Belief aggregation, updating and dynamic collective choice

This paper decision-theoretically investigates the belief aggregation method which allows consistently updating the aggregate belief.
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\nAfter 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.
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\nWe 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.
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\nFinally, we investigate the role of ambiguity aversion.