| paper | d4-journals-jet-2007-0007 |
| 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 characterize coalitional voting and core concepts; none gives an algorithm, complexity bound, or formulation used to compute. The proposed large-economy question would require a newly specified population and information model, and has no computational result in this paper to anchor it.
fails bit a — no named computational result to mirror
No numbered result in the paper is covered by a continuous computational mirror; the proposed large-economy study is a follow-on question.
I can’t make an anchor-based positive case under your criteria: the paper has no named computational result. Its numbered results are characterizations of economic solution concepts, not claims about an algorithm, running time, or complexity class.
The closest result is Proposition 3, proved here. It says that, for an incentive-compatible status quo \(x\) and coalition \(S\), an equilibrium rejection in a mediated voting game exists exactly when there is a truthful direct mediated equilibrium, and exactly when there is a feasible allocation \(y'\in A_S\) and a positive-prior event \(E\) such that coalition types in \(E\) weakly gain, with at least one strict gain, and the associated weighted-surplus inequalities rule out profitable type misreports. Corollary 2, also proved here, identifies resilience to coalitional voting with membership in the credible core. These are structural equivalences, not computational classifications or encodings the paper uses to compute a problem’s complexity.
A plausible *future* computational question would be whether a mediated objection exists in a large exchange economy with many households drawn from finitely many preference, endowment, and information classes. Class masses would replace household counts; a candidate objection would allocate resources to a coalition’s mass while satisfying feasibility, gain, and incentive constraints. That sounds like a recognizable extension of the paper’s subject, but specifying the continuum information and coalition model requires choices the paper does not make, and the paper provides no computational anchor for the question. I therefore can’t honestly present it as the continuous mirror of one of its named results or predict whether it is tractable or hard.
The paper’s introduction does mention that non-emptiness can be difficult, citing results from Forges, Mertens, and Vohra and from Vohra. Those are externally cited economic results, not numbered computational results of this paper. The most I can say for the positive side is that the paper offers a natural *subject* for a later high-multiplicity complexity study; it does not supply the required anchor for this case.
The strongest case against a ChoCo mirror is that this paper has no computational result to continuize. Proposition 3 characterizes when a mediated voting equilibrium rejects a status quo; Corollary 2 identifies resilience with membership in the credible core. Both are economic equivalences. Neither gives an algorithm, a complexity bound, or a computational problem with an input encoding. The non-emptiness results mentioned in the introduction are cited work by other authors, and are economic results too.
The strongest upgraded candidate would be to ask whether a mediated objection exists in a large exchange economy whose households fall into finitely many classes, with class masses replacing household counts. One could encode a restricted economy with rational data and study core membership or objection-finding. That is a plausible computational project, but it is newly specified: the paper indexes agents individually, gives them potentially different utilities, endowments, and type sets, and puts a prior on the full state \(T=\prod_i T_i\). Its objections depend on events in that joint state space and on each agent’s interim incentives. A mass model must choose how to represent joint information, coalitions of positive mass, and incentive compatibility for a continuum of agents. Those choices define a new problem; they do not supply a continuous version of either proposition.
That distinction defeats the proposed anchors without claiming that large-economy core computation could never be worthwhile. A continuous exchange economy may be a sensible subject for a separate complexity study, and existing high-multiplicity work would support that regime. But it would be a follow-on built from this paper’s economic concepts, not a continuous mirror of a computational claim the paper makes. The negative case is strong on the programme’s stated requirement; the broader claim that no related project could be worthwhile is harder to defend.
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.