| paper | d4-conf-ijcai-2009-0297 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The paper presents an exact-choice procedure, but it has no numbered theorem, lemma, corollary, or proposition asserting a computational result. The opponent’s collective welfare scenario is recognizable, but its unnumbered algorithm and experiments do not meet the required anchor criterion.
fails bit a — no named computational result to mirror
No qualifying result is covered; the exact-choice method and runtime experiments do not supply a numbered computational anchor.
The paper has no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result, so it offers no qualifying anchor for a continuous mirror under your criteria. Its exact-choice method is supported by an unnumbered correctness argument, and its performance claims by experiments; Definitions 1–4 are definitions, not computational results. With no valid anchor, there is no per-anchor continuous problem to state.
The claim that there is no computational result to mirror is too strong. The paper’s Section 3 presents a fast exact choice procedure: rank alternatives under a more decomposable upper-bound utility \(g\), and stop when the best true utility found so far is at least \(g\)’s value for the next alternative. That stopping condition certifies an optimal choice. The paper also gives a practical construction of \(g\) and reports experiments on its runtime. These are computational results even though the authors did not package them as numbered complexity theorems. The case for a mirror should not claim that the paper proves a general polynomial-time bound; it need not.
A strong mirror comes from the paper’s own collective decision-making setting. Suppose a public body must choose one configuration \(x\) from a product of discrete attributes. Stakeholders have complete GAI utility types \(t\), and \(\mu_t\) is the fraction of the population with type \(t\). The collective objective is \(U_\mu(x)=\sum_t \mu_t u_t(x)\). The continuous question is whether the paper’s upper-bound method can find the exact welfare-maximizing configuration efficiently, with performance depending on the number of attributes, support size \(\tau\), input bit length, and the structure of the aggregate GAI network. A stronger version would construct the upper bound jointly from the mass-weighted utilities, since different types may have different factor structures.
This keeps the population as the continuous object and leaves the alternatives discrete. It is also a scenario the authors would recognize: they explicitly discuss collective decision-making and sums of individual GAI utilities. The mirror may turn out to be a straightforward extension of their method, or may show that differing type structures make the upper-bound construction costly. Either outcome answers a computational question about a population model the paper itself points toward. The case for a mirror is therefore real, though weaker than for a paper with an explicit complexity theorem: its motivation rests on the exact algorithm and the authors’ collective setting, not on a demonstrated continuous-population speedup.
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.