| paper | d4-journals-geb-2024-0037 |
| authors | — |
| venue | ? |
| filed under | unclassified |
| judged by | gpt-6-luna / xhigh (triple__luna__xhigh__c6r1) |
| judge confidence | medium |
| authors would recognise it | no |
Theorem 1 gives an analytical characterization of an optimal action, but the paper states no named computational result to carry into a continuous society. The portfolio scenario is plausible as an application, yet its aggregation does not make the paper’s result a computational population problem.
fails bit a — no named computational result to mirror
No computational result is covered; the paper’s named results characterize prices and analyze efficiency, utility comparisons, and correlation in a two-owner game.
The strongest positive intuition is a high-volume portfolio of co-owned firms. If many partnerships share a small number of complete types—each type specifying the owners’ valuations, utilities, and beliefs—then mass could mean the fraction of partnerships of each type, and the action could be a price announcement for each type. That is a plausible high-multiplicity setting. But it changes the paper’s object: the paper studies two owners dissolving one partnership, not an aggregate decision across many independent partnerships. Aggregating copies of that game does not, by itself, create the computational question ChoCo studies.
The closest numbered result is Theorem 1, proved here. It characterizes the divider’s optimal price under a distribution band: \(m(x_D)=m_1(x_D)\) when \(x_D<\mu^-_{G_1}\), \(m(x_D)=x_D/2\) when \(\mu^-_{G_1}\le x_D\le\mu^+_{G_0}\), and \(m(x_D)=m_0(x_D)\) when \(x_D>\mu^+_{G_0}\). Here \(m_i(x_D)\) is the unique point separating the increasing and decreasing portions of the strictly quasiconcave payoff function induced by \(G_i\); \(\mu^-_{G_1}\) is the smallest median of \(G_1\), and \(\mu^+_{G_0}\) is the largest median of \(G_0\). This is an analytic characterization of an optimal action, not a complexity result: the paper gives no running-time claim or computational problem over a population of types. Its other named results likewise concern equilibrium, efficiency, and utility comparisons.
The distribution band describes uncertainty about one peer’s valuation. It is not a continuous society: the mechanism still has exactly two owners, and the paper’s continuous price and valuation spaces do not continuize the population. A continuum of repeated partnerships would be an added application, not a mirror of a computational result in this paper.
So the honest positive case does not yield a prover-ready continuous problem anchored in the paper’s results. The paper contains no named computational-complexity result of the kind required for an anchor. Its analysis may be useful background for a future model of many partnership dissolutions, but that would be a new problem rather than the continuous-population mirror requested here.
The best population scenario is a large portfolio of independent partnerships, with each partnership type recording both owners’ valuations, utility, beliefs, and any correlation between them. That is a plausible high-multiplicity regime. But it still does not give a computational mirror of this paper’s results: the paper has no numbered result about the complexity of a computational problem.
Theorem 1 is the strongest proposed anchor. It characterizes the divider’s optimal price pointwise in her valuation and the bounds of her prior set. Across a portfolio, one could ask for the distribution of optimal prices, aggregate payoffs, or the share of efficient dissolutions. With finitely many partnership types, those quantities follow by evaluating the relevant price rule type by type and aggregating. There is no shared choice among partnerships for a continuous society to make. If instead the question is to compute an optimal price from a CDF or distribution band, its complexity depends on how those functions are encoded; the paper supplies no finite-input computational problem to mirror.
The natural extensions of the paper’s efficiency, utility, and correlation results face the same problem. Aggregate versions would integrate type-level outcomes or compare them across types. Making the computation substantive would require adding something like a shared resource, a portfolio-wide constraint, or a decision about how to pair owners. Those could be worthwhile new models, but their central computational questions would come from the added coupling, not from the results in this paper.
The distribution band is also not a society: it represents uncertainty about the valuation of one chooser. Treating its probabilities as actual population mass changes their meaning. One could preserve the band as part of each partnership type in a portfolio model, but then it remains a local two-owner game repeated across types; the mass aggregation still does not create the paper’s missing computational problem.
This is a strong case against a *mirror of this paper’s results*, not proof that no useful population model could be built around Texas Shoot-Outs. The proposed portfolio is sensible, but the computational question it might motivate would be a new research direction, not a continuous-population counterpart of a named computational result here.
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.