| paper | d4-journals-geb-2022-0074 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | yes |
P→P discrete result → its continuous mirror
Answer: Exact computation is polynomial-time solvable in \(m,\tau,L\). The specified rational mass IDAM always terminates at the unique student-optimal stable allocation. It has at most \(mD\) proposal rounds, where \(D\) is the common denominator of masses and capacities; its worst-case round count and round-by-round bit complexity are \(2^{\Theta(L)}\), already for \(m=\tau=2\). · discrete side: polynomial · adjudication: proved_with_minor_gaps
full proof & adversarial review →
Proposition 1
statement extracted from the paper’s text layer
Given rational masses \(\mu_t\) over finitely many student types, each with a strict program ranking, score vector, and eligibility, and programs with rational per-capita capacities, compute a stable mass allocation \(x_{t,c}\) that is student-optimal among stable allocations. In a type-level IDAM, each type proposes to its best currently available program and a program may split mass at a score cutoff: does the process terminate and return such an allocation, and what is its complexity in the number of programs, support size, and input bit length?
A finite-support population of student types with rational masses \(\mu_t\), complete rankings, score vectors, and eligibility; per-capita program capacities; and assignment variables \(x_{t,c}\) plus unmatched mass. The type-level IDAM makes preference-ordered proposals and lets programs hold the highest-priority mass up to capacity, splitting a type at a cutoff when needed.
Proposition 1 gives finite termination and correctness but no input encoding or running-time bound, so a complexity analysis of the continuous version needs an explicit computational model.
fatal: False
The mirror covers Proposition 1’s termination and student-optimal stable-outcome claim in the exam-based admissions setting; it leaves the equilibrium claims of Theorems 1 and 2 and the manipulation and equilibrium results for the other mechanisms aside.
I can’t produce a qualifying anchor under your rule: the paper has no named result classifying a computational problem as polynomial-time solvable, hard, or parameterized. Its nearest result is Proposition 1, proved here: assuming every college’s choice function satisfies IRC and contracts are substitutes, if all students use straightforward strategies in the unbounded IDAM, the mechanism terminates after finitely many steps and produces the student-optimal stable outcome. Theorem 1 adds that straightforward strategies form an ex-post equilibrium under those assumptions. These are outcome and incentive results, not computational-complexity results. Proposition 3 characterizes equilibrium outcomes in the Brazilian mechanism; it also gives no complexity classification.
There is a plausible high-multiplicity setting nearby: national university admissions with very large cohorts and many repeated profiles. A type could include a student’s full ranking of programs, exam-score vector, and eligibility or contract terms; its mass is the fraction of applicants with that profile. Program capacities would scale with the applicant population. A natural follow-on problem is: given rational type masses, type rankings and program priorities, and rational per-capita capacities, compute a stable allocation of mass that is student-optimal among stable allocations. The solution would specify \(x_{t,c}\), the mass of type \(t\) assigned to program \(c\), including any unmatched mass.
That is a sensible continuous matching problem, and Proposition 1 makes it relevant to the paper’s benchmark outcome. But it is not a compliant mirror anchor here: the paper does not analyze the complexity of computing that allocation, and the proposed problem leaves out the sequential information and strategic interaction that motivate IDAM. The gap is sharper still for Theorem 1: a continuum game would need a carefully chosen notion of deviation and equilibrium, since an individual deviation has vanishing mass while a type-level deviation can move cutoffs.
So the strongest honest positive case is a credible high-multiplicity *follow-on question* about stable allocations, not a continuous mirror anchored in one of this paper’s named computational results. Its weakest point is that it mirrors the outcome the mechanism implements while dropping the mechanism’s central strategic contribution.
The strongest negative is that this paper has no named result about the computational complexity of a problem. Proposition 1 proves that, under its assumptions, straightforward play in IDAM terminates and produces the student optimal stable outcome. Theorems 1 and 2 concern equilibrium strategies; Propositions 3 and 4 concern equilibrium outcomes and resistance to manipulation. None gives a complexity classification or an algorithmic result of the kind ChoCo seeks. Proposition 1’s finite termination is a correctness property, not a running time bound: the paper specifies no complexity measure or input representation for such an analysis.
The proposed mass allocation problem is a sensible follow-on. Large admissions cohorts and capacities scaled by population make a high multiplicity model plausible, with types that include preferences, scores, and relevant contract details. But computing a stable allocation of mass is a new static matching problem. It does not analyze the complexity of a problem this paper studies, and it removes the menus, changing information, and strategic interaction that make IDAM the paper’s contribution. A richer attempt to preserve those interactions would need a continuum game. There, a single agent’s deviation cannot change aggregate cutoffs or other agents’ menus, so the strategic channel behind the paper’s individual manipulation results changes; positive mass deviations would pose a different, coalition level question.
So the case against a *qualifying mirror* is strong: none of the other analyst’s proposed questions is anchored in a computational result of this paper. The broader claim that no continuous question here could be worthwhile is weaker. A mass matching problem, or a coalition manipulation problem for large admissions cohorts, may be worthwhile in its own right. The case is that those would extend the paper’s subject rather than continuize one of its computational results.
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.