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The Anscombe-Aumann representation and the independence axiom: a reconsideration

机译：Anscombe-Aumann表示法和独立公理：重新考虑

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摘要

We provide a new behavioral foundation for subjective expected utility (SEU) within the Anscombe-Aumann framework. In contrast to the original axiomatization of SEU, our behavioral foundation establishes that to be consistent with SEU maximization, we need not explicitly assume that preferences satisfy the independence axiom over the domain of all acts. Rather, the substantive implications of independence for an SEU representation may equivalently be derived from less demanding conditions over certain smaller classes of acts. These acts, which we refer to as uncertainty-free comparable acts, have the property that they are relatively simple for a decision maker to compare because she can rank acts within any such class based on her risk preferences alone, without having to consider the underlying uncertainty. Acts of this kind comprise constant acts and acts that are almost identical in the sense that they differ from one another in at most one state.
机译：我们为Anscombe-Aumann框架内的主观预期效用（SEU）提供了新的行为基础。与SEU最初的公理化相反，我们的行为基础确定为与SEU最大化相一致，我们无需明确假设偏好满足所有行为领域的独立性公理。相反，独立性对SEU代表制的实质性影响可能等效地来自某些较小类别行为的要求较低的条件。这些行为，我们称为无不确定性的可比行为，具有相对容易决策者比较的特性，因为她可以仅根据风险偏好将行为归入任何此类类别，而不必考虑潜在的风险。不确定。这种行为包括恒定的行为和在至多一种状态下彼此不同的意义上几乎相同的行为。

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