Belief aggregation, updating and dynamic collective choice

This paper decision-theoretically investigates the belief aggregation method which allows consistently updating the aggregate belief.After confirming that the Pareto axiom and dynamic consistency require the decision power of an individual to evolve proportionally to how much his/her prior has been successful, we propose a weaker Pareto axiom that applies only to one-step-ahead uncertainties and puts no restriction on how the decision powers should evolve.We show in the binary tree domain that taking the median belief satisfies the proposed axiom, even full ex-ante efficiency under a single-crossing condition and that dynamic voting implements it.Finally, we investigate the role of ambiguity aversion.