| paper | d4-conf-atal-2017-0106 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The named results establish participation properties, which do not assert that an object can be computed or that computing it is hard. The computational claims about RSD and popular assignments are cited background, so a mass-coalition search would be a new computational project rather than a mirror of a result in this paper.
fails bit a — no named computational result to mirror
No numbered result yields a computational mirror; the participation theorems remain axiomatic, while cited computational facts belong to earlier work. The paper randomizes assignments for a finite agent set, which is outcome-space randomization rather than a continuous population.
This paper has no numbered computational complexity result to anchor a continuous mirror. Its numbered results concern axiomatic properties: for example, Corollary 1 says RSD satisfies very strong participation; Theorems 1 and 3 say RSD and PS satisfy strong group-participation; Theorems 4–6 cover Boston-mechanism participation; and Corollary 2 covers group-participation for popular random assignment rules. None classifies an underlying problem as tractable or hard.
The computational claims in the background—that computing RSD’s outcome is \(\#\)P-complete and that popular random assignments can be found by linear programming—are cited prior results, not numbered computational results asserted by this paper. They therefore do not meet the requested anchor standard.
A plausible high-multiplicity setting exists: a large school or office assignment round with many applicants or workers drawn from a finite set of preference types. But turning the participation theorems into a computational question about abstaining mass would create a new anchor, rather than mirror a named computational result in this paper. Under the stated criteria, there is no honest per-anchor continuous problem to hand to a prover.
The case for a mirror has no computational anchor to preserve. The paper’s numbered results ask whether assignment rules satisfy participation axioms; none states a complexity result for a computational problem. The references to the \(\#\)P-completeness of computing RSD and the LP algorithm for popular assignments are background results from other work, not results this paper establishes.
The strongest proposed mirror would take a large school or office assignment round, represent applicants by preference types and mass, and ask whether some coalition of positive mass benefits from abstaining. That is a sensible continuous version of the paper’s setting. But its central question is still whether a rule satisfies a participation property—the kind of axiomatic question the programme excludes. To make it computational, one could ask for a beneficial coalition or optimize a participation margin. The former merely restates the axiom as a search task; the latter adds an objective the paper does not define, and stochastic-dominance preferences provide no natural scalar margin.
The assignment model also ties the number of agents to the number of distinct objects. A large-population mirror therefore needs a growing object space or a new model of repeated object types and capacities. That co-modification may be defensible, but it does not supply the missing computational question.
This is not a proof that no useful computational project could grow out of the paper. It is a case that such a project would extend its subject rather than continuize a computational result it contains.
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.