| paper | d4-journals-geb-2016-0070 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | yes |
other→P discrete result → its continuous mirror
Answer: Polynomial-time solvable: rational type-consistent utilities can be constructed, or nonexistence determined, in time polynomial in \(m,\tau,L\). · discrete side: other · adjudication: proved
full proof & adversarial review →
Theorem 2
statement extracted from the paper’s text layer
Given atomless unit-mass populations with finite male and female type sets, rational type masses, strict rankings over counterpart types, and an ex-post-stable mass assignment \(x\) represented by stable measurable matchings, can one construct type-consistent utilities such that \(x\) lies in the transferable-utility core against every coalition taking equal masses from both sides and rematching internally?
A balanced atomless matching market with finite preference types and rational masses; the assignment is a mass coupling, each type receives a lottery over counterpart types, and the output is a consistent type-utility profile supporting that assignment in the core against equal-mass coalitions.
Theorem 2 relies on a finite well-ordered stable decomposition, and the paper does not establish a corresponding measurable decomposition for mass assignments.
fatal: False
Covers Theorem 2's stability-to-core supporting-utility construction over type masses; leaves Theorem 1, Proposition 1, and the many-to-one extension unresolved.
This paper has no eligible computational anchor under your rule. It proves structural and economic claims, but none classifies a problem as tractable, hard, FPT, or otherwise computationally difficult.
The nearest candidates are Theorem 1, proved here: for every preference profile and every assignment that is sd-efficient at that profile, there is a consistent utility profile under which the assignment maximizes ex-ante utilitarian welfare; and Theorem 2, also proved here: with strict preferences, every ex-post stable probabilistic assignment belongs to the core of the associated TU game for some consistent utility profile. Proposition 1 characterizes sd-efficiency through weak acyclicity, but it does not state a complexity result. These are not eligible anchors, so I cannot honestly assign them continuous problems and predict a complexity class as if the paper had made a computational claim.
Theorem 2 is the nearest research lead: one could study large markets with repeated worker and employer categories, model each category by its preference ranking and population mass, and ask whether a stable mass assignment is in the core for some consistent type utilities. But that would be a new high-multiplicity extension. In the paper, probabilistic assignments make the outcome fractional while the society remains finite; they do not make the population continuous. The lack of a named computational result is the decisive limitation on a positive case here.
The proponent identifies the strongest objection: this paper has no named computational result to continue. Theorem 1 and Theorem 2 are existence claims about utility profiles; Proposition 1 is an order-theoretic characterization. None states the complexity of a decision or optimization problem, or gives an algorithm with a running-time claim. “Constructively prove” describes how the authors establish a witness exists; it does not supply the computational question that ChoCo’s mirrors are meant to classify.
The best candidate is a large two-sided market with repeated worker and employer categories, rational masses, and rankings over counterpart categories. One could ask whether a stable mass assignment admits type utilities that put it in the core. That is a coherent research question. But it changes the paper’s object: the theorem takes a lottery over assignments of named individuals as given and establishes a welfare or core property for it. To make the category version computational, one must add a task—such as finding an assignment, testing stability, or constructing supporting utilities—that the paper does not pose. The connection is an economic analogy, not a computational result whose population axis can be continued.
The same issue holds for the other two possible anchors. Proposition 1’s acyclicity criterion concerns a relation on individual man–woman pairs. Aggregating people into types could yield a related graph on type pairs, but that would be a new characterization in a new model. Theorem 1’s utility construction could likewise inspire a type-level construction, yet the paper makes no complexity claim about computing that witness. Theorem 2 is the most promising lead because its core condition concerns coalitions, but a continuum version needs a new definition of measurable coalitions and of admissible mass deviations before there is a computational problem to classify.
The paper does study probabilistic, fractional assignments, but that makes the outcome fractional while the agents remain finite and individually identified. That fact alone is not an objection; it does, however, underline how much new modeling is needed to make the population continuous.
I cannot establish that no continuous matching question in any scenario would be worthwhile. A category-based large-market model could be valuable adjacent research. The negative case is strongest—and less universal—on ChoCo’s stated remit: this paper offers no computational result to mirror, and its best large-market extension would need to create a new computational problem rather than continuize one the paper actually studies.
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.