A Subjective Spin on Roulette Wheels
为Anscombe-Aumann决策框架中的“混合”行为提供了主观基础,无需随机化设备即可构建混合空间公理,简化了仅使用行为数据的公理模型开发,并避免了概率扭曲问题。
We provide a behavioral foundation to the notion of 'mixture' of acts, which is used to great advantage in the decision setting introduced by Anscombe and Aumann. Our construction allows one to formulate mixture-space axioms even in a fully subjective setting, without assuming the existence of randomizing devices. This simplifies the task of developing axiomatic models which only use behavioral data. Moreover, it is immune from the difficulty that agents may 'distort' the probabilities associated with randomizing devices. For illustration, we present simple subjective axiomatizations of some models of choice under uncertainty, including the maxmin expected utility model of Gilboa and Schmeidler, and Bewley's model of choice with incomplete preferences.