Crowded field, rung 7 — 7 candidates, 65 voters, counted by STAR¶
Generated from crowded_field_c7_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: Clara
Official tie-break (lot) order: Ana > Bruno > Clara > Diego > Elsa > Felix > Greta — consulted only if every deterministic tiebreaker stays tied (how the ladder works).
Scenario¶
RUNG 3 — seven candidates, and the score ballot runs out of room.
Clara (9) and Felix (16) join, one on each side again, both closer in than the last pair. Diego STILL beats every one of the other six head-to-head — six wins out of six, the Condorcet winner for the third rung running, and Ranked Robin returns him (crowded_field_c7_ranked_robin.yaml).
STAR does not. Clara, standing two steps from Diego, edges him in the scoring round 225 to 219. Both reach the runoff — so this is NOT the top-two rule discarding anyone, the mechanism people usually reach for — and Clara wins it 23–17, with 25 of the 65 voters expressing no preference at all between the two. That is the lesson in one line: seven candidates on a six-rung ballot (0–5) leaves little room to separate two candidates standing near each other, so a preference that is perfectly real on the spectrum is not on the paper.
Read the pairwise matrix against the score totals. Diego wins every column and loses the election. On the ranked ballots of the same voters he beats Clara 36–29 (crowded_field_c7_ranked_robin.yaml); on this 0–5 ballot that margin has been rounded away.
One warning about this file's [Divergence from STAR] block: it converts scores to ranks to guess at RCV-IRV and Choose-One, and the engine's own note says how many ballots carry tied scores. Take those two results from crowded_field_c7_irv.yaml instead, where the ballots are real rankings.
Construction: build_ladder.py in this folder. 65 voters in seven blocs at 0, 4, 8, 12, 16, 20, 24 (sizes 6, 10, 13, 9, 12, 8, 7); candidates fixed at Ana 1 · Bruno 6 · Clara 9 · Diego 11 · Elsa 14 · Felix 16 · Greta 22; utility = minus distance; scores = each bloc's own min-max scaling onto 0–5. Nothing is tuned, and no count at any rung is settled by a tie-break.
Ballots¶
Row 1 = candidate names; each later row is one voter's 0–5 scores (a N × prefix = N identical ballots).
Count:Ana,Bruno,Clara,Diego,Elsa,Felix,Greta
6:5,4,3,3,2,1,0 # bloc at 0
10:5,5,4,3,2,2,0 # bloc at 4
13:3,5,5,4,3,2,0 # bloc at 8
9:0,2,4,5,4,4,0 # bloc at 12
12:0,2,3,3,4,5,3 # bloc at 16
8:0,1,2,3,4,4,5 # bloc at 20
7:0,1,2,2,3,4,5 # bloc at 24
What the engine says¶
The count, step by step — the rounds and how the winner is reached:
[Divergence from STAR]
STAR = Clara
Choose-One (Plurality) = Ana (differs from STAR)
RCV-IRV = Felix (differs from STAR)
Approval = Diego (differs from STAR)
Note: 65 of 65 ballots (100%) had equal non-zero scores, so their ranks
were decided by candidate priority order. The RCV-IRV result may be
an artifact of score-to-rank tie-breaking rather than a deep
difference.
Note: Ranked Robin (RCV-RR) agrees with STAR, so RCV-IRV is the lone
outlier — the classic center-squeeze signature.
Full round-by-round reports (generated for review):
RCV-IRV rounds: cases_tabulated/crowded_field_c7_star_RCV-IRV_tabulated.txt
--- STAR Voting Method (single winner) ---
[STAR Voting]
Tabulating 65 ballots.
Count × Ana,Bruno,Clara,Diego,Elsa,Felix,Greta
13 × 3, 5, 5, 4, 3, 2, 0
12 × 0, 2, 3, 3, 4, 5, 3
10 × 5, 5, 4, 3, 2, 2, 0
9 × 0, 2, 4, 5, 4, 4, 0
8 × 0, 1, 2, 3, 4, 4, 5
7 × 0, 1, 2, 2, 3, 4, 5
6 × 5, 4, 3, 3, 2, 1, 0
[STAR Voting: Scoring Round]
The two highest-scoring candidates advance to the next round.
Clara -- 225 -- First place
Diego -- 219 -- Second place
Elsa -- 208
Felix -- 208
Bruno -- 196
Ana -- 119
Greta -- 111
Clara and Diego advance.
[STAR Voting: Automatic Runoff Round]
The candidate preferred in the most head-to-head matchups wins.
Clara -- 23 -- First place
Diego -- 17
Equal Support -- 25
Clara wins.
Runoff math:
65 ballots cast
− 25 Equal Support (no preference between the two finalists)
──
40 voters with a preference (majority = 21)
Clara 23 (57%) · Diego 17 (42%)
[STAR Voting: Winner — STAR Voting Method (single winner)]
Clara
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
| Ana | Bruno | * Clara | * Diego | Elsa | Felix | Greta |
---------------------------------------------------------------------------------------------------------------------
Ana > | --- | 6 - 10 - 49 |16 - 0 - 49 |16 - 0 - 49 |16 - 13 - 36 |29 - 0 - 36 |29 - 9 - 27 |
Bruno > | 49 - 10 - 6 | --- |16 - 13 - 36 |29 - 0 - 36 |29 - 0 - 36 |29 - 0 - 36 |38 - 0 - 27 |
* Clara > | 49 - 0 - 16 |36 - 13 - 16 | --- |23 - 25 - 17 |29 - 9 - 27 |29 - 9 - 27 |38 - 12 - 15 |
* Diego > | 49 - 0 - 16 |36 - 0 - 29 |17 - 25 - 23 | --- |38 - 0 - 27 |38 - 0 - 27 |38 - 12 - 15 |
Elsa > | 36 - 13 - 16 |36 - 0 - 29 |27 - 9 - 29 |27 - 0 - 38 | --- |19 - 27 - 19 |50 - 0 - 15 |
Felix > | 36 - 0 - 29 |36 - 0 - 29 |27 - 9 - 29 |27 - 0 - 38 |19 - 27 - 19 | --- |50 - 0 - 15 |
Greta > | 27 - 9 - 29 |27 - 0 - 38 |15 - 12 - 38 |15 - 12 - 38 |15 - 0 - 50 |15 - 0 - 50 | --- |
[Condorcet Winner]
Condorcet Winner: Clara — matches the STAR winner
[Condorcet Loser]
Condorcet Loser: Greta — loses every head-to-head matchup
[Score Distribution] (how many ballots gave each star rating)
Score
Candidate 5 4 3 2 1 0 | Total Avg
Ana 16 0 13 0 0 36 | 119 1.8
Bruno 23 6 0 21 15 0 | 196 3.0
Clara 13 19 18 15 0 0 | 225 3.5
Diego 9 13 36 7 0 0 | 219 3.4
Elsa 0 29 20 16 0 0 | 208 3.2
Felix 12 24 0 23 6 0 | 208 3.2
Greta 15 0 12 0 0 38 | 111 1.7
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/crowded_field/cases/crowded_field_c7_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)
- Runoff reversal (worked set)
- Glossary · all cases by method
More cases in this set: crowded_field_c3_approval · crowded_field_c3_irv · crowded_field_c3_ranked_robin · crowded_field_c3_star · crowded_field_c5_approval · crowded_field_c5_irv · crowded_field_c5_ranked_robin · crowded_field_c5_star · crowded_field_c7_approval · crowded_field_c7_irv · crowded_field_c7_ranked_robin