| paper | d4-conf-sigecom-2010-0040 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 5 is an analytic result, and its proposed continuum version does not make it computational. Theorem 4 gives an explicit posterior inference formula, but the proponent stated no continuous computational question for that result. The only proposed mirror changes the finite-trader game into a continuum-agent game, so no computational mirror survives as stated.
fails bit b-changes — the continuum limit changes the question
The proposed extension covers Theorem 5's information-aggregation setting; it leaves Theorem 4's posterior-inference formula, Theorem 3's efficiency result, and the other results without a stated computational mirror.
I don’t find a named computational result in this paper, so it has no anchor that meets your rule. Theorems 1–6 concern information aggregation, competitive equilibrium, efficiency, and inference in a finite-trader market. None establishes a complexity classification or a computational formulation used to compute a solution.
The closest hook is Theorem 5, proved here in Section 6: in any perfect Bayesian equilibrium of a cost-function market with hierarchically conditionally independent signals, if traders’ portfolios converge, then the market aggregates their information. That is a useful economic result, but it is not a result that information aggregation is in \(P\), is hard, or can be computed by a specified algorithm. Calling the cost-function market “algorithmic” describes its pricing mechanism, not the theorem’s computational content.
A plausible population extension would group prediction-market participants who share a signal law, utility and risk preferences, initial portfolio, and market access pattern. A type’s mass would be its share of the population; its action could be aggregate trades in the contingent securities, priced from total order flow by the market maker’s cost function. That would mirror only Theorem 5’s setting and conclusion. But asking whether such a continuum equilibrium aggregates information is an analytic question, and the theorem does not establish that the finite-player result survives the continuum limit. The market already aggregates orders through its pricing rule; that alone does not make the society continuous.
So I can offer a plausible population-side extension, but not a qualifying continuous computational problem per anchor. I would not assign it to Class A, B, or C: the paper supplies no computational hardness or algorithmic result whose fate under continuization can be assessed. The absence of such an anchor is the decisive weakness, not a gap that a more inventive mirror can fix honestly.
The strongest negative case is that this paper has no computational result to continuize. Theorems 1–6 establish analytic properties of equilibria; none gives an algorithm, a complexity bound, or a computational problem. In particular, the market’s being called “algorithmic” means its pricing rule is specified by a cost function. Theorem 5 proves an information-aggregation property for that market; it says nothing about the cost of computing an equilibrium or an outcome.
Theorem 5 is the proponent’s closest anchor, but its best population version remains outside ChoCo’s target. A prediction market could plausibly have many traders grouped by signal law, utility, initial portfolio, and market-access pattern. That is a sensible high-multiplicity regime, so lack of plausible types is not the objection. The continuous question would be whether a continuum-agent dynamic game has equilibria that aggregate information under analogous assumptions. That is an analytic equilibrium question. To make it computational, one would have to add a new problem—such as finding a PBE, testing aggregation, or computing limiting portfolios—and specify how utilities, cost functions, infinite-horizon strategies, and equilibrium selection are encoded. The theorem supplies none of that. Such a project might be worthwhile on its own, but it would not be a computational mirror of Theorem 5.
The strongest alternative anchors do not repair the gap. Theorem 3 identifies a competitive equilibrium and hence ex post Pareto efficiency; its continuum counterpart would again be an analytic welfare result. Theorem 4 gives an inference formula, not a computational classification. One could study algorithms for computing the resulting exchange equilibrium or posterior, but those would be newly posed tasks rather than continuizations of computational results in this paper.
So the negative case does not depend on claiming that markets lack high multiplicity, or that a continuum version has no interesting answer. It rests on a narrower point: the paper provides no computational anchor for the programme to mirror. The limit of this argument is that it cannot rule out every useful follow-up someone might devise; it can only say that those follow-ups would be new computational work, not a continuous mirror of this paper’s results.
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.