| paper | d4-journals-geb-2024-0087 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
No named theorem, lemma, corollary, or proposition asserts an algorithm, complexity bound, hardness result, or computationally used formulation. The numbered results establish axiomatic postulates and monotonicity, so computing a continuous version of RM would be a new problem rather than a mirror of a computational result in this paper.
fails bit a — no named computational result to mirror
No named computational results are covered. Theorems 4.1, 4.2, 5.1, 6.1, 6.2, 7.1, and 8.2 establish postulates; Theorem 8.1 proves monotonicity.
I can’t make an anchor-based case for a continuous computational mirror: the paper contains no named computational result asserting tractability, hardness, or a parameterized complexity classification.
Its numbered theorems concern axiomatic properties of RM: iso-invariance (Theorem 4.1), the dummy postulates (Theorem 4.2), dominance (Theorem 5.1), donation (Theorems 6.1 and 6.2), the minimum-power bloc postulate (Theorem 7.1), and the quarrel postulate (Theorem 8.2). Theorem 8.1 establishes monotonicity of the modified game. None is a complexity result.
The paper’s probability is over divisions of a finite set of players, and its recursive measure uses the finite lattice of those divisions. Treating that probability or those axioms as the continuized object would miss ChoCo’s population-continuization scope. Exact computation of RM could be a separate computational question, but the paper gives no named complexity result to anchor its continuous mirror.
The proponent raises no anchor to defend: they name no theorem, lemma, or corollary about computational complexity. The numbered results establish axiomatic properties of RM; Theorem 8.1 establishes monotonicity. None classifies the cost of computing RM. A continuous version of those theorems would continue axiomatic questions, which are outside ChoCo’s scope. Computing RM for a compactly represented game could be a worthwhile new problem, but it would not mirror a computational result in this paper.
The best population scenario is a large weighted voting body with many players of the same weight. Its type distribution could describe the population, and its outcome could depend on the total yes-vote weight. But RM’s recursion averages over *one-player* changes: its loyal children remove one voter at a time. In an atomless model, an individual has zero mass, so that step—and the chance that a particular voter survives the recursive walk to a decisive division—is not specified by the mass distribution. Replacing the voter with a positive-mass atom restores the step but introduces an individually identifiable player. Defining RM as a limit of finite games instead requires choosing an approximation and normalization; those choices become extra input to the question.
That leaves a plausible asymptotic research direction, but the paper supplies neither a computational result to continuize nor a canonical continuous RM whose computation would mirror one. The negative case is strongest on that scope gap. It is not airtight against a carefully designed tagged-voter or finite-approximation theory, which could be interesting in its own right.
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.