| paper | d4-conf-atal-2008-0027 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Theorems 7 and 8 characterize an allocation rule through axioms; neither states a computational result. Section 7.1 gives an \(O(n)\) cost only after the grand-coalition Shapley value is already known, and that discussion is not a named result. Without an eligible result to anchor, the proposed continuous extension cannot qualify as a mirror under the stated criteria.
fails bit a — no named computational result to mirror
No named computational result is covered. Theorems 7 and 8 give axiomatic results; Section 7.1 discusses computing smaller-coalition allocations once the grand-coalition Shapley value is known.
I can’t make the requested anchor-based case: the paper has no numbered computational-complexity result. None of its theorems or lemmas says that a problem is in P, NP-hard, FPT, or otherwise classifies its complexity.
The closest results are Theorems 7 and 8, both proved here. Theorem 7 says the anonymity-proof Shapley value satisfies Pareto efficiency, the weak-null property, weak-symmetry, weak-additivity, and best-approximate-monotonicity. Theorem 8 says it is the unique solution concept satisfying weak-null, weak-symmetry, weak-additivity, and best-approximate-monotonicity. These are axiomatic characterizations, not computational results. Section 7.1 discusses costs—the value for each smaller coalition can be calculated in \(O(n)\) time once the grand-coalition Shapley value is known—but that discussion is unnumbered, and it does not establish a polynomial-time algorithm for computing that Shapley value.
A continuous-population extension is imaginable: let society have mass over skill-portfolio types, define coalition value on aggregate skill quantities, and seek an allocation of value across those quantities that preserves the paper’s efficiency and anonymity-proofness goals. But the paper supplies no eligible named result to anchor that as a ChoCo mirror. It would also require extending its set of distinct, indivisible skills to repeated or divisible skill quantities. I would not present that conjectural extension as a qualifying continuous problem under the requested rules.
I would not select this paper for ChoCo. The decisive issue is that it has no numbered result classifying the complexity of a computational problem. Theorems 7 and 8 characterize an allocation rule axiomatically; Theorems 1–6 are impossibility and implication results about axioms. Section 7.1 is the closest computational hook: it gives an \(O(n)\) cost for computing a smaller-coalition allocation *after* the grand-coalition Shapley value is known. That conditional cost is not a complexity result about computing the paper’s main object.
The strongest possible population mirror would group firms with the same portfolios of interchangeable skill copies, represent their prevalence as mass, and define coalition value over aggregate skill quantities. But the paper’s primitive is \(v:2^T\to\mathbb R\), which may distinguish every subset of skills, and its skills are unique. In the general model, an exact type must retain skill identity, so repeated types do not compress the instance. Restricting \(v\) to depend only on counts of interchangeable copies makes a coherent new model, but removes the identity-specific structure that motivates the paper. Also, anonymity-proofness concerns an agent hiding part of its own skill set; in a nonatomic population, an individual has zero mass. Making the strategic actor a positive-mass cohort could repair that, but it changes the unit of manipulation.
Neither repair produces a computational mirror of a named result. One could study computation for a measure-valued game, but that would require a new input model and new computational question; the paper supplies no complexity claim for it to mirror. The universal claim that no useful adjacent project could ever be formulated is stronger than the evidence supports. The narrower negative case is strong: any plausible continuous extension here is a new continuous-skill or axiomatic project, not a worthwhile mirror of this paper for ChoCo.
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.