Collective decision under ignorance

This paper studies aggregation of preferences under ignorance, in which everybody knows that the true probability distribution over outcomes lies in some objective set but knows nothing about which one in it is true or which one in it is more likely to be true. We consider two decision models which express the precautionary principle under ignorance, the maximin criterion and the \(\alpha \)-maximin criterion. We show that the Pareto axiom implies dictatorship, in each decision model. The impossibility results force us to choose between two options, one is to give up the precautionary principle as modelled at the social level, the other is to weaken the Pareto axiom. We provide possibility results for each of the options.