| paper | d4-journals-jet-2014-0065 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
No named result asserts an algorithm, complexity bound, computational hardness, or a solver-backed formulation; the theorems concern axiomatic compatibility and existence. A cohort-based computational project would add a population model and objective that this paper does not specify, so it cannot supply a computational mirror of a result here.
fails bit a — no named computational result to mirror
No result is covered by a computational mirror; the theorems and lemmas concern axiomatic impossibility, existence, and allocation-rule properties.
This paper has no named computational result to anchor a continuous mirror on. Theorem 1, proved in the paper, says that on the stated domain of linear, time invariant economies, no allocation rule can satisfy Pareto efficiency, \(\varepsilon\)-no-domination, and \(\varepsilon'\)-equal treatment of equals when both parameters are positive. Theorem 2 establishes the corresponding trade-off between weakening the fairness conditions and limiting the generations compared. The later theorems extend these axiomatic results to an infinite horizon. None asserts that a computational problem is in P, NP-hard, FPT, or otherwise classifies its complexity.
There is a tempting population story: treat many people in each generation as a cohort and represent cohorts by masses. But the paper assigns one consumption bundle to each time-ordered generation; its sequential fairness condition depends on which generations are adjacent. A cohort-mass model would need to add within-generation agents and specify how their resources and preferences aggregate. That could motivate a new computational problem, but it would not mirror a computational result of this paper. The paper’s goods are already divisible; its population is not continuized.
The strongest case against a mirror is that the paper has no computational result to mirror. Theorem 1 rules out an allocation rule satisfying three axioms across a broad domain of economies; Theorem 2 classifies which weakenings restore existence. The later theorems extend those claims to an infinite horizon. None classifies the complexity of a decision or search problem. And the economies include arbitrary continuous production correspondences and preference relations, with no finite input encoding or notion of instance size. Divisible goods do not supply that missing computational problem.
A plausible repair would restrict the model to finitely represented technologies and preferences, then ask for an efficient allocation meeting some fairness conditions, or for one minimizing fairness violations. But the paper does not select such a task. Its impossibility results concern rules defined over whole domains, not the cost of computing an allocation for a given economy. Choosing an encoding, a fairness objective, and an algorithmic output would create a new problem; a complexity result for it would not be a computational mirror of these theorems.
The best population scenario is to treat each generation as a large cohort of people with common preferences and per-capita consumption. That can make cohort sizes into masses, but the paper’s comparisons are between time-indexed generations, especially successive ones. Keep the dates to preserve those comparisons, and the population dimension is an added feature of a new model. Collapse dates into types, and the ordering, adjacency, and changing capital position that drive the axioms are lost. Make time itself continuous, and there is no immediate successor generation: sequential solidarity either becomes vacuous for individual dates of measure zero or needs a new local-comparison axiom. The paper’s countably infinite horizon does not change this; countably many ordered generations are not a continuous population.
A cohort-based algorithmic allocation project could still be worthwhile, and that is the weak point in a categorical rejection: the authors might recognize such an extension as related work. But no choice of cohort story supplies the missing computational target while preserving the paper’s central object and results. On the material here, the case against a continuous mirror is strong.
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.