We study the problem of risk sharing within a household or syndicate. A household shares risky prospects using a social welfare functional. We characterize the social welfare functionals such that the household is collectively less risk averse than each member, and satisfies the Pareto principle...

This note shows that for two social welfare functions which are inequality averse with respect to certainty equivalents, if one is more inequality averse for certainty equivalents than the other, the household preference induced by optimally allocating aggregate bundles according to this social...