| paper | d4-journals-geb-2019-0106 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper's named propositions establish equilibrium, strategic incentives, and accuracy results, but none asserts a computational result. A continuum accuracy calculation can be stated for Proposition 5.3's construction, but the faithful two-sender limit is a simple probability calculation; making the sender count variable introduces a new problem that the proposition does not anchor.
fails bit a — no named computational result to mirror
The candidate covers only the limiting accuracy of Proposition 5.3's construction; it does not computationally mirror the paper's equilibrium claims, strategic incentives, network comparisons, or experiments.
I can’t give a conforming anchored case: the paper contains no named result about computational complexity. Propositions 2.1–2.3 and 5.1–5.3 concern equilibrium existence, strategic incentives, and the probability that the vote selects the correct policy. Those are substantive results, but “informationally efficient” does not mean computationally tractable.
The closest candidate is Proposition 5.3, proved in the paper. It says that there are networks where sincere communication is both an equilibrium and informationally inefficient, and that this inefficiency need not vanish as the number of experts grows. The authors’ construction is a plausible starting point for a continuous mirror. In its \(t\)-th network, the two senders’ audiences each approach one third of the population, while the independent experts without audiences approach one third. The two senders themselves become a vanishing fraction of voters, but each still informs a large audience.
A candidate problem would take rational masses \(\rho,a_1,\ldots,a_r\), summing to one, for an independent-expert population and \(r\) follower groups, plus rational signal precisions. Each follower group hears one sender; the expert population votes its independent signals; followers vote their sender’s recommendation. The question is to compute the exact ex ante probability that the resulting continuum vote selects the true state under sincere communication. A solution would evaluate the aggregate vote for each possible pattern of sender signals, then average over those patterns. In the paper’s construction, \(\rho=a_1=a_2=1/3\), and all signal precisions equal \(p\); the limiting accuracy is \(1-(1-p)^2\), since the vote is wrong when both senders receive the wrong signal.
This is a credible continuous-population question about the outcome accuracy that Proposition 5.3 studies. With a variable number \(r\) of senders, exact evaluation looks like a weighted threshold-counting problem, so \(\#\mathrm{P}\)-hardness is a plausible conjecture; it is not a result of this paper. Nor is this a fully faithful continuum equilibrium problem: individual pivotality disappears in an atomless population, while the construction relies on a few senders retaining influence over positive mass. The mirror therefore needs a limit model with vanishing-mass signal senders and positive-mass audiences. That is its weakest point—and why I would present it as a research lead, not as a case anchored in a computational result of this paper.
The case against this anchor starts with a category error: none of the paper’s numbered propositions is a computational result. Propositions 2.1–2.3 and 5.1–5.3 concern equilibria, incentives, and the probability of choosing the correct policy. “Informational efficiency” here means accuracy, not computational efficiency. Proposition 5.3 proves that an inefficient sincere equilibrium can persist as the number of experts grows; it says nothing about the complexity of finding an equilibrium, changing the outcome, or computing a strategy.
The proposed accuracy calculation is the closest mirror, but its faithful version is exceptionally small. In the paper’s construction, the number of senders stays at two as the population grows. In the continuum limit, the independent experts’ mass votes correctly with probability approaching one. The outcome is then wrong only when both senders receive the wrong signal, giving accuracy \(1-(1-p)^2\). That is a constant-size calculation, not a computational landscape opened by treating the population continuously.
Making the number of sender groups \(r\) variable creates a harder question: exact accuracy can become a weighted threshold count over the senders’ random signals. But the new complexity comes from enumerating distinct signal-generating hubs, not from the high multiplicity of the audience. The proposed question evaluates a fixed, prescribed strategy profile; it does not compute strategic behavior or solve an optimization problem from the paper. A hardness result for that count might be useful in its own right, but it would be a new weighted-voting reliability problem, not a continuization of Proposition 5.3’s result.
The more faithful strategic question faces the opposite problem. In an atomless population, one voter’s action has zero effect on the outcome, so individual pivotality—and with it the paper’s swing-voter incentive—disappears. Equilibrium conditions on receivers become vacuous. Keeping a few senders able to sway positive audience masses could preserve the network effect, but then the model needs finite, individually consequential hubs linked to continuous cohorts. That is a plausible hybrid model, yet its computational content would need to be supplied by a new question, such as optimizing or analyzing the network; Proposition 5.3 does not provide one.
So this is a strong objection to the proposed anchor as a ChoCo mirror: the paper reports no computational result, its actual asymptotic example has a simple accuracy formula, and preserving its strategic mechanism in an atomless population erases the pivotality on which it depends. The universal claim that *no* worthwhile mirror exists is harder to defend. A carefully motivated network-design or reliability problem might be worth studying, but on the evidence here it would be a new research direction rather than a computational mirror of a named result.
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.