| paper | d4-conf-aaai-2002-0048 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | high |
| authors would recognise it | yes |
The multi-unit, high-multiplicity auction model is a plausible extension, but the paper states no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result. Its IP formulation and experiments do not meet the required named-result anchor, so bit (a) fails.
fails bit a — no named computational result to mirror
The proposed mirror concerns multi-unit winner determination with repeated LGB valuation types and per-capita supplies; it does not cover the paper's original single-unit formulation or its experiments as an anchored result.
I can’t provide a qualifying anchor: the paper has no numbered Theorem, Lemma, Corollary, or Proposition asserting a computational result. Its NP-completeness statement for winner determination is background attributed to [11], not a result proved here. Section 3.1 gives a direct IP formulation, and Section 4 reports computational experiments, but neither is a numbered result of the kind your anchor rule requires.
The strongest *unanchored* mirror would be high-multiplicity winner determination for logical bids. Let each type \(t\) be a complete LGB valuation, with mass \(\mu_t\), and let \(q_g\) be the supply of good \(g\) per capita. Choose masses \(x_{t,S}\ge 0\) of type-\(t\) buyers to receive each integral bundle \(S\subseteq G\), maximizing
\[
\sum_{t,S} x_{t,S}v_t(S)
\]
subject to \(\sum_S x_{t,S}\le\mu_t\) and \(\sum_{t,S:g\in S}x_{t,S}\le q_g\). This models many buyers with repeated logical valuations and per-capita goods supply; the type-level allocation can be fractional even though each buyer receives an integral bundle. The authors would plausibly recognize it as a continuous-population version of their winner-determination problem. But it does not meet the required anchor condition, so I can’t honestly present it as the requested case or assign it a verdict as an anchored result.
There is no qualifying anchor in this paper. Its NP-completeness statement is background attributed to prior work; Section 3.1 gives an IP formulation, and Section 4 reports solver experiments. Neither is a numbered result establishing the complexity of a computational problem. Under the requested anchor standard, no continuous question has been tied to a result of this paper.
The proposed high-multiplicity model is still plausible as a research direction. Repeated LGB valuation types and per-capita supplies give a coherent multi-unit allocation problem, and the authors themselves identify multi-unit CAs as future work. I cannot honestly claim that no scenario makes this worthwhile. The strongest negative case is narrower: that direction would extend the paper’s model, but it cannot supply the missing computational-result anchor. That makes the case against this paper as a target strong under the stated grading rule, while leaving the universal claim that no worthwhile mirror exists weak.
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.