| paper | d4-journals-geb-2016-0004 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 1 is an axiomatic impossibility theorem, and Theorems 2–4 characterize agenda-invariance; none asserts a computation, algorithm, computational formulation, or complexity result. The consultation idea makes population mass plausible, but its agenda search requires a rule, feasible agenda family, and objective that the paper does not specify, so it would be a new problem rather than a mirror of a named result.
fails bit a — no named computational result to mirror
No result is covered by a continuous computational mirror; Theorems 1–4 present axiomatic impossibility or characterization results.
I don’t see an honest positive case that meets your anchor requirement. The paper contains no named result asserting a computational complexity bound or hardness result for a problem.
The nearest tempting result is Theorem 1, proved in this paper: for an agenda \(X\), there is no independent, implicit-consensus-preserving, non-dictatorial aggregation rule \(F:J^n\to J\) if and only if \(X\) is non-nested and non-tiny. That is an axiomatic impossibility theorem, not a result about the complexity of solving a computational problem. Theorem 2 similarly characterizes agenda-invariance through coherence and independence. Neither supplies an eligible computational anchor.
There is a plausible population setting for a *new* problem: a large public consultation over a finite universe of policy propositions, where each type is a complete rational judgment set and \(\mu_J\) is the share of participants holding judgment set \(J\). An agenda setter could choose a feasible agenda, with the objective of changing the collective judgment on a target proposition. That makes population mass natural, but the paper does not formulate or analyze this optimization problem. It leaves the aggregation rule general and studies its axioms and properties.
So I can’t write a per-anchor continuous problem for this paper under the stated rules: there is no qualifying anchor. The weak point is decisive for this assignment—the paper’s contribution is axiomatic, a part of continuization the programme explicitly places outside scope.
The strongest case against a mirror is that the paper has no computational result to mirror. Theorem 1 is a possibility result about aggregation rules \(F:J^n\to J\): under specified axioms, non-dictatorial rules exist exactly for nested or tiny agendas. Theorems 2–4 likewise characterize agenda-invariance through properties of aggregation systems. None studies an encoded computational problem, its complexity, or an algorithm.
A natural attempt to make a computational question would be to represent a consultation by masses \(\mu_J\) over rational judgment sets, then ask whether some feasible agenda reverses the collective judgment on a target proposition. But that requires choices the paper does not make: a particular aggregation rule or system of rules, a feasible agenda set, and a computational objective. The paper’s axioms quantify over profiles and rules; they do not specify this search problem. Choosing those ingredients could produce a sensible new agenda-control problem, but it would not be a continuous version of Theorem 1 or the paper’s other results.
Nor does directly extending the axioms supply an in-scope mirror. A rule on a continuum of agents would raise a new axiomatic question about how to aggregate a measure of judgments—precisely the kind of continuized axiomatic question the programme excludes. Some of the paper’s conclusions also turn on named individuals: dictatorship selects one person’s judgment, while a distribution over types forgets which person supplied which judgment. Restoring that identity, or changing dictatorship into a positive-mass bloc, changes the object being studied.
So the proponent’s consultation scenario establishes that a continuous population is plausible here; it does not establish a computational result to continuize. The negative case is strong for this paper’s contribution. It cannot rule out every useful computational problem inspired by agenda manipulation, but such a problem would need its own justification rather than count as a mirror of this paper.
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.