| paper | d4-journals-mss-2025-0042 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 5 and Theorem 6 are axiomatic results: neither gives an algorithm, complexity bound, hardness result, or computational formulation used to compute. The proposed population repair would add a new aggregate model, so it cannot supply the missing computational anchor.
fails bit a — no named computational result to mirror
No continuous mirror covers the paper's named results; the suggested population repair would be a separate problem.
The best honest positive-side answer is that this paper has no named computational result to anchor a continuous mirror on. Theorem 5, proved here, says that an RCF \(p\) on an arbitrary nonempty menu set has a rationalisable general Luce model if and only if it satisfies strong cyclical independence; SCI also implies congruence of its support function. Theorem 6, also proved here, says that SCI implies the choice axiom. These are characterisation results, not complexity or algorithmic results.
A population of agents whose types encode choice behavior could be a separate model, but this paper’s \(p(x,E)\) is a single decision-maker’s probability of choosing \(x\) from \(E\). Its continuity is in choice probabilities, not in the population. Without a qualifying computational anchor from the paper, I can’t state the requested per-anchor continuous problems or predict their complexity without inventing a connection the authors’ results do not establish.
The paper has no computational result to mirror. Theorem 5 characterizes when one person’s random choice function has a rationalisable general Luce model; Theorem 6 shows that strong cyclical independence implies the choice axiom. Neither asserts the complexity of a computational problem. Under ChoCo’s stated gate, that is decisive: there is no named algorithmic result here whose population version could be the proposed mirror.
The strongest rescue would be to pose a new computational task around the characterizations—for example, given rational choice probabilities on finitely many menus, decide whether they satisfy SCI, or find the smallest change to observed data that makes them do so. That may be useful work, but the recognition question takes a single random choice function as input. It stays the same whether its probabilities are written as decimals or as population percentages; the population is not the object being continuized.
A more ambitious rescue would treat observed choice shares as a continuum of people and ask how much mass must be moved between behavioral types to make the aggregate satisfy SCI. That is a different model. The paper’s \(p(x,E)\) describes randomness in one decision-maker’s choice, not the fraction of a heterogeneous population choosing \(x\). Aggregating people can produce choice probabilities that fail SCI even when each person has a Luce model, so the theorem does not carry over as the characterization of that population. Defining the types, allowable changes, and repair objective would supply a new problem, rather than mirror one established in the paper.
That distinction leaves room for a separate study of computational methods for choice-data validation or repair. It does not make this paper a continuous-population computational-social-choice paper. The negative case is strongest at the programme’s entry gate: the paper offers axiomatic characterizations, but no computational result for continuization to mirror.
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.