| paper | d4-journals-geb-2026-0049 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
Theorems 2 and 3 are constructive representation results, so they have computational character even without runtime bounds. But the proposed class-based population does not preserve their central object: coalitions of particular voters, whose unanimity and pivotal deviations do not carry over directly to a nonatomic mass model. Defining bloc unanimity, a terminal bloc, or a fallback would supply new semantics rather than a continuous analogue of either anchored result.
fails bit b-changes — the continuum limit changes the question
A distribution over class and preference does not retain which individuals belong to the paper's coalitions; preserving that information can make types grow with the electorate, while class-level rules change the unanimity test and nonatomic agents have no individual pivotality.
fatal: True
The proposed anchors are Theorems 2 and 3, which establish equivalence between the two rule representations. Theorem 1 is Moulin's cited characterization; the other results and the full-domain extensions are not mirrored.
I can’t give a compliant positive case with a named complexity anchor: the paper has no numbered result establishing that a problem is in \(P\), NP-hard, FPT, or otherwise classifying its complexity. Its algorithms are constructive, but the paper gives no running-time analysis.
The closest anchor is Theorem 2, proved here: for an \(M\)-winning coalition rule \(\mathcal C\), every sequential unanimity rule \(\mathcal S\) whose sequence Algorithm 1 produces from \(\mathcal C\) selects the same candidate as \(\mathcal C\) on every strict-preference profile. Theorem 3, also proved here, gives the reverse construction: Algorithm 2 turns a sequential unanimity rule into an \(M\)-winning coalition rule with the same outcome on every profile. These are representation-equivalence results, not complexity results.
The most plausible high-multiplicity setting would be a large electorate organized into a few recurring voting-power classes: a type records a voter’s class and binary preference, and its mass is that fraction of the electorate. One could ask for the winner under a rule defined by winning coalitions or a sequential list of class coalitions. But that would be a new winner-evaluation problem, not a continuous version of a named complexity result in this paper. The paper’s central contribution is the representation of neutral, strategy-proof rules, and continuizing that axiomatic question is outside ChoCo’s stated scope.
There is also a specific modeling snag: sequential unanimity ends with a singleton voter. In an atomless population, a singleton has zero mass and its preference is absent from the distribution, so it cannot serve as the rule’s backstop without changing the model. That change might be worth studying, but it makes the proposed mirror less clearly recognizable as the authors’ problem. Under the requested anchor requirement, there are therefore no continuous problems to state per anchor.
The strongest case against a ChoCo mirror is unusually direct: this paper states no computational complexity result to continuize. Theorem 1 is a prior axiomatic characterization. Theorem 2 and Theorem 3 prove that two representations select the same outcome profile by profile. Algorithms 1 and 2 construct those representations, but the paper gives no running-time, approximation, or parameterized analysis, and does not specify an encoded computational problem whose complexity they classify. The closest anchors the proponent identified are therefore representation results, not complexity results.
A plausible high-multiplicity setting does exist: many voters in a few recurring voting-power classes, with type recording class and preference and mass recording its share of the electorate. That makes winner determination or constructing a sequential procedure over class-level coalitions natural questions. It also shows why the singleton-backstop objection is not decisive: a mass model could use a positive-mass terminal bloc or a suitable default. But that repair supplies a new model and a new computational question. If the game is specified by a succinct class-level rule, its encoding determines the problem; if it is specified by the paper’s arbitrary coalition family, that family concerns named voters and may grow with the electorate. The paper picks neither formulation.
The deeper obstacle is that the paper’s central object is how coalitions of particular voters define a rule. A distribution over finitely many types retains the amounts of each type but not, by itself, which individuals belong together in those coalitions. One can preserve that information by making coalition role part of type, but then the number of types may grow with the electorate. Or one can require the rule to treat clones alike and define it directly on class masses, but that is an additional invariance condition and a new model. Neither route turns Theorem 2 or 3 into a continuous version of a computational result in the paper.
So the negative case is strong against calling this paper a ChoCo computational mirror: its results are axiomatic and representational, and its algorithms are not complexity claims. It does not prove that no worthwhile computational follow-up can be built around high-multiplicity voting. The honest point is narrower: such a follow-up would need its own problem definition and results, rather than continuing a computational question this paper already poses.
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.