| paper | d4-conf-aldt-2011-0009 |
| 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 theorems characterize fairness properties and impossibilities for online procedures, but do not state an algorithmic guarantee or hardness result for a computational problem. A fluid cohort model could motivate new work, but asking whether its fairness guarantees persist would be a new axiomatic question rather than a computational mirror of these results.
fails bit a — no named computational result to mirror
No computational result is covered; Theorems 3–5 characterize procedure properties, while Theorems 1–2 likewise provide no computational result to mirror.
I can’t give a result-backed continuous mirror for this paper under the programme’s anchor rule: it contains no numbered theorem, lemma, corollary, or proposition asserting a computational complexity result.
The closest candidates are Theorems 3–5, proved in the paper. They characterize fairness and other properties of the online cut-and-choose, moving-knife, and mark-and-choose procedures. Those are substantive results, but they do not establish that a computational problem is tractable or hard. Theorem 1 is an impossibility result about fairness axioms, and Theorem 2 shows that a trivial allocation procedure has several properties; neither supplies a computational anchor either.
There is a plausible population regime: many users arriving and departing while a divisible resource is allocated, with users drawn from a small set of complete types sharing valuation functions and relevant arrival conditions. A fluid model could represent each type by its mass and track mass receiving each slice. But asking whether a fluid version preserves Theorem 3’s fairness guarantees would be an axiomatic question about a new procedure, not a computational mirror of a named result in this paper. The cake is already continuous as an outcome; that alone does not continuize the population.
So the positive case is limited to the possibility that online allocation has a meaningful high-multiplicity regime. Its weakest point is decisive here: the paper provides no named computational result to anchor the requested question, and turning its fairness analysis into one would require inventing a different research problem.
The strongest point is that the paper supplies no computational result to continuize. Theorems 3–5 classify fairness and other properties of three fixed procedures; Theorem 1 gives fairness impossibilities, and Theorem 2 exhibits a trivial allocation. None states the complexity of a computational problem. That leaves no result-anchored computational mirror in the sense ChoCo is studying.
The best repair is to take Theorem 3’s online cut-and-choose procedure and model a large population as cohorts with shared valuations and arrival windows. One could then ask whether its guarantees survive, or optimize a fairness measure over online policies. But the first is a new axiomatic question about a mass-level procedure; the second changes the fixed procedure into a policy-search problem. Either might be interesting, but neither continuizes a computational result in this paper. Theorems 4 and 5 have the same limitation.
Theorem 1 is no stronger as an anchor. A pointwise fairness requirement keeps the individual-player question, but offers no computational problem. A mass-level fairness requirement or an approximation such as “what fraction of the population can be served proportionally?” changes the question. In particular, treating a cohort as one mass changes the role of the final player in the impossibility argument; keeping agents sequential instead preserves the online process but supplies no compression result.
There is a plausible high-multiplicity setting—many users with a small set of valuation profiles arriving in recurring time windows—so I would not claim that a continuous population model is meaningless here. That is the honest weakness of the negative case: a useful new computational project could be built around it. But under ChoCo’s stated criterion, it would be a new project, not a continuous mirror of a named computational result in 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.