| paper | d4-conf-atal-2016-0275 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | no |
The paper reports analytical probability calculations, simulations, and empirical counts, but contains no numbered theorem, lemma, corollary, or proposition stating a computational result. The proposed mass-distribution detection problems are adjacent questions, not continuous mirrors of a qualifying result in this paper.
fails bit a — no named computational result to mirror
No result qualifies for mirroring under the required computational-result criterion; the paper's probability analyses, simulations, and empirical findings remain outside the mirror.
This paper contains no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational complexity result, so it has no valid anchor under the required criteria. Its numbered statements are Definitions 1 and 2; its other results are probability bounds and calculations, simulation findings, and empirical counts. The paper does report that Young’s and Dodgson’s rules are complete for parallel access to NP, but only as prior work, not as a numbered result proved here.
The closest possible mirrors would concern detecting the Condorcet Loser Paradox or Agenda Contraction Paradox from a rational mass distribution over rankings. But those would be newly proposed questions, not mirrors anchored to a qualifying named result of this paper. I can’t honestly present them as the required positive case.
The proponent’s case leaves no qualifying anchor to defeat. Definitions 1 and 2 define the Condorcet Loser Paradox and Agenda Contraction Paradox; they do not state computational results. The paper’s numbered analytical output is about probabilities under IAC, while its simulations and empirical counts measure how often the paradoxes occur. The complexity statements about Young’s and Dodgson’s rules are background, not results of this paper. That is a substantive gap for this programme: there is no named computational result here whose continuous-population counterpart the authors could recognize as their problem.
The strongest rescue would be to ask for the complexity of detecting either paradox in a society represented by rational masses over rankings. That is a coherent new computational question, but it is not a mirror of a result this paper establishes. A different rescue—computing asymptotic paradox probabilities—fits the paper more closely, but for IAC the continuous limit is already the volume of the paradox region in the profile simplex, and the paper reports such limit probabilities. For example, it gives the MaxiMin CLP limit for four alternatives and the MaxiMin ACP limit. That is an existing continuous analysis, not a missing complexity result.
Other stochastic models do not supply a stronger anchor. Under IC, independent voters’ type proportions converge to a fixed population distribution, so the limiting paradox question becomes evaluation at that society. A richer law over society distributions could support new probability-computation problems, but choosing such a law would add a model and a question the paper does not study.
So the negative case is strongest as a scope judgment: this paper may motivate adjacent continuous computational questions, but it does not provide a computational result to mirror, and its closest continuous asymptotic analysis is already present. I would not claim that no useful continuous problem related to voting paradoxes could ever be posed; the material does not support that universal claim. It does support rejecting this paper as an anchored mirror for the continuization programme.
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.