| paper | d4-conf-aaai-2011-0005 |
| 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’s named results characterize mechanisms and state a revelation principle, but none asserts an algorithm, computational complexity, or a formulation used to compute. The proposed population extension would therefore need a new computational question rather than continuizing a computational result of this paper.
fails bit a — no named computational result to mirror
No result qualifies for a computational mirror: Theorem 14 characterizes dominant-strategy auctions, Theorem 12 gives a revelation principle, and Theorem 1 is a cited mechanism impossibility; Corollary 15 likewise states mechanism properties.
I can’t make a qualifying positive case under ChoCo’s rules: the paper has no numbered result asserting a computational complexity classification or an algorithm for a computational problem.
The closest candidate is Theorem 14, proved in this paper. It says that every sequential posted-price auction has a dominant-strategy equilibrium in every independent-private-value deliberative setting, and that there are such settings in which the only dominant-strategy-implementable social choice functions are those implemented by sequential posted-price auctions. That is a mechanism characterization, not a tractability or hardness result. Theorem 12, also proved here, is a revelation principle for deliberative agents; Theorem 1 is an impossibility result cited from Larson and Sandholm. Neither supplies a computational-complexity anchor.
One could imagine extending Theorem 14 to a population with finitely many deliberation types, where \(\mu_t\) is the fraction of buyers with a given prior, deliberation technology, and cost structure. But the resulting question would still be a mechanism-characterization question, not the computational question this programme targets. With no eligible anchor, I would not present that extension as a ChoCo mirror.
The strongest case against is that this paper gives ChoCo no computational result to continuize. Theorem 14 characterizes dominant-strategy auctions; Theorem 12 proves a revelation principle; and Theorem 1, which the paper cites, is an impossibility result about mechanism properties. None states a complexity classification or gives an algorithm for a computational problem. The paper’s references to hard computation describe why agents may deliberate; the paper does not analyze the complexity of that deliberation.
Theorem 14 is the best candidate for a mirror. A plausible setting would have many buyers drawn from finitely many complete deliberation types, each specifying their valuation prior, information source, and costs. But the theorem’s social choice function identifies which named agent gets the single good, and its sequential auctions depend on agents’ positions and on who accepts first. A type distribution over \(\tau\) categories does not record those individual roles. Encoding each position as a type can make \(\tau\) grow with the population; merging agents into positive-mass types loses the identity of the recipient. In an atomless population, a single winner has zero mass, so the aggregate model does not capture that person’s utility or incentive to deliberate.
Scaling the supply with the population and allocating mass could make a continuous market model sensible. It would also create a new mechanism-characterization or optimization problem. For example, computing a revenue-maximizing price policy for a distribution of deliberation types could be a worthwhile follow-up, but this paper does not formulate or solve that problem. Nor do its revelation-principle results supply a computational anchor: they concern which social choice functions mechanisms implement, not the runtime for finding or evaluating them.
So the negative case is strong for ChoCo’s stated remit: there is no computational result here for a continuous mirror to extend. The absolute claim that no scenario could make continuous analysis worthwhile is harder to defend. A high-volume market with repeated buyer types is plausible. It could motivate a new project, but it does not turn this paper’s results into computational mirrors.
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.