| paper | d4-journals-geb-2011-0036 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorem 1 and Corollaries 1–3 classify strategy-proof rules, but none asserts an algorithm, complexity result, or computational formulation. A distribution over peaks is a plausible population model, yet turning it into a computational task requires adding an objective and a deviation model absent from the paper.
fails bit a — no named computational result to mirror
No computational result is covered; Theorem 1 and Corollaries 1–3 are axiomatic characterizations of strategy-proof rules and their subclasses.
The strongest honest positive angle is a plausible extension, but this paper supplies no qualifying computational anchor for it. Theorem 1, proved in the paper, characterizes strategy-proof social choice functions on symmetric single-peaked preferences: they are exactly “disturbed minmax” rules, built from monotone fixed ballots, countably many compatible discontinuity intervals, and upward-closed tie-breaking sets. Corollaries 1–3 specialize that characterization to anonymity, efficiency, and efficiency relative to a feasible set. These are axiomatic characterizations; none asserts a complexity result or presents a formulation that the paper uses to compute one. So there are zero valid anchors here, and no per-anchor continuous problem to hand to a prover. Calling Theorem 1 a computational anchor would misstate it.
A plausible population regime would be a municipality choosing a public-facility location: many residents share a small number of ideal locations, and \(\mu_t\) records the share at each peak \(t\). A rule would map that distribution to a feasible location. But this would be a new question about rules on population distributions, not a computational version of a named result in this paper. In an atomless population, one resident’s report has zero effect; replacing individual strategy-proofness with profitable positive-mass coalition deviations changes the strategic question.
The main weakness is therefore decisive for ChoCo’s scope: the paper keeps the population finite and makes the outcome space continuous. Its mathematical results are axiomatic, not computational. The resident-distribution scenario is credible as motivation for separate work, but it cannot support a positive continuous mirror of this paper’s computational results.
The proponent raises no valid computational anchor. Theorem 1 and Corollaries 1–3 characterize strategy-proof rules and their anonymous, efficient, and feasibility-constrained subclasses. They do not analyze an algorithmic problem or establish a complexity result. The strongest named results in the paper are therefore axiomatic, not computational.
A municipality with many residents sharing ideal locations is a credible high-multiplicity setting: the type is a peak, and a distribution over peaks is sensible. That answers the modelling question in its favor, but it does not supply a computational question from the paper. The results classify whole functions from preference profiles to outcomes; they do not take a society distribution as an instance and ask for an optimum, a minimum cost, or a complexity bound. One could add such a task—for example, the minimum mass needed to move an outcome—but that requires specifying a target, costs, and a deviation model absent from the paper. With an atomless population, individual deviations have zero mass; using positive-mass coalitions is a plausible choice, but it changes the strategic question rather than continuizing a computational one the authors studied.
Nor does the paper provide a canonical finite encoding for an algorithmic version of its characterization. Its rules may have countably many discontinuities and tie-breaking choices across sets of profiles. Restricting those to a finite representation could yield a computational problem, but its definition and complexity would depend on added choices about how rules and feasible sets are encoded. That would be new computational work motivated by the paper, not a mirror of one of its results.
So the negative case is strong on ChoCo’s stated criterion: this paper offers no computational result to continuize. The residents-to-peaks scenario is plausible, and it would be wrong to dismiss it because individuals have zero mass. The limitation is narrower: making that society continuous does not turn this axiomatic characterization into a computational mirror. The universal claim that no worthwhile follow-on question could ever be built from the paper is harder to establish; the case is strongest against calling such a question this paper’s continuous mirror.
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.