2,4,4,5,5 # voter at +0.72
0,2,3,3,3,5,5,3,3 # voter at +0.34
0,1,2,2,2,4,4,5,5 # voter at +0.69
0,2,3,3,3,5,4,2,2 # voter at +0.23
3,5,5,5,4,3,2,0,0 # voter at -0.30
5,5,4,4,4,2,2,0,0 # voter at -0.51
0,1,2,2,2,3,4,5,5 # voter at +0.89
1,3,5,5,5,4,3,0,0 # voter at -0.05
0,2,2,2,3,4,5,5,5 # voter at +0.60
0,2,3,3,3,5,5,2,2 # voter at +0.28
4,5,4,4,4,2,2,0,0 # voter at -0.40
0,2,2,2,3,4,5,5,5 # voter at +0.62
5,4,4,4,3,2,2,0,0 # voter at -0.63
0,2,3,3,3,5,4,2,2 # voter at +0.27
5,5,4,4,4,2,2,0,0 # voter at -0.61
5,4,3,3,3,2,1,0,0 # voter at -1.33
3,5,5,5,5,3,2,0,0 # voter at -0.23
5,4,3,3,3,2,1,0,0 # voter at -1.82
What the engine says¶
The count, step by step — the rounds and how the winner is reached:
[Divergence from STAR]
STAR = Finn
Choose-One (Plurality) = Ada (differs from STAR)
Approval = Emma (differs from STAR)
--- STAR Voting Method (single winner) ---
[STAR Voting]
Tabulating 25 ballots.
Count × Ada,Ben,Cleo,Dev,Emma,Finn,Gus,Hugo,Iris
4 × 0, 2, 2, 2, 3, 4, 5, 5, 5
2 × 4, 5, 4, 4, 4, 2, 2, 0, 0
2 × 0, 1, 2, 2, 2, 3, 4, 5, 5
2 × 0, 1, 2, 2, 2, 4, 4, 5, 5
2 × 0, 2, 3, 3, 3, 5, 4, 2, 2
2 × 5, 5, 4, 4, 4, 2, 2, 0, 0
2 × 5, 4, 3, 3, 3, 2, 1, 0, 0
1 × 5, 4, 4, 3, 3, 2, 1, 0, 0
1 × 0, 2, 3, 3, 4, 5, 4, 2, 1
1 × 2, 4, 5, 5, 5, 3, 2, 0, 0
1 × 0, 2, 3, 3, 3, 5, 5, 3, 3
1 × 3, 5, 5, 5, 4, 3, 2, 0, 0
1 × 1, 3, 5, 5, 5, 4, 3, 0, 0
1 × 0, 2, 3, 3, 3, 5, 5, 2, 2
1 × 5, 4, 4, 4, 3, 2, 2, 0, 0
1 × 3, 5, 5, 5, 5, 3, 2, 0, 0
[STAR Voting: Scoring Round]
The two highest-scoring candidates advance to the next round.
Finn -- 84 -- First place
Emma -- 83 -- Second place
Cleo -- 81
Dev -- 80
Gus -- 80
Ben -- 75
Hugo -- 51
Iris -- 50
Ada -- 47
Finn and Emma advance.
[STAR Voting: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Finn -- 13 -- First place
Emma -- 12
Equal Support -- 0
Finn wins.
Runoff math:
25 ballots cast
− 0 Equal Support (no preference between the two finalists)
──
25 voters with a preference (majority = 13)
Finn 13 (52%) · Emma 12 (48%)
[STAR Voting: Winner — STAR Voting Method (single winner)]
Finn
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
| Ada | Ben | Cleo | Dev | * Emma | * Finn | Gus | Hugo | Iris |
-------------------------------------------------------------------------------------------------------------------------------------------------
Ada > | --- | 4 - 2 - 19 | 6 - 2 - 17 | 6 - 2 - 17 | 6 - 2 - 17 | 8 - 2 - 15 |10 - 1 - 14 |12 - 0 - 13 |12 - 0 - 13 |
Ben > | 19 - 2 - 4 | --- | 6 - 8 - 11 | 7 - 7 - 11 | 9 - 1 - 15 |11 - 0 - 14 |11 - 1 - 13 |12 - 4 - 9 |13 - 3 - 9 |
Cleo > | 17 - 2 - 6 |11 - 8 - 6 | --- | 1 - 24 - 0 | 3 - 17 - 5 |12 - 0 - 13 |12 - 0 - 13 |16 - 1 - 8 |16 - 1 - 8 |
Dev > | 17 - 2 - 6 |11 - 7 - 7 | 0 - 24 - 1 | --- | 2 - 18 - 5 |12 - 0 - 13 |12 - 0 - 13 |16 - 1 - 8 |16 - 1 - 8 |
* Emma > | 17 - 2 - 6 |15 - 1 - 9 | 5 - 17 - 3 | 5 - 18 - 2 | --- |12 - 0 - 13 |12 - 1 - 12 |16 - 1 - 8 |16 - 1 - 8 |
* Finn > | 15 - 2 - 8 |14 - 0 - 11 |13 - 0 - 12 |13 - 0 - 12 |13 - 0 - 12 | --- |10 - 9 - 6 |17 - 0 - 8 |17 - 0 - 8 |
Gus > | 14 - 1 - 10 |13 - 1 - 11 |13 - 0 - 12 |13 - 0 - 12 |12 - 1 - 12 | 6 - 9 - 10 | --- |17 - 4 - 4 |17 - 4 - 4 |
Hugo > | 13 - 0 - 12 | 9 - 4 - 12 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 0 - 17 | 4 - 4 - 17 | --- | 1 - 24 - 0 |
Iris > | 13 - 0 - 12 | 9 - 3 - 13 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 1 - 16 | 8 - 0 - 17 | 4 - 4 - 17 | 0 - 24 - 1 | --- |
[Condorcet Winner]
Condorcet Winner: Finn — matches the STAR winner
[Condorcet Loser]
Condorcet Loser: Ada — 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
Ada 6 2 2 1 1 13 | 47 1.9
Ben 6 5 1 9 4 0 | 75 3.0
Cleo 4 6 7 8 0 0 | 81 3.2
Dev 4 5 8 8 0 0 | 80 3.2
Emma 3 6 12 4 0 0 | 83 3.3
Finn 5 7 5 8 0 0 | 84 3.4
Gus 6 7 1 8 3 0 | 80 3.2
Hugo 8 0 1 4 0 12 | 51 2.0
Iris 8 0 1 3 1 12 | 50 2.0
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/ballot_expressiveness/cases/bv2280_37yf8x_star.yaml
See also¶
- Methods disagree on this election — its entry in the divergence review ledger
- Condorcet efficiency (topic hub)
- Ties & tie-breaking (topic hub)
- The tie-breaking ladder (full chain)
- Glossary · all cases by method
More cases in this set: ballot_expressiveness_c9_irv_top5 · bv2280_37yf8x_irv_full · bv2280_37yf8x_rr_full · bv2280_37yf8x_rr_top5