Decreasing higher-order absolute risk aversion and higher-degree stochastic dominance

Fishburn and Vickson (Stochastic dominance: an approach to decision-making under risk, Lexington Books, D.C. Heath and Company, Lexington, pp. 39–113, 1978) showed that, when applied to random alternatives with an equal mean, 3rd-degree and decreasing absolute risk aversion stochastic dominances represent equivalent rules. The present paper generalizes this result to higher degrees. Specifically, higher-degree stochastic dominance rules and common preference by all decision makers with decreasing higher-order absolute risk aversion are shown to coincide under appropriate constraints on the respective moments of the random variables to be compared.