| paper | d4-conf-aaai-2014-0251 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | unclear |
The paper discusses \(\#\mathrm{P}\) membership and presents Algorithms 1–5 with an \(O(n^3)\) bound, but neither is a numbered Theorem, Lemma, Corollary, or Proposition. The proponent explicitly offers only an unanchored asymptotic lead; its scaling is unspecified, and the tagged-team probability is not determined by \(\mu\) alone. It therefore cannot supply the required computational result with a continuous analogue.
fails bit a — no named computational result to mirror
No named computational result qualifies as an anchor. The \(\#\mathrm{P}\) discussion and the \(O(n^3)\) symmetric-case bound appear outside a numbered theorem-like result.
There is no admissible anchor under your rule: the paper has no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result. It does make computational claims in prose. Brute-force enumeration places the probability that a given team is a co-winner in \(\#\mathrm{P}\), while explicitly leaving \(\#\mathrm{P}\)-hardness and NP-hardness open. Algorithms 1–5 give upper and lower bounds, with an \(O(n^3)\) dynamic-programming analysis, for the symmetric-probabilities case. Those claims are not stated as numbered results of the required kind.
The most I can offer is an unanchored lead: a block random-tournament limit. Let \(T\) be finitely many complete competitor types, \(\mu_t\) their rational population masses, and \(p_{tu}\) the independent pairwise win probabilities between types. At each population scale \(N\), instantiate \(N\mu_t\) competitors of type \(t\). One could ask for the limit, as \(N\) grows, of the scaled probability that a tagged type-\(t\) competitor is a Copeland co-winner. This gives a concrete many-competitors, few-types regime, and the one-type fair case relates to the paper’s symmetric-tournament bounds.
But that is an asymptotic, type-level statistic, not the paper’s finite-tournament probability problem; the input distribution \(\mu\) alone also loses the tournament size, which affects that probability. I would not claim the authors’ required problem-recognition test is met, or present this as a mirror of a named result.
The proponent offers no admissible anchor: they identify no named theorem, lemma, corollary, or proposition asserting a computational result. The paper does contain computational claims—the \(\#\mathrm{P}\) membership discussion and an \(O(n^3)\) algorithm for bounding victory probabilities in the symmetric case—but the former is not a hardness result, and the latter is an algorithm described in prose, not a named result of the required kind. That is a serious problem for the case for a mirror.
The proposed block model is the strongest lead, but its best version changes the question. Give each of finitely many types \(t\) a mass \(\mu_t\) and pairwise win probabilities \(p_{tu}\), then instantiate \(N\mu_t\) competitors. A natural continuous score is \(q_\mu(t)=\sum_u\mu_u p_{tu}\). It is computable directly from the type data; it does not capture the paper’s probability that a particular team wins. In the continuum, an individual has zero mass, and the finite tournament’s stochastic fluctuations and extreme-score comparisons—the source of that probability—are lost. In nondegenerate symmetric cases, the mass of co-winners collapses toward zero. Asking instead for a scaled tagged-team probability retains finite-size fluctuations, but then \(N\) and the chosen scaling are essential inputs; the result is an asymptotic random-tournament problem, not a probability determined by the continuous society \(\mu\).
A finite-\(N\) tournament with repeated types and shared pairwise probabilities is coherent, and it might be worth studying as a high-multiplicity stochastic problem. But that possibility does not establish a worthwhile continuous mirror of a named result in this paper. The negative case is strongest under the programme’s anchor and population-continuum tests; it is weaker as a universal claim, since I cannot rule out the authors recognizing a carefully formulated block-type asymptotic problem as a useful extension.
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.