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We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyistyle utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are (...) 

Can a group be an orthodox rational agent? This requires the group's aggregate preferences to follow expected utility (static rationality) and to evolve by Bayesian updating (dynamic rationality). Group rationality is possible, but the only preference aggregation rules which achieve it (and are minimally Paretian and continuous) are the lineargeometric rules, which combine individual values linearly and combine individual beliefs geometrically. Lineargeometric preference aggregation contrasts with classic linearlinear preference aggregation, which combines both values and beliefs linearly, but achieves only static (...) 

As stochastic independence is essential to the mathematical development of probability theory, it seems that any foundational work on probability should be able to account for this property. Bayesian decision theory appears to be wanting in this respect. Savage’s postulates on preferences under uncertainty entail a subjective expected utility representation, and this asserts only the existence and uniqueness of a subjective probability measure, regardless of its properties. What is missing is a preference condition corresponding to stochastic independence. To fill this (...) 

Stochastic independence has a complex status in probability theory. It is not part of the definition of a probability measure, but it is nonetheless an essential property for the mathematical development of this theory. Bayesian decision theorists such as Savage can be criticized for being silent about stochastic independence. From their current preference axioms, they can derive no more than the definitional properties of a probability measure. In a new framework of twofold uncertainty, we introduce preference axioms that entail not (...) 

