| paper | d4-journals-geb-2018-0061 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Proposition 7 is an axiomatic characterization, and the paper states no named computational result to mirror. Computing a mass-based allocation would be a new problem; the paper also supplies no input model for coalition worths that would make that computation concrete.
fails bit a — no named computational result to mirror
No results are covered: Propositions 1–8 characterize solution concepts or establish axiomatic properties, and the Shapley–Shubik voting-power application is also axiomatic.
This paper contains no named computational result. Propositions 1–8 give axiomatic characterizations and properties of solution concepts; none classifies a computational problem as tractable or hard, or presents an algorithm. For example, Proposition 7, proved in the paper, characterizes the extended Shapley value for partition-function games through efficiency, equal gains in two-player games, and undominated merge-externalities. That is an axiomatic result, not a complexity result.
The closest positive seed is a high-multiplicity setting with many economically similar firms grouped into a few bargaining-relevant types, where coalition worth depends on the masses of types in a coalition and its complement. One could ask how to compute the limiting per-capita extended Shapley allocation. But that would be a new computational question attached to Proposition 7; the paper neither asks nor computes it. So I cannot honestly provide a continuous problem anchored to one of this paper’s computational results. The weakness is decisive: the paper studies finite-player axiomatic characterizations, not computational questions about a population.
The paper has no named computational result to continuize. Propositions 1–8 characterize solution concepts or establish properties of them; none studies an algorithm, a complexity class, or a computational problem. Proposition 7—the proponent’s anchor—says that certain axioms characterize the extended Shapley value. It does not ask how to compute that value. “Compute the limiting per-capita extended Shapley allocation” is a new question attached to the proposition, not its continuous mirror.
The proposed high-multiplicity setting of similar firms is plausible, but it does not fix that gap. To compute an allocation, one must specify how coalition worth is represented as a function of type masses: an arbitrary table, a formula, a circuit, or something else. The paper supplies no such input model. With an arbitrary worth function, there is no finite description of the continuum game; choosing a succinct family creates a new computational problem whose tractability depends on that choice. Alternatively, a continuum analogue of the characterization would ask whether new mass-based axioms select an allocation. That would be axiomatic work, outside ChoCo’s computational scope.
The paper’s closer social-choice result does not provide a firmer anchor. Section 5 applies the axiomatic characterization to the Shapley–Shubik power index for monotonic simple games. In a nonatomic population, changing one voter’s coalition membership changes no mass-defined coalition, so individual pivotality—and thus the individual power being characterized—disappears. Aggregating power by type might preserve a nonzero quantity, but that requires choosing a particular representation of voting games and a new limit question. The paper does not pose or solve either one.
So the negative case is strong against calling any of these proposals a *mirror of this paper*: the paper offers no computational result to mirror, and the most attractive computational proposals require new input models or new observands. It is weaker against the broader claim that a separately formulated continuum computation problem could be worthwhile. A suitably restricted family of coalition games might support one; the paper simply gives no basis for deciding which family or computational question to study.
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.