| paper | d4-conf-ecai-2024-0054 |
| 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 named results establish that MMS allocations exist under stated conditions; they do not claim an algorithm, a complexity bound, or hardness. The constructive proof techniques do not turn those existence theorems into a named computational result to mirror.
fails bit a — no named computational result to mirror
Theorem 2 and its component results concern existence; the computational results mentioned in related work belong to other papers. The proposed continuous search problem would not mirror a computational result of this paper.
I can’t make a compliant anchor based on this paper: it contains no numbered result about computational complexity or an algorithm. Theorem 2, proved here, says that an MMS allocation exists when \(m\le n+5\) and either \(n\le3\), some agent has a nonnegative MMS guarantee, or all agents are chores agents. The other main theorems also establish existence. Their constructive proofs do not state a runtime or complexity classification.
The paper mentions an NP-hardness result for approximate MMS allocation in related work, but that is attributed to another paper and concerns a different problem. A continuous high-multiplicity MMS question may be worth studying, but it would not be anchored in a named computational result of this paper. Under your anchor rule, there is no honest per-anchor continuous problem to put to a prover.
The proponent raised no anchor. Their point is the strongest negative ground available: this paper has no named computational result to mirror. Theorem 2 and the results it builds on—Theorems 13, 15 and 17—establish existence. The open Problem 1 is also an existence question. The paper gives constructive proof techniques, but it states no algorithm or complexity bound. The NP-hardness and tractability results in the related-work section belong to other papers and different problems.
The best repair is to recast the existence theorem as a search problem: given a distribution over complete additive-utility types and per-capita supplies of item types, find an assignment of integral bundles that meets each type’s continuous MMS benchmark. That is a plausible high-multiplicity fair-division question. Grouping identical utility vectors is legitimate, and a mass distribution over integral bundles could preserve indivisibility for each agent.
But that repair creates a new computational question; it does not mirror a computational result of Hsu’s paper. The paper’s \(m\le n+5\) condition and its proofs rely on finite item and bundle counts. Under a population limit, the five-item slack vanishes per capita, and the continuous MMS benchmark would need its own definition. The resulting model might be worthwhile, but this paper supplies no algorithmic finding for it to continue.
So the case against a paper-anchored continuous mirror is strong: there is no computational anchor, and the proponent supplied none. The broader claim that no continuous high-multiplicity MMS project could be worthwhile is much weaker. Fair division admits a plausible repeated-type regime, and I cannot honestly rule out a useful computational question there.
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.