Probabilistic opinion pooling generalized. Part one: general agendas
研究了在一般议程（不要求事件集是σ-代数）上如何将多个人的概率赋值汇总为集体概率赋值，刻画了线性汇总和中立汇总，并统一了概率、二元判断和偏好聚合的结果。
How can several individuals’ probability assignments to some events be aggregated into a collective probability assignment? Classic results on this problem assume that the set of relevant events—the agenda—is a $$\sigma $$ -algebra and is thus closed under disjunction (union) and conjunction (intersection). We drop this demanding assumption and explore probabilistic opinion pooling on general agendas. One might be interested in the probability of rain and that of an interest-rate increase, but not in the probability of rain or an interest-rate increase. We characterize linear pooling and neutral pooling for general agendas, with classic results as special cases for agendas that are $$\sigma $$ -algebras. As an illustrative application, we also consider probabilistic preference aggregation. Finally, we unify our results with existing results on binary judgment aggregation and Arrovian preference aggregation. We show that the same kinds of axioms (independence and consensus preservation) have radically different implications for different aggregation problems: linearity for probability aggregation and dictatorship for binary judgment or preference aggregation.