Aggregating and Updating Information

We study information aggregation problems where to a set of measures a single measure of the same dimension is associated. The collection of measures could represent the beliefs of agents about the state of the world, and the aggregate would then represent the beliefs of the population. Individual measures could also represent the connectedness of agents in a social network, and the aggregate would reflect the importance of each individual. We characterize the aggregation rule that resembles the Nash welfare function. In the special case of probability aggregation problems, this rule is the only one that satisfies Bayesian updating and some well-known axioms discussed in the literature.