| paper | d4-journals-mss-2013-0012 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Theorem 2 and Theorem 3 establish implementation properties, while Lemma 1 gives an equilibrium construction for unrestricted utility and allocation functions. None states a computational guarantee over an encoded input, so there is no named computational result to anchor a ChoCo mirror.
fails bit a — no named computational result to mirror
No result is covered by a computational mirror. Theorem 2 and Theorem 3 concern secure implementation, and Lemma 1 establishes equilibrium uniqueness; none gives a computational guarantee.
I can’t make a qualifying positive case under your anchor rule: the paper has no named result about computational complexity or an algorithm for a finite, encoded input. Theorem 2, proved here, says that every generalized serial mechanism is securely implementable. Theorem 3, also proved here, says that under Theorem 1’s assumptions, every fixed-path social choice function is a special case of a generalized serial one and is therefore securely implementable. Lemma 1 establishes a unique Nash equilibrium for the induced game. These are results about strategic properties and implementation, not claims that a computational problem is in P, hard, or parameterized tractable. Theorem 1 is cited from Friedman and asserts O-solvability under stated assumptions; it supplies no complexity bound either.
The closest population mirror I can imagine would take many residents or clients in a production economy, grouped into finitely many complete utility types \(T\), with mass \(\mu_t\) for each type. A mechanism would assign each type a per-capita allocation \(x_t\), subject to aggregate production feasibility. One could ask whether a continuum version of a generalized serial allocation rule is securely implementable. But deciding whether individual agents or whole types can deviate changes the strategic model, and the paper gives no computational input representation or complexity result to anchor that question. Divisible goods and a smooth production technology make the *outcome* continuous; the paper still has a finite set of agents.
So there are no valid anchors, no per-anchor prover questions, and no paper results this mirror would cover. The strongest positive observation is only that the production setting offers a plausible place to formulate a new population-continuum implementation problem. That would be a new research question, not a computational mirror of a named result in this paper.
The proponent’s opening observation is decisive for ChoCo: this paper has no named computational result to mirror. Theorem 2 says generalized serial mechanisms are securely implementable; Theorem 3 extends that claim to fixed-path social choice functions; Lemma 1 establishes a unique Nash equilibrium. These are results about incentives and implementation, not complexity or algorithms on encoded instances. The cited O-solvability result is also about strategic behavior. And the appendix’s equilibrium construction assumes arbitrary utility and allocation functions, so it supplies no running-time bound over a finite input representation.
The strongest repaired mirror would place many consumers or clients in a production economy, grouped into finitely many complete utility types with specified masses, and ask whether mass-allocation versions of the generalized serial or fixed-path mechanisms remain securely implementable. That is a plausible population model; the paper’s divisible goods are not an objection, and repeated consumers could make multiplicity meaningful. But the resulting question is about continuum-agent implementation, not the computational landscape ChoCo studies. There is also a strategic modeling choice to resolve: with individual deviations in an atomless population, one agent has no effect on aggregate allocation; treating positive-mass groups as deviators instead changes the strategic unit. Either choice may motivate new theory, but neither gives this paper a computational theorem to continuize.
One could impose finite encodings and ask how quickly an equilibrium or allocation can be computed. That would be a new algorithmic problem, not a mirror of a result here: the paper specifies no encoded function class or computational task, and uniqueness alone gives no complexity claim. So the proposed continuum-economy mirror may be worthwhile economics, but it does not qualify as a ChoCo mirror of this paper. The negative case is strongest on that scope boundary; it does not establish that continuum-agent implementation is uninteresting in its own right.
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.