| paper | d4-journals-geb-2014-0020 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
Theorem 2 gives a rule characterization, not a named computational result of the kind required by the brief. The proponent states no continuous computational question, and the opponent’s population-share cutoff is a reformulation of the characterization rather than such a question.
fails bit a — no named computational result to mirror
Theorems 1–10 characterize efficient rules, equilibria, and sincerity; none supplies a computational result for a continuous mirror.
I find no qualifying computational anchor in this paper. Theorems 1–10 characterize efficient and sincere voting rules in a Bayesian game; none asserts that a computational problem is in P, NP-hard, FPT, or another complexity class. For example, Theorem 2, proved in the paper, says that under simple preferences informative voting is efficient exactly for the quota rule with thresholds \(k_p\) and \(k_q\). That is a rule characterization, not a complexity result.
A large jury with voters grouped by their private-signal types could motivate a continuous-population model. But without a named computational result to anchor it, that would not meet the requested standard. The paper’s results also depend on strategic incentives and pivotal votes, which a nonatomic model would need to reformulate. So I can’t honestly give an anchor-based continuous problem for this paper.
The appended case offers no continuous anchor; it argues that the paper has none. The strongest candidate I can infer is Theorem 2, extended to \(m\) issues by Theorem 9: under simple preferences, informative voting is efficient exactly at particular quota thresholds. The jury setting itself is a natural high-multiplicity regime: voters fall into a small number of signal types. I would not argue that mass is meaningless here.
The problem is that these theorems characterize a Bayesian decision rule; they do not pose a computational task. In the mass version, the count of signals for \(p\) becomes a share of the population, and the theorem’s likelihood comparison becomes a scalar cutoff on that share. Computing the rule means evaluating the posterior odds or its cutoff. That may be a useful reformulation of the theorem, but it supplies no algorithmic problem for the continuous-computation programme to classify.
The other half of the paper is harder to carry over. In an atomless population, one voter cannot change the outcome, so the pivotality behind the Bayesian voting incentives disappears and equilibrium behavior loses its bite. Meanwhile, under the paper’s independent-signal assumptions, the natural exact-continuum limit makes aggregate signal shares reveal the state: the share of voters reporting \(p\) differs across the two states because signals are informative. Retaining finite uncertainty requires keeping finite sampling noise or adding correlated signals. Either changes the model’s information structure.
One could instead ask how much signal mass must be altered to change the aggregate decision. That is a plausible control or robustness problem, but it adds an intervention objective absent from the paper; it does not mirror a result about efficient information aggregation. Its simplest version is again just distance to a quota cutoff.
So the negative case is strong at the programme’s computational gate, not at the population-regime gate. A large jury is entirely credible, and a continuous Bayesian aggregation model can be written down. What I do not see is a worthwhile computational mirror of these results without adding a new problem the paper does not study. That is a reasoned negative judgment, not a proof that no adjacent computational question could interest the authors.
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.