| paper | d4-journals-mss-2012-0021 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Neither named theorem asserts an algorithm, hardness result, or computational formulation used to compute. The proposed type-mass problem of computing or recognizing pairwise decisiveness would require a new computational model, so it is not a continuous analogue anchored in a result of this paper.
fails bit a — no named computational result to mirror
Theorems 1 and 2 characterize pairwise decisiveness and construct rules with specified properties; neither is covered by a continuous computational mirror.
I can’t make a valid anchored case for a computational mirror: the paper contains no named computational result classifying a problem as tractable, hard, or otherwise.
Theorem 1, proved in this paper, says that if a collective choice rule is acyclical and satisfies weak Pareto, its family \(A_g\) of pairwise decisive coalition pairs is a product filter. Theorem 2, also proved here, says that every product filter can be realized as \(A_g\) by a Suzumura-consistent collective choice rule satisfying weak Pareto and neutrality. These are structural characterization and existence results; neither gives a computational problem or a complexity claim.
A plausible setting for a *new* question would be a large electorate with finitely many complete-ranking types, where mass represents each type’s share. But asking how to compute or recognize pairwise decisiveness in that setting would be a proposed extension, not a mirror anchored in a computational result of this paper. The article does study infinite populations, but its focus is axiomatic and set-theoretic, outside ChoCo’s computational scope.
The strongest negative is that the paper has no computational result to continuize. Theorem 1 shows that \(A_g\) is a product filter under acyclicity and weak Pareto; Theorem 2 constructs a Suzumura-consistent rule for each product filter. Both are structural results about unrestricted collective choice rules. Neither specifies a computational problem, an encoded input, an objective, or an algorithm whose complexity could be studied. The article’s infinite electorate does not supply that missing computational target.
The natural type-mass model also fails to preserve the object those theorems characterize. A distribution over ranking types records fractions of voters, while \(A_g\) is defined using exact coalitions of named individuals and product-filter conditions on their unions. For identity-dependent rules such as dictatorship, coalitions with the same type masses can have different decisiveness properties. Passing to an atomless measure erases a dictator’s singleton mass; retaining the dictator’s identity requires information the finite-support distribution does not contain.
The strongest proposed alternative is to impose anonymity and study product filters over measurable populations. That may yield a coherent new axiomatic question, but anonymity changes the class of rules and the paper’s theorems give no computational task for that restricted class. To ask for an algorithm, one would still need to specify how a rule over profiles is represented. A truth-table representation makes the input itself enormous; a succinct representation makes the resulting complexity depend on choices the paper never makes. Computing or recognizing \(A_g\) is therefore a possible extension, not a mirror of a named result.
This is a strong negative case, but it cannot rule out every useful project someone might build from the paper. A computational study of measurable product filters could be worthwhile on its own. Its value would come from new modeling and new questions, though; the paper supplies no computational result for a continuous mirror to carry forward.
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.