| paper | d4-journals-geb-2019-0015 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The paper’s Results 1–5 report experimental findings, and its equilibrium calculations do not state a named computational result. The proposed continuum equilibrium task is a new extension; as the opponent explains, making voters atomless removes the individual influence that drives the paper’s information-acquisition incentives.
fails bit a — no named computational result to mirror
No computational result is covered; Results 1, 2, 3, R4, and 5 report experimental behavior and outcomes.
This paper has no eligible computational anchor. Its numbered statements—Results 1, 2, 3, R4, and 5—report experimental findings about information acquisition, voting, efficiency, and beliefs. The equilibrium calculations in Table 1 and the supplementary material do not assert a complexity result. So I cannot honestly give the required numbered theorem, lemma, corollary, or proposition, or a prover-ready mirror for each anchor. The paper’s main contribution is experimental, not a classification of computational problems.
The strongest prospective mirror I can see is a continuum version of its common-interest voting game. Let a voter type be an information-cost class \(c\), with mass \(\mu_c\); the state, signal accuracy, expert competence, and payoffs follow the paper. Actions are petition signing, information acquisition after a successful petition, and voting or abstaining after observing a signal. A plausible regime is a large electorate deciding a shared civic project, with many residents but only a few cost classes. The question would be to compute equilibrium action masses and the resulting probability of choosing the correct policy under endogenous versus imposed voting.
That extension has a serious fidelity problem: with atomless voters and the paper’s material payoffs, one voter has no effect on the group decision, so the incentive to acquire information that drives the experiment disappears. Recovering the paper’s behavioral findings would require a formal model of civic duty or conditional cooperation, which the paper does not provide. This is a recognizable research extension, but it is not an anchor-based continuous mirror of a named computational result in the paper.
The strongest objection is upstream: this paper gives no computational result to mirror. Results 1–5 report experimental behavior, efficiency, and beliefs. The equilibrium calculations concern a fixed seven-person game; they do not define a computational problem with an input family, output, or complexity claim. The proposed task—compute equilibrium action masses in a continuum—is a new question, not a continuous version of a named result.
Even that new question loses the mechanism the paper studies. In an atomless electorate, one voter has zero effect on the petition threshold and the majority outcome. With independent signals of accuracy \(0.6\), any positive mass of informed voters gives the majority the correct signal with probability tending to one as the electorate grows. But each individual’s benefit from buying information vanishes with their influence, while their cost remains positive. The material model therefore loses the free-riding trade-off that drives the experiment. The petition’s success can still affect a population’s aggregate behavior, but an individual cannot cause that success; the observed commitment and belief effects would need additional preferences the paper measures but does not formally specify.
A planner version does not rescue the mirror. If the planner chooses an informed mass \(x\), the natural continuum limit makes the expected per-capita return jump at \(x=0\): no informed mass leaves the decision at chance, while any \(x>0\) makes it correct with certainty under the law-of-large-numbers interpretation. With information cost \(c>0\), welfare is \(12.5\) at \(x=0\) and \(25-cx\) for \(x>0\). Its supremum is approached as \(x\) tends to zero from above, but no positive mass attains it. Keeping finite-electorate noise or pivotality may restore a meaningful optimization, but then the feature that makes the problem interesting is precisely what the atomless mirror discards. A subsidy-allocation or equilibrium-computation project could still be designed, but it would need new modeling choices and a new computational question.
The negative case is not a proof that no worthwhile research can grow from this experiment. Large civic electorates with a few information-cost types are a plausible high-multiplicity setting. The narrower, stronger conclusion is that the paper supplies no computational anchor, and its best-looking continuum extension either loses the incentives behind its findings or requires a substantially new model.
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.