Belief Aggregation, Updating and Dynamic Collective Choice

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