| paper | d4-journals-geb-2007-0049 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
Neither numbered theorem asserts an algorithm, complexity bound, hardness result, or computational formulation used to compute. A positive-mass version of bribe-proofness could motivate new axiomatic questions, but it does not supply a computational result from this paper to mirror.
fails bit a — no named computational result to mirror
The proposed population setting concerns mass analogues of Theorems 1 and 2, but both results are axiomatic; the paper has no computational result for the mirror to cover.
The strongest plausible population mirror would involve a large population of resource claimants with a small number of distinct, complete single-peaked preference types. A type’s mass would be its share of the population; the rule would assign each type a per-capita allocation subject to an aggregate resource constraint. One could ask whether a positive mass of agents, by misreporting their type and redistributing allocations, can all become strictly better off. That is a sensible setting for studying high multiplicity.
But it changes the paper’s strategic question: the paper studies one agent changing their report, whereas an individual has zero mass in an atomless population. Making a positive mass change reports instead is a new manipulation model. More decisively, the paper contains no named computational result asserting a complexity classification or giving an algorithm. Theorem 1, proved in this paper, characterizes bribe-proof rules as exactly the efficient, strategy-proof, and weak replacement monotonic rules. Theorem 2, also proved here, characterizes bribe-proof tops-only rules as exactly the weak sequential rules. Both are axiomatic characterizations, not computational results. The divisible good is already part of the finite-agent model; it does not itself continuize the population.
So there is no qualifying anchor, and I cannot honestly state the required continuous problem as a mirror of one of this paper’s computational results. The proposed population setting may motivate a new axiomatic question, but it does not support a compliant positive case for this programme.
The decisive objection is that this paper has no named computational result to continuize. Theorem 1 characterizes bribe-proof rules through efficiency, strategy-proofness, and weak replacement monotonicity; Theorem 2 characterizes bribe-proof tops-only rules as weak sequential rules. Both are axiomatic characterizations. Neither asks for an algorithm, classifies computational complexity, or provides an instance-based optimization problem.
The strongest population model is still plausible: a large rationing community with finitely many complete preference types, each type having a population share and a per-capita allocation. One could define a bribe as a positive-mass coalition changing reports and redistributing shares. That is a sensible high-multiplicity setting. The natural questions would be whether mass versions of the three properties characterize resistance to such bribes, and whether tops-only rules have a mass analogue of the weak-sequential form.
Those are credible new axiomatic questions, not mirrors of this paper’s computational results. The paper gives no finite encoding for a rule or decision problem for an allocation instance. Turning its characterizations into questions such as “compute the least mass needed to bribe” would require choosing a rule representation, a coalition model, and an objective absent from the paper. That could start a separate computational project, but it would not supply the missing anchor.
So the candidate scenario survives as a possible direction for continuous-population theory. The case against a worthwhile ChoCo computational mirror is stronger: neither named theorem supplies a computational problem to mirror. This is a scope-based conclusion, not a claim that mass bribe-proofness could never be interesting.
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.