| paper | d4-journals-mss-2026-0015 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
Proposition 4.1 constructs fairness violations, while Propositions 4.2–4.5 and 6.1 establish fairness properties or their failure. The empirical section reports heuristic searches without a named algorithmic guarantee or complexity result. Finding the minimum mass removal that changes a committee would be a new computational question, not a mirror anchored in these results.
fails bit a — no named computational result to mirror
A mass-based ILVB restatement would cover Proposition 4.1's loser-bloc violations for Scottish STV, Meek STV, and EAR; it supplies no computational mirror for the other propositions or the empirical findings.
I can’t make a qualifying case from this paper: it contains no named result classifying a computational problem as tractable, hard, FPT, or similar. Its numbered propositions establish fairness properties and construct profiles with violations; the empirical section uses heuristic searches but gives no named complexity result.
The closest candidate is Proposition 4.1, proved here: for every \(k>0\), Scottish STV, Meek STV, and the expanding approvals rule each admit a profile where removing ballots that rank only losing candidates changes the winner set to a disjoint committee. A continuous version could treat ballot types as having rational masses and ask whether removing mass supported only on losers changes the committee. But that is a continuized fairness criterion, which is axiomatic rather than computational under ChoCo’s scope. Turning it into a minimum-mass search problem would be a new question, not a mirror anchored in the proposition.
So there is no honest anchor, lead mirror, or expected complexity outcome to provide here. The paper offers a plausible high-multiplicity setting—large electorates with mass distributed over ballot types—but its results do not supply the computational result this assignment requires.
The strongest case against a mirror is a scope objection: this paper gives no named result about computational complexity. Proposition 4.1 is the closest anchor, but it proves that certain rules admit profiles where removing losing-candidate ballots changes the committee. Propositions 4.2–4.5 establish fairness properties, and Section 5 reports heuristic searches without a complexity classification. A continuous version of ILVB is therefore an axiomatic question, outside ChoCo’s computational scope. Optimizing the mass that must be removed to change a committee would be a new computational problem, not a mirror of Proposition 4.1.
That does not support the stronger claim that no worthwhile mirror exists in any scenario. The paper’s own profiles aggregate voters by ballot type, and large elections with many repeated truncated ballots are a sensible high-multiplicity regime. A natural computational question would be how much mass must be removed from specified ballot types to change a committee or its party composition. The paper’s empirical search gives that question some motivation, even though it does not establish it as a result to mirror.
So the case against is strong only under the assignment’s anchor requirement: this paper supplies no qualifying computational result. I cannot honestly defend the universal claim that no worthwhile continuous mirror is possible; the best candidate is plausible, but would extend the paper’s research question.
The adversarial triple: the proponent anchors on up to three named results; the opponent sees that case and must defeat every anchor; the judge decides which case convinced it. These are the pipeline’s own outputs, generated by tools/triple_run.py — no human edited them. The paper’s own text is not reproduced here beyond the quoted statement above.