| paper | d4-journals-mss-2015-0040 |
| 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, Theorem 2, and Proposition 1 state axiomatic relationships among preference properties; none asserts a computational result. A population of decision makers would require an aggregation rule and a new computational question that the paper does not provide, so bit (a) fails.
fails bit a — no named computational result to mirror
The paper’s theorems and proposition concern preference axioms over lotteries; none yields a computational result to mirror.
I can’t make a valid positive case under the programme’s anchor rule: this paper has no numbered computational result asserting tractability, hardness, or a parameterized complexity classification.
Its Theorem 1, proved in the paper, says that for a non-trivial partial order on the lottery simplex \(V(X)\) satisfying betweenness, any two of Archimedean, mixture continuity, and completeness imply the third. Theorem 2, also proved here, gives the corresponding implication on \(\operatorname{int}V(X)\) under cone-monotonicity, and states that completeness extends to \(V(X)\) when mixture continuity holds there. Proposition 1 relates betweenness to cone-monotonicity under additional assumptions. These are axiomatic results about preference relations, not computational results about a problem an algorithm must solve.
A population mirror would also change the paper’s object. Its continuous simplex describes lotteries over outcomes for a decision maker; the paper does not represent a society as mass distributed over agent types. One could invent a population of consumers with different preference relations over lotteries, but the paper supplies neither a canonical way to aggregate those relations nor a computational question about that aggregate. That would be a new problem, not a continuous version of one of its results.
So the best honest positive reading is only a resemblance: the paper studies continuity, but continuity of lotteries and preference axioms is expressly outside ChoCo’s scope. There is no defensible mirror question to hand to a prover from this paper’s results.
The proponent raises no computational anchor, and the reason is decisive: this paper states no computational problem whose complexity an algorithmic mirror could study. Theorem 1 and Theorem 2 connect axioms on a single decision maker’s preference relation over lotteries; Proposition 1 relates two such axioms. They contain no algorithmic task, input size, or complexity result to continuize.
The strongest candidate mirror would put a continuous population over types of decision makers and ask whether the axioms hold for the aggregate. But the paper supplies no aggregation rule, and its theorems concern each preference relation individually. A distribution over those relations does not enter their statements. Choosing an aggregator or asking for the fraction of types satisfying an axiom would add a new problem rather than mirror a result. Encoding a relation and asking a computer to check its axioms would likewise require a representation and decision problem absent from the paper.
The simplex of lotteries is already continuous in the *outcome* sense, which ChoCo explicitly puts outside its scope. That resemblance does not supply the missing continuous population or computational question. One can invent related research, but I see no worthwhile continuous mirror of this paper’s results. The negative case is strongest for that precise claim; it cannot rule out every interesting project one might build nearby.
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.