| paper | d4-journals-jet-2009-0070 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Neither named anchor asserts a computational result, and the proponent explicitly acknowledges that gap. The reservoir proposal keeps sequential individual queries and pivotal incentives; treating the society as atomless mass removes an individual's influence, so it does not yield a continuous-population computational mirror.
fails bit a — no named computational result to mirror
The proposed reservoir formulation would cover the ex-post-efficient sequential information-acquisition problem; it leaves the ex-ante inefficient-mechanism result and the paper's other characterizations aside, and does not provide a continuous-population computational mirror.
The best positive scenario is a very large pool of interchangeable expert assessors, such as reviewers who share the same signal accuracy \(p\), information cost \(c\), and common objective. The type is that full bundle of properties; \(\mu\) records the fraction of the pool of each type. A natural mirror has one type, so the number of agents can be huge while \(\tau=1\).
One precise candidate is Continuum-Reservoir Sequential Information Acquisition. Its instance is a unit-mass, atomless reservoir of identical assessors, a binary state with equal prior probabilities, signal accuracy \(p>1/2\), cost \(c>0\), and decision value \(A>0\). A planner samples fresh assessors sequentially; after each report, a possibly randomized policy either continues or stops and chooses an action. Queried assessors do not learn their position or earlier reports. A feasible policy must make acquisition and truthful reporting optimal for an assessor conditional on being queried. The question is to find a feasible policy maximizing
\[
A\Pr[\text{correct decision}]-c\,\mathbb E[Q],
\]
where \(Q\) is the number queried. A solution is an optimal policy and its value. A standing pool of potential assessors gives this regime a plausible high-multiplicity interpretation.
The closest named results are Theorem 1 and Proposition 3, both proved in this paper, but neither is a qualifying computational-complexity anchor under your rules. Theorem 1 characterizes the finite-\(N\), ex-post-efficient optimum: it has a decreasing step function \(f\), with \(f(l+1)=f(l)\) or \(f(l)-1\) and \(f(N)=1\); away from boundary states it stops and takes the majority decision when \(f(l)\leq |d|\), and otherwise continues. Randomization can occur only at boundary states, and generically an optimal mechanism can randomize at just one such state. Proposition 3 gives a related characterization for the paper’s infinite-voter variant with objective \(A\mathbb E u-cL\): when the first-best mechanism is not incentive compatible, the ex-post-efficient optimum generically has a decreasing threshold that reaches \(1\) at a finite \(K\), with randomization at one boundary state. Both results support the proposed model’s structure, but neither states that a problem is in \(P\), NP-hard, or in another complexity class. So there is no named result here that can honestly serve as the required anchor, and no per-anchor continuous problem to report.
If the anchor requirement were relaxed, I would tentatively expect this candidate to be tractable: the paper’s threshold characterization suggests a dynamic program over posterior states. That is a conjecture, not a result; the paper gives no runtime or polynomial bit-complexity bound for computing an optimal policy. The mirror would cover only the ex-post-efficient sequential mechanism problem, not the paper’s result that ex-ante optimal mechanisms can sometimes use ex-post inefficient decisions.
The soft spot is that a queried individual has vanishing mass in the continuum. The model therefore needs interim incentives conditional on being selected from the reservoir, and a referee could regard that as a sampling convention rather than a genuine continuum-agent incentive model. The paper’s own infinite-voter result makes the reservoir extension plausible, but it does not remove that issue or supply the computational anchor the programme asks for.
There is no named computational result here to anchor a ChoCo mirror. Theorem 1 and Proposition 3 characterize optimal mechanisms; neither gives an algorithm or a complexity classification for an encoded computational problem. Theorem 2 is a uniqueness result, and Proposition 5 concerns equilibrium behavior. Those results can motivate questions, but under the programme’s stated standard they do not supply its computational anchor.
The strongest proposed rescue—a reservoir of identical assessors—is the paper’s infinite-voter extension with reservoir language. Its distribution over types is always \(\mu=1\), whatever the reservoir size. What drives the model is still a sequence of individually queried agents: the state uses integer signal counts, each report can change the decision, and incentive compatibility depends on an assessor’s chance of being pivotal. In a population model based on queried mass, each individual has zero influence on aggregate reports, so the acquisition incentive disappears. If the planner instead samples individuals one by one and imposes incentives conditional on being queried, the model preserves the paper’s discrete sequence and pivotality, but the continuous object does no computational work. That conditional-sampling repair is coherent, but it is an unlimited supply of discrete agents rather than a computational problem over a continuous society.
Theorem 1’s finite-\(N\) threshold characterization has the same issue: representing a homogeneous electorate by a one-type distribution does not replace the integer population that the mechanism queries one voter at a time. Changing the model to query positive mass alters the incentive problem; changing it to retain sequential individual queries returns to the original count-based process. A richer type distribution could make the mass representation matter, but varying signal quality or information costs would add a mechanism-design problem the paper does not study.
The honest weakness in this negative case is that a very large pool of interchangeable assessors is plausible, and the infinite-reservoir optimization could be worth studying on its own. But that case does not make the population itself continuous in ChoCo’s sense, and the paper offers no named complexity result for it to mirror.
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.