One lottery over a vector outcome space is said to be riskier than another if every risk averse decision-maker prefers the latter to the former. We consider two other criteria for making such comparisons, one of which is a generalization of second-order stochastic dominance. Our main result is...

Given a utility defined on a Hilbert outcome space, we define at each outcome a generalized Arrow-Pratt (GAP) coefficient belonging to the Hilbert space. Comparing the risk aversion of such utilities using their GAP coefficients is equivalent to doing so in terms of other standard,...