Abstract We manage decisions under “objective” ambiguity by considering generalized Anscombe-Aumann acts, mapping states of the world to generalized lotteries on a set of consequences. A generalized lottery is modeled through a belief function on consequences, interpreted as a partially specified randomizing device. Preference relations on these acts are given by a decision maker focusing on different scenarios (conditioning events). We provide a system of axioms which are necessary and sufficient for the representability of these “conditional preferences” through a conditional functional parametrized by a unique full conditional probability P on the algebra of events and a cardinal utility function u on consequences. The model is able to manage also “unexpected” (i.e., “null”) conditioning events and distinguishes between a systematically pessimistic or optimistic behavior, either referring to “objective” belief functions or their dual plausibility functions. Finally, an elicitation procedure is provided, reducing to a Quadratically Constrained Linear Program (QCLP).

中文翻译：

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Dempster-Shafer 理论中客观模糊下建模代理的条件偏好

摘要 我们通过考虑广义 Anscombe-Aumann 行为，将世界状态映射到一组后果的广义彩票来管理“客观”模糊下的决策。广义彩票通过对结果的置信函数建模，解释为部分指定的随机化设备。这些行为的偏好关系由关注不同场景（条件事件）的决策者给出。我们提供了一个公理系统，这些公理对于这些“条件偏好”的可表示性来说是必要的和充分的，它通过一个条件函数参数化，该函数由关于事件代数的唯一完全条件概率 P 和关于结果的基数效用函数 u 参数化。该模型还能够管理“意外”（即，“空”）条件事件，并区分系统的悲观或乐观行为，指的是“客观”信念函数或它们的双重似然函数。最后，提供了一个启发程序，简化为二次约束线性程序 (QCLP)。