Aggregation of multiple prior opinions

• 成果类型: Article
• 署名作者: Cres, Herve; Gilboa, Itzhak; Vieille, Nicolas
• 署名单位: Hautes Etudes Commerciales (HEC) Paris; Institut d'Etudes Politiques Paris (Sciences Po); Tel Aviv University
• 刊物名称: JOURNAL OF ECONOMIC THEORY
• ISSN/ISSBN: 0022-0531
• DOI: 10.1016/j.jet.2011.06.018
• 发表日期: 2011
• 页码: 2563-2582
• 关键词: Aggregation of opinions; ambiguity; multiple priors

摘要

Experts are asked to provide their advice in a situation of uncertainty. They adopt the decision maker's utility function, but each has a potentially different set of prior probabilities, and so does the decision maker. The decision maker and the experts maximize the minimal expected utility with respect to their sets of priors. We show that a natural Pareto condition is equivalent to the existence of a set Lambda of probability vectors over the experts, interpreted as possible allocations of weights to the experts, such that (i) the decision maker's set of priors is precisely all the weighted-averages of priors, where an expert's prior is taken from her set and the weight vector is taken from Lambda; (ii) the decision maker's valuation of an act is the minimal weighted valuation, over all weight vectors in Lambda, of the experts' valuations. (C) 2011 Elsevier Inc. All rights reserved.