The diversification theorem restated: Risk-pooling without assignment of probabilities

Bayesian decision theory assumes that agents making choices assign subjective probabilities to outcomes, even in cases where information on probabilities is obviously absent. Here we show that agents that presume that they are equal risks can share risks mutually beneficially, even if the probabilities of losses are unpredictable or genuinely uncertain. We show also that different risk aversions among pool members do not exclude mutually beneficial loss sharing at uncertainty. Sharing when individuals' losses differ in probabilities or in amount may still make individuals better off. Our findings are related to the theory of the insurance firm, to the management of development risks, and to the theory of justice.