| paper | d4-journals-jet-2004-0050 |
| 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 Expected Multi-Utility Theorem gives a representation of one person’s incomplete preference over lotteries; it does not state a computational result. Without a named computational result to anchor, there is no result of this paper for a continuous-population mirror to preserve.
fails bit a — no named computational result to mirror
No computational result is mirrored; the main theorem, uniqueness result, and monetary-lottery corollary are representation results.
I can’t make a positive case that meets your anchor requirement: the paper has no named computational result asserting tractability, hardness, or a parameterized complexity classification.
Its main result, the *Expected Multi-Utility Theorem* (proved in the paper), is a representation theorem: for a compact metric prize space, independence and continuity characterize when an incomplete preference over lotteries can be represented by a set of continuous bounded utility functions. That is an existence result, not a computational result. The paper gives no named complexity anchor to mirror.
One could imagine a new problem about a large population of consumers with a small number of shared incomplete preferences over lotteries. But the paper studies one decision maker, and its set of utility functions represents that person’s incompleteness; it is not a population of voter types. Treating it as one would change the problem rather than continuize it. And the paper’s continuous lottery space is continuity of outcomes, which your scope explicitly excludes as the goal. So there is no honest, anchor-based continuous problem to hand to a prover from this paper.
The proponent raises no computational anchor, and that is the strongest case against a mirror. The paper’s main theorem characterizes when one person’s incomplete preference over lotteries has a representation by a set of continuous utility functions. Its uniqueness results and monetary-lottery corollary remain representation results. None states the complexity of a computational problem.
The strongest population version would assign each consumer a type describing their preferences or utility functions, then study an aggregate choice or welfare problem. But the theorem’s set of utility functions encodes one person’s incompleteness; it is not a population of agents. Adding consumers and an aggregation objective would create a new social-choice problem, with no result in this paper to continuize.
One could also ask for an algorithm to check the axioms or construct a representation. The paper gives no finite input model for that task: it allows arbitrary compact metric prize spaces and preference relations over lotteries, so the computational problem would depend on additional encoding choices. Such a project might be worthwhile on its own, but it would not be a continuous-population mirror of a result here. The negative case is unusually strong: there is no named computational result for a mirror to preserve.
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.