| paper | d4-journals-geb-2005-0045 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper's numbered results define share functions, prove consistency properties, and give axiomatic characterizations; none states an algorithmic guarantee or hardness result. The explicit formulas are not presented with a complexity claim or used as computational procedures, so bit (a) fails before a continuous-population mirror can be anchored.
fails bit a — no named computational result to mirror
No result is covered by a computational mirror: the paper's results are axiomatic characterizations, formulas, and consistency statements.
I can’t make an anchored positive case: this paper contains no named computational result of the required kind. Theorem 2.1 characterizes when a share function with specified axioms exists uniquely; Theorem 2.2 gives its formula for weighted marginal contributions. Theorem 3.1 constructs a coalition-structure share function and proves consistency properties, and Proposition 3.2 identifies the Owen and Banzhaf cases. Theorems 4.5, 4.8, and 5.3 give further axiomatic characterizations. None asserts an algorithm, a complexity classification, or hardness. The explicit formula in Theorem 2.2 is not presented or used as a computational result.
One could imagine a continuum of interchangeable players grouped by coalition type, with mass representing each group’s share of the population, and ask how to allocate the grand coalition’s worth. But that would continuize an axiomatic allocation problem; it would not mirror a computational question established by this paper. A computational problem built on that model would be a new extension without a named result here to anchor it.
There are no named computational anchors to defeat. Theorem 2.1, Theorem 2.2, Theorem 3.1, Proposition 3.2, and Theorems 4.5, 4.8, and 5.3 establish formulas, consistency properties, and axiomatic characterizations. None studies an algorithm, a complexity class, or hardness. In particular, Theorem 2.2’s explicit formula does not make computing the share a computational result of this paper.
The best version of the proposed mirror would take interchangeable players as types, represent a type’s prevalence by mass, and ask how to compute each type’s share in the grand coalition’s worth. That is a coherent extension, but it supplies the computational question the paper itself does not ask. To make it a high-multiplicity problem, one must also specify how worth is defined for groups of type-masses and how individual shares become share densities. A symmetric or otherwise structured game could make that plausible, but restricting the model that way still does not turn this paper’s axiomatic theorem into an algorithmic result.
For a general TU-game, a player’s type must capture their behavior in every coalition. Arbitrary coalition-specific synergies can make players distinguishable and leave no small set of types to continuize. Imposing anonymity or repeated-player structure repairs that obstacle, but it is a substantive restriction and the resulting computation problem would be new. Even computing shares from an explicitly listed characteristic function would be a possible algorithmic follow-on; it would not be a continuous mirror of a computational result here.
A continuum treatment of the paper’s allocation rules could be worthwhile as an axiomatic project. Under ChoCo’s stated scope, though, that is precisely the wrong kind of continuity: it continuizes an allocation model without mirroring a computational question. I cannot rule out every useful future extension, but on the material in this paper the case against a worthwhile continuous *mirror* is strong because there is no computational result for a mirror to preserve.
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.