| paper | d4-journals-geb-2008-0007 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The paper has no named computational result to anchor a mirror: its numbered Results 1–5 report experimental findings, and its mechanism properties are theoretical. A district model over distributions of preference and priority types could be a follow-on, but modeling aggregate reporting behavior would add a question the paper does not computationally formulate.
fails bit a — no named computational result to mirror
No result is mirrored. The experimental findings and theoretical properties of the Boston, Gale–Shapley, and TTC mechanisms remain outside a computational mirror of this paper.
The strongest plausible scenario is a large public school district: many applicants, but only a moderate number of distinct preference and priority types. A type would include a family’s complete ranking of schools and its priority positions; \(\mu_t\) would be that type’s share of applicants. School capacities would scale with the population. One could ask for the mass of each type assigned to each school under Boston, Gale–Shapley, and TTC, then compare truthful reporting and aggregate welfare.
That is a plausible high-multiplicity school-choice model, but this paper gives no eligible computational anchor for it. It has no numbered Theorem, Lemma, Corollary, or Proposition asserting a complexity result. Its numbered “Results 1–5” report experimental findings—for example, Result 5 says TTC achieved significantly higher average efficiency than Boston and Gale–Shapley in each information setting. Those findings are not claims about computational complexity, and turning them into a computational mirror would go beyond what the paper establishes. The mechanism properties discussed in Section 2 are also not computational results.
So I cannot give a prover-ready continuous problem per anchor without inventing an anchor the paper does not contain. The district scenario is a credible direction for a separate population-level study, but the paper does not supply a named computational result whose hardness might dissolve, transfer, or become continuum-specific.
The district scenario is plausible, but it does not supply a computational result from this paper to mirror. The paper’s numbered Results 1–5 are experimental findings about human choices and treatment averages. Result 5, for example, reports that TTC achieved higher average efficiency in the experiment. It does not assert the complexity of computing an outcome, an equilibrium, or an optimum. The mechanism properties in Section 2 are theoretical properties of the rules, not computational results; turning them into a complexity question would start a different project.
The proposed mass model could ask what assignments and welfare follow from distributions of preferences and priorities. But to compare truthful reporting or efficiency under different information conditions, it also needs a model of how agents choose reports. The paper measures that behavior experimentally; it does not specify a response rule that a population model could simply aggregate. Adding beliefs, risk attitudes, or equilibrium behavior could make a coherent new model, but those additions would define the question rather than continuize a result in this paper.
So the strongest case against is narrow but firm: even granting that large school districts make high multiplicity sensible, this paper offers no named computational claim for ChoCo to continuize. A continuum study of these mechanisms might be worthwhile on its own, but the district proposal is a follow-on to the paper’s subject matter, not a continuous mirror of its findings. I cannot establish that no useful scenario exists; I can say the case for a mirror of this paper has no computational anchor.
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.