Nine candidates, 25 voters — ranking only five, counted by RCV-IRV¶
Generated from ballot_expressiveness_c9_irv_top5.yaml — do not edit by hand. Regenerate: python STARVote_LH_tabulation_engine/tools_adam/scripts/build_yaml_pages.py.
Method: rcv-irv · 1 seat · Expected winner: Ben
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¶
BOTH LIMITS AT ONCE, and the winner does not move again. Five ranks out of nine, counted by instant runoff: Ben, exactly as in bv2280_37yf8x_irv_full.yaml.
This file is the honest control on the rest of the folder, and it is the one that stops the lesson from overreaching. Ranked Robin's winner DID change when the ballot was capped (Finn → Gus). IRV's did not — because IRV had already lost Finn on the uncapped ballot, for a completely different reason: too few first choices. Truncation and elimination are separate failures, and here stacking them changes nothing.
So "the cap costs you the answer" is a claim about the COUNT as much as the paper. It bites a method that reads the whole ballot, and glances off one that only reads the top of it.
Convention, stated: an unranked candidate is beaten by everyone the voter ranked. A ballot whose five names have all been eliminated is EXHAUSTED — it leaves the count and the majority denominator, which is what a rank cap really does to an instant runoff.
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¶
Each row is one voter's ranking, most-preferred first (N: prefix = N identical ballots).
Ben>Cleo>Dev>Ada>Emma # voter at -0.43
Gus>Hugo>Iris>Finn>Emma # voter at +0.60
Ada>Ben>Cleo>Dev>Emma # voter at -0.67
Iris>Hugo>Gus>Finn>Emma # voter at +0.89
Finn>Gus>Emma>Dev>Cleo # voter at +0.18
Emma>Dev>Cleo>Ben>Finn # voter at -0.13
Gus>Hugo>Iris>Finn>Emma # voter at +0.59
Hugo>Iris>Gus>Finn>Emma # voter at +0.72
Gus>Finn>Emma>Hugo>Iris # voter at +0.34
Hugo>Iris>Gus>Finn>Emma # voter at +0.69
Finn>Gus>Emma>Dev>Cleo # voter at +0.23
Ben>Cleo>Dev>Emma>Ada # voter at -0.30
Ben>Ada>Cleo>Dev>Emma # voter at -0.51
Iris>Hugo>Gus>Finn>Emma # voter at +0.89
Emma>Dev>Cleo>Finn>Ben # voter at -0.05
Gus>Hugo>Iris>Finn>Emma # voter at +0.60
Finn>Gus>Emma>Dev>Cleo # voter at +0.28
Ben>Cleo>Dev>Emma>Ada # voter at -0.40
Hugo>Gus>Iris>Finn>Emma # voter at +0.62
Ada>Ben>Cleo>Dev>Emma # voter at -0.63
Finn>Gus>Emma>Dev>Cleo # voter at +0.27
Ada>Ben>Cleo>Dev>Emma # voter at -0.61
Ada>Ben>Cleo>Dev>Emma # voter at -1.33
Cleo>Dev>Emma>Ben>Finn # voter at -0.23
Ada>Ben>Cleo>Dev>Emma # voter at -1.82
What the engine says¶
Where the votes went. Band thickness is votes; a band leaving an eliminated candidate lands on whoever that ballot ranked next, or on inactive if it ranked nobody who was left.
The count, step by step — the rounds and how the winner is reached:
--- RCV / Instant-Runoff Voting (single winner) ---
Nine candidates, 25 voters — ranking only five, counted by RCV-IRV
Tabulating 25 ballots (ranked ballots).
ROUND 1
Candidate Votes Status
----------- ------- --------
Ada 5 Hopeful
Gus 4 Hopeful
Ben 4 Hopeful
Finn 4 Hopeful
Hugo 3 Hopeful
Iris 2 Hopeful
Emma 2 Hopeful
Cleo 1 Rejected
Dev 0 Rejected
ROUND 2
Candidate Votes Status
----------- ------- --------
Ada 5 Hopeful
Ben 4 Hopeful
Gus 4 Hopeful
Finn 4 Hopeful
Hugo 3 Hopeful
Emma 3 Hopeful
Iris 2 Rejected
Cleo 0 Rejected
Dev 0 Rejected
ROUND 3
Candidate Votes Status
----------- ------- --------
Hugo 5 Hopeful
Ada 5 Hopeful
Gus 4 Hopeful
Ben 4 Hopeful
Finn 4 Hopeful
Emma 3 Rejected
Iris 0 Rejected
Cleo 0 Rejected
Dev 0 Rejected
ROUND 4
Candidate Votes Status
----------- ------- --------
Ben 6 Hopeful
Ada 5 Hopeful
Finn 5 Hopeful
Hugo 5 Hopeful
Gus 4 Rejected
Emma 0 Rejected
Iris 0 Rejected
Cleo 0 Rejected
Dev 0 Rejected
ROUND 5
Candidate Votes Status
----------- ------- --------
Hugo 8 Hopeful
Finn 6 Hopeful
Ben 6 Hopeful
Ada 5 Rejected
Gus 0 Rejected
Emma 0 Rejected
Iris 0 Rejected
Cleo 0 Rejected
Dev 0 Rejected
ROUND 6
Candidate Votes Status
----------- ------- --------
Ben 11 Hopeful
Hugo 8 Hopeful
Finn 6 Rejected
Ada 0 Rejected
Gus 0 Rejected
Emma 0 Rejected
Iris 0 Rejected
Cleo 0 Rejected
Dev 0 Rejected
FINAL RESULT
Candidate Votes Status
----------- ------- --------
Ben 12 Elected
Hugo 9 Rejected
Finn 0 Rejected
Ada 0 Rejected
Gus 0 Rejected
Emma 0 Rejected
Iris 0 Rejected
Cleo 0 Rejected
Dev 0 Rejected
Blank Votes 4 Rejected
Winner(s) — RCV / Instant-Runoff Voting (single winner)
Ben
Full audit — preference matrix, Condorcet, and score distribution¶
--- Smith Set (the generalized Condorcet winner) ---
The smallest group whose every member beats every candidate outside it —
the honest answer to "who is even in contention?".
Smith set (1 of 9): Gus
Outside (8): Ben, Cleo, Dev, Ada, Emma, Hugo, Iris, Finn
One member ⇒ Gus is the Condorcet winner, beating every rival head-to-head.
RCV-IRV winner Ben is OUTSIDE the Smith set. ✗
Every member of the set (Gus) beats Ben head-to-head, yet
RCV-IRV elected Ben anyway. RCV-IRV is not Smith-efficient (nor
Condorcet-efficient) — this is the shape a center squeeze leaves behind.
More: 07_Concepts/topics/smith_set.md
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/ballot_expressiveness_c9_irv_top5.yaml
See also¶
- Ties & tie-breaking (topic hub)
- The tie-breaking ladder (full chain)
- Runoff reversal (worked set)
- Exhausted ballots (untangled)
- Glossary · all cases by method
More cases in this set: bv2280_37yf8x_irv_full · bv2280_37yf8x_rr_full · bv2280_37yf8x_rr_top5 · bv2280_37yf8x_star