| paper | d4-journals-mss-2020-0010 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The named propositions are axiomatic characterizations or an axiomatic impossibility result, so none supplies the computational result required for a mirror. The opponent also shows that a role-mass version would change Proposition 4.1's unilateral deviation into a block deviation; that redesigned question is not anchored by the paper.
fails bit a — no named computational result to mirror
No result is covered: Propositions 3.1, 3.2, and 4.2 are axiomatic characterizations, and Proposition 4.1 is an axiomatic impossibility result.
This paper has no named computational result of the kind required for a continuous mirror. Its numbered propositions are axiomatic characterizations and an axiomatic impossibility result; none studies the complexity of a problem or an algorithm for solving one.
The closest result is Proposition 4.1, proved here: no coalition aggregation function simultaneously satisfies unanimity (UN), pairwise disagreement (PD), and monotonicity (MO). In full, it rules out any map from coalition profiles to partitions of the player set that meets all three axioms. Propositions 3.1, 3.2, and 4.2, also proved here, characterize \(B^\delta\), \(B^\gamma\), and \(B^\approx\) by their respective axiom systems. These are formal results, but they are not computational anchors.
There is a plausible population story nearby: many participants in a large organization submit coalition proposals, and one might ask how those proposals should be aggregated. But a participant’s type here is a proposed subset of named players. As the population grows, the proposal space grows with it; a distribution over proposal types does not by itself preserve who proposed a coalition with whom. A continuum model could be devised by changing the domain, but this paper’s propositions would not establish results about that model.
More fundamentally, Proposition 4.1 asks whether certain axioms can coexist. A continuous version of that question would continuize an axiomatic question, whereas ChoCo’s scope is computational questions about a continuous population. There is no honest per-anchor continuous computational problem to hand to a prover, so I would not manufacture one. The paper motivates coalition aggregation, but it does not provide the computational result needed to make a positive case under this programme’s criteria.
Proposition 4.1 is the closest anchor, and its main difficulty is that it is not a computational result. It says no coalition aggregation function can satisfy UN, PD, and MO; it does not pose an input problem whose complexity a continuous model could reveal. Propositions 3.1, 3.2, and 4.2 likewise characterize functions. The natural computational task they suggest is to evaluate those functions on a profile: group identical proposals for \(B^\delta\), check unanimity for \(B^\gamma\), or find connected components of mutual-acceptance links for \(B^\approx\). With an explicit profile, those are direct combinatorial procedures. On a finite support of proposal types, the corresponding mass computations are similarly just grouping, checking, or graph traversal. That looks like little complexity landscape for ChoCo to chart.
The better population mirror would use many anonymous participants of a few roles, with proposals directed at sets of roles and the output a partition of role masses. That is a plausible model for an organization with large, repeated cohorts. But it does not preserve Proposition 4.1’s central move: one named player changes their proposal, and the axiom tracks which named player belongs to which coalition afterward. In a nonatomic society, one person has zero mass, so their deviation leaves the distribution unchanged; their coalition membership is not even an output of a distribution-level rule. Treating a whole role’s mass as the deviator repairs that problem only by changing unilateral deviation into coordinated block deviation. The resulting axioms might be interesting, but the paper’s impossibility and characterizations do not anchor them. Asking whether new axioms can coexist would remain axiomatic; adding an optimization problem would require supplying a new objective.
Keeping named people and their exact target sets avoids that loss of information, but weakens the continuization case. Proposals are subsets of particular people, so a type must encode whom the proposer accepts. As the population grows, this type space grows with the named population, and preserving the output partition requires recovering membership at that same granularity. Restricting proposals to a few anonymous categories can produce a sensible mass model, but that is the redesigned problem above, not a computational mirror of these results.
So the negative case is strong for the paper’s actual results: they offer no computational anchor, and the natural evaluations appear elementary. It is weaker as a universal claim. A role-based mass version of coalition formation could be worth studying on its own, but its interest would come from new modeling and new questions, not from continuizing this paper’s results.
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.