| paper | d4-journals-jet-2022-0055 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The three numbered theorems establish equivalences among finite allocation rules, but none states an algorithmic guarantee, hardness result, or computational formulation. A mass-based housing allocation problem may be worthwhile, but it would require defining a new mechanism rather than continuizing a computational result in this paper.
fails bit a — no named computational result to mirror
No named result is covered by a continuous computational mirror; the proposed mass-based housing allocation extension would be a separate project.
Under the required anchor rule, this paper has no eligible computational anchor. Its numbered results do not classify a problem as tractable or hard.
The closest results are Theorem 1, proved here, which says the ascending and descending crawlers choose the same allocation; Theorem 2, proved here, which says the crawler’s allocation is invariant across reference orders that make the profile single-peaked; and Theorem 3, proved here, which says that, for a finite society, the lottery from uniformly random endowments followed by the crawler equals the lottery from uniformly random priority orders followed by serial dictatorship. These are rule-equivalence results, not complexity results. The paper’s statement that the crawler is efficient, individually rational, and strategy-proof is unnumbered and attributed to Bade (2019); it does not assert a complexity bound either.
There is a plausible high-multiplicity setting nearby: a large housing exchange in which many households share the same single-peaked preferences and initial housing category. A mass-based assignment model for those households could be worth studying. But the paper’s theorems concern finite agents and individually distinct objects; extending them would require defining what the crawler and random priority mean for a continuum. That would be a new result, and these equivalence theorems cannot serve as its required computational anchors.
So I cannot give one continuous computational problem per anchor without misrepresenting the paper. The honest positive case is limited to a possible allocation-theoretic extension, outside the requested ChoCo complexity analysis.
The strongest negative case is that the paper has no computational result for ChoCo to mirror. Theorem 1 says the ascending and descending crawlers produce the same allocation; Theorem 2 says the crawler is invariant across reference orders; Theorem 3 equates two finite lotteries. None classifies the complexity of a computational problem. Asking for a mass version of any of them would pose a new question, not continuize a computational result in this paper.
Theorem 3 is the closest candidate, but its finite setup is doing essential work: it pairs the \(n!\) endowment profiles with the \(n!\) priority orders. A continuum has no uniform random permutation, and an i.i.d. priority order over an atomless population has no first agent from whom serial dictatorship can proceed. One could define a different random assignment mechanism or an aggregate transport problem, but that would not be this theorem’s computational mirror. Theorem 1 and Theorem 2 offer even less computational foothold: the crawler’s unit-by-unit removal process becomes a new mass-allocation procedure whose properties and complexity would need to be established from scratch.
I would not claim that no worthwhile continuous model exists in any scenario. A large housing exchange with repeated preference and housing categories is a plausible high-multiplicity setting; a mass assignment problem there could be useful. But it would be an independent computational project, not a mirror of the paper’s results. So the absolute negative claim is weak; the narrower case against treating this paper as a ChoCo computational anchor is strong.
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.