We develop joint foundations for the fields of social choice and opinion pooling using coherent sets of desirable gambles, a general uncertainty model that allows to encompass both complete and incomplete preferences. This leads on the one hand to a new perspective of traditional results of social choice (in particular Arrow’s theorem as well as sufficient conditions for the existence of an oligarchy and democracy) and on the other hand to using the same framework to analyse opinion pooling. In particular, we argue that weak Pareto (unanimity) should be given the status of a rationality requirement and use this to discuss the aggregation of experts’ opinions based on probability and (state-independent) utility, showing some inherent limitation of this framework, with implications for statistics. The connection between our results and earlier work in the literature is also discussed.

我们使用连贯的期望赌博集合为社会选择和意见收集领域建立了联合基础，这是一个通用的不确定性模型，可以同时包含完全偏好和不完全偏好。一方面，这为传统的社会选择结果提供了新的视角（特别是阿罗定理以及寡头政治和民主存在的充分条件），另一方面，使用了相同的框架来分析意见库。特别是，我们认为应该赋予弱Pareto（一致）合理性要求的地位，并使用它来讨论基于概率和（独立于状态的）效用的专家意见的汇总，这表明该框架存在一些固有的局限性，对统计有影响。