| paper | d4-journals-jet-2021-0074 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
None of the named results asserts an algorithm, a hardness result, or a computational formulation used to compute, so no anchor passes bit (a). The paper already models a unit-mass continuum of applicants and derives assignment cutoffs from that population. A type-mass restatement would repeat that model, while the proposed rational-type algorithms would add a new computational agenda.
fails bit a — no named computational result to mirror
No result is covered: the proposed mass-type view restates the continuum applicant model and adds no computational analysis of Theorems 1–9 or the simulations.
The paper’s strongest positive fit is that it takes information acquisition, school assignment, and welfare seriously at the population level. Its main model already has mass \(1\) of applicants, a distribution \(F\) of utility shocks, and an equilibrium informed fraction \(\gamma\). In a high-multiplicity extension, a type could be an applicant’s information cost, \(\mu_t\) the mass of that type, and \(x_t\in[0,\mu_t]\) the mass that acquires information. That is a plausible object for the authors.
But it cannot serve as a new continuous mirror of this paper: the paper itself already continuizes the population. Its setup explicitly builds on the continuum matching framework of Azevedo and Leshno, which relates large finite economies to continuum assignments. A mirror that just replaces applicants with masses would restate the paper’s model.
The closest named result is Theorem 4, proved in the paper. In the symmetric three-school RSD environment, for any equilibrium informed fraction \(\gamma_{Eq}\in\Gamma\), if \(\gamma_{Eq}p\le 1/3\) and \(\gamma_{Eq}<1\), then the socially optimal informed fraction \(\gamma_{SO}\) is strictly greater than \(\gamma_{Eq}\). This is a substantive under-acquisition result, but it is not a computational-complexity result. Theorem 8’s subsidy result and Theorem 9’s comparison with Immediate Acceptance are economic results of the same kind. The simulations do not supply a named complexity classification either.
So, under your anchor rule, the paper contains no named computational result, and there is no eligible anchor or per-anchor mirror problem to state. A computational follow-up could ask for an equilibrium and welfare-maximizing information allocation from rationally represented cost types and utility shocks, but that would be a new algorithmic question about a population model the paper already makes continuous—not a valid continuous mirror anchored in one of its computational results.
The decisive fact is that Artemov already makes the population continuous: the model has mass \(1\) of applicants, represents applicants by distributions of costs and utility shocks, and derives assignments from mass-based cutoffs. The paper even builds on the continuum matching framework and uses it to study learning incentives. A distribution-over-types version would therefore restate or re-encode the paper’s population model.
Theorem 4 is the closest proposed anchor, but it proves a comparative-static welfare claim: under its conditions, the equilibrium informed fraction is below the socially optimal fraction. It gives no complexity classification or algorithmic result to mirror. The strongest computational reformulation would ask for an algorithm to compute equilibrium and optimal learning from finitely represented rational types. In the paper’s three-school setting, that reduces to its scalar cutoff and welfare equations; the paper identifies no computational obstacle there. Moreover, finite type bins would approximate the paper’s atomless cost and shock distributions. That could be a computational extension, but it would not be a continuous mirror of Theorem 4.
Theorem 8’s subsidy result and Theorem 9’s comparison with Immediate Acceptance have the same problem. They establish policy and equilibrium claims in an already continuous population model. Asking an algorithm to find a subsidy or compare equilibrium fractions would add a computational question the paper did not study; it would not supply a missing population continuization. The same applies to the other equilibrium and welfare results.
I cannot rule out every useful algorithmic project one could build from the richer school-choice model. The paper’s many-school simulations, for example, could motivate such work. But that would be a new computational agenda on an existing continuum model. Under the programme’s mirror standard, none of the named results survives as an anchor: the paper has no named computational result, and its population is already the continuous object.
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.