论文标题
非线性可取性理论
Nonlinear desirability theory
论文作者
论文摘要
可渴望可以理解为ANSCOMBE和AUMANN的贝叶斯决策理论的扩展，以延伸到一组预期的实用程序。可取性的核心在于一个测量奖励的量表线性的假设。它是一种传统的假设，用于得出预期的效用模型，该模型与理性决策做出的一般表示。尤其是，阿莱斯（Allais）在1953年以他著名的悖论指出了这一点。我们注意到，当我们将可取性视为逻辑理论时，公用事业量表起着封闭操作员的作用。该观察结果使我们能够通过一般闭合操作员表示实用程序量表来扩展到非线性情况。新理论直接以实际的非线性货币（货币）表达了奖励，这在野蛮的精神上很大程度上表达，同时可以说将基础假设削弱到最低限度。我们从一组赌博的角度及其上价和高价（预防）来表征新理论的主要特性。我们展示了Allais悖论如何在新理论中找到解决方案，并讨论了该理论中概率集的作用。
Desirability can be understood as an extension of Anscombe and Aumann's Bayesian decision theory to sets of expected utilities. At the core of desirability lies an assumption of linearity of the scale in which rewards are measured. It is a traditional assumption used to derive the expected utility model, which clashes with a general representation of rational decision making, though. Allais has, in particular, pointed this out in 1953 with his famous paradox. We note that the utility scale plays the role of a closure operator when we regard desirability as a logical theory. This observation enables us to extend desirability to the nonlinear case by letting the utility scale be represented via a general closure operator. The new theory directly expresses rewards in actual nonlinear currency (money), much in Savage's spirit, while arguably weakening the founding assumptions to a minimum. We characterise the main properties of the new theory both from the perspective of sets of gambles and of their lower and upper prices (previsions). We show how Allais paradox finds a solution in the new theory, and discuss the role of sets of probabilities in the theory.
