| paper | d4-journals-geb-2022-0025 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorems 1 and 2 give explicit mechanism constructions, so their lack of runtime bounds alone does not rule them out as computational anchors. But neither case states a distributional population problem anchored in those results, and the nearest continuum lift turns individually strategic players into nonatomic agents, changing the implementation question and its equilibrium model.
fails bit b-changes — the continuum limit changes the question
The candidate anchors are Theorems 1 and 2; no continuous analogue survives, so neither result is covered.
I don’t see a qualifying computational anchor in this paper. Theorem 1 says that, with complete information and at least three agents, any social choice function is uniquely implementable if “all agents are selfish” is never common knowledge. Theorem 2 says that, under information diversity and the same epistemic condition, any incentive-compatible social choice function is fully implementable. Both are existence results about mechanisms and their equilibria; neither classifies an underlying problem as tractable, hard, or otherwise computationally complex.
The mechanisms use finite agents, their higher-order beliefs, and sequences of messages. Turning agents into masses would raise a new question, but the paper provides no named computational result for that question to mirror. Its stochastic allocations do not change this: they continuize the outcome, not the population. So I can’t state a continuous problem per anchor without inventing a computational contribution the paper does not make.
Theorem 1 and Theorem 2 are the paper’s strongest candidates, but they establish existence of implementing mechanisms, not the complexity of a computational problem. There is no input, encoded output, running time, or resource bound to carry over into a continuous-population complexity result. The attached case’s one substantive point therefore stands; it is an argument against a mirror, rather than an anchor for one.
The best attempt at a computational version would ask whether a planner can efficiently synthesize a mechanism for a society of many agents sharing a finite set of characteristics. Large consultations or polling populations make that a plausible setting. One could also impose limits on message length, rounds, or liability and ask for a minimum-cost implementation. But those limits and objectives are not in the paper. Its mechanisms range over broad message spaces and are tailored to each finite epistemic model. Choosing a finite mechanism language and an optimization objective would define a new algorithmic problem, not supply the missing computational result.
The deeper obstacle is what must count as a “type.” Here an agent’s relevant characteristics include beliefs about the types of all the other agents, and those beliefs are part of a common-prior epistemic structure. Theorem 1 turns on whether “all agents are selfish” is common knowledge; Theorem 2 additionally uses pairwise conditional beliefs about private signals. A vector of type masses does not determine either structure. Two populations with the same marginal shares can differ in the higher-order beliefs that govern the theorem’s condition. Keeping those beliefs intact means carrying a potentially growing, identity-linked model rather than compressing the society into a small-support distribution.
Nor does the paper give a natural way to price mechanism synthesis in that richer model. Its message sequences, penalties, and peer comparisons are designed for a fixed finite set of named participants. A continuum extension might be worth studying, but it would need to specify how individual incentives and common knowledge work in that setting, then choose a representation for mechanisms and their costs. The paper supplies no computational target that selects those choices.
This is a strong case against treating the paper as a ChoCo mirror, but it cannot establish the universal claim that no worthwhile continuous model could ever be built. A bespoke continuum epistemic implementation problem remains possible. It would be new work in a substantially specified model, not a computational mirror anchored in these 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.