| paper | d4-conf-atal-2015-0284 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper's numbered propositions state logical and axiomatic relationships, but none gives an algorithm, complexity result, or computational formulation used to compute. Proposition 6 is the closest candidate, yet a mass-weighted extension would still be axiomatic; asking how quickly particular operators compute their outputs would introduce a new problem.
fails bit a — no named computational result to mirror
Proposition 6 is the closest candidate; the other propositions characterize decision policies, compatibility, and correspondences between rationality properties, without computational results.
This paper contains no named computational result to anchor a continuous mirror. Its numbered propositions establish logical and axiomatic relationships between belief merging and judgment aggregation; none asserts that a computational problem is in P, NP-hard, fixed-parameter tractable, or similar.
So I can’t give the requested continuous problem *per anchor* without treating a non-complexity result as one. The closest candidate is Proposition 6, proved here: with a complete agenda, the judgment aggregation method induced by a merging operator yields a collective judgment equivalent to merging first and then projecting. That could motivate asking whether this correspondence extends to a society represented by a distribution over belief-base types. But it is an axiomatic correspondence, not a computational result, so it does not qualify as an anchor under your criteria.
The strongest case against a continuous mirror is that the paper gives no named computational result to mirror. Its propositions establish axiomatic facts: which decision policy satisfies the stated conditions, when the two aggregation paths can conflict, and how merging postulates correspond to judgment aggregation properties. None analyzes the complexity of a computational problem.
Proposition 6 is the proponent’s closest candidate, but it says that, for a complete agenda, two defined aggregation paths yield equivalent collective judgments. That is a representational correspondence, not an algorithmic result. The stronger version would put rational masses over complete belief-base types and compare weighted merging with weighted judgment aggregation. Such a population could be sensible; repeated agents with the same beliefs are not a problem for high multiplicity. But extending Proposition 6 in that way remains an axiomatic question. To make it computational, one would have to choose particular operators and ask how quickly their outputs can be computed—an interesting possible follow-on, but a new problem the paper does not formulate or answer. The same gap applies to the other results: none supplies a computational anchor.
So no anchor raised here survives as a continuous computational mirror of this paper. The limit of this negative case is that it cannot show a continuous, high-multiplicity study of belief or judgment aggregation would be uninteresting. It can show that such a study would draw its computational question from beyond this paper, rather than continuize one of its results.
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.