This paper discusses criteria for comparing risk aversion among decision makers when outcomes are multidimensional. It introduces two concepts: "commodity specific greater risk aversion," which compares risk premia paid in a specific commodity, and "uniformly greater risk aversion," which compares risk premia regardless of the commodity used for payment. Neither concept assumes that von Neumann-Morgenstern utility functions are equivalent. The paper shows that nonincreasing consumption-specific risk aversion is sufficient to make randomization undesirable in an agency problem with hidden characteristics. The paper extends the Arrow-Pratt concept of absolute risk aversion to multidimensional outcomes and applies it to an incentive problem with hidden characteristics. It discusses the role of premium specificity versus uniformity in risk aversion, showing that the comparison of risk attitudes can depend on the specification of the risk premium. It also defines and characterizes "uniformly greater risk aversion," which applies regardless of the units in which the premium is paid. The paper provides an example of utility functions that are comparable by the criterion of "uniformly greater risk aversion" even though they do not satisfy the Kihlstrom-Mirman assumption of ordinal equivalence. The paper also shows that under certain assumptions, such as weakly decreasing consumption-specific risk aversion, it is never desirable to use randomized incentive schemes. It concludes that the concept of i-premium specific risk aversion is useful for studying differences in risk attitudes when ordinal preferences over the underlying outcome space are not identical. However, it warns that in situations involving differences in ordinal preferences, the comparative assessment of risk attitudes through the concept of i-premium specific risk aversion depends on the commodity in which risk premia are paid. The paper also introduces the notion of uniformly greater risk aversion, which is independent of how risk premia are paid.This paper discusses criteria for comparing risk aversion among decision makers when outcomes are multidimensional. It introduces two concepts: "commodity specific greater risk aversion," which compares risk premia paid in a specific commodity, and "uniformly greater risk aversion," which compares risk premia regardless of the commodity used for payment. Neither concept assumes that von Neumann-Morgenstern utility functions are equivalent. The paper shows that nonincreasing consumption-specific risk aversion is sufficient to make randomization undesirable in an agency problem with hidden characteristics. The paper extends the Arrow-Pratt concept of absolute risk aversion to multidimensional outcomes and applies it to an incentive problem with hidden characteristics. It discusses the role of premium specificity versus uniformity in risk aversion, showing that the comparison of risk attitudes can depend on the specification of the risk premium. It also defines and characterizes "uniformly greater risk aversion," which applies regardless of the units in which the premium is paid. The paper provides an example of utility functions that are comparable by the criterion of "uniformly greater risk aversion" even though they do not satisfy the Kihlstrom-Mirman assumption of ordinal equivalence. The paper also shows that under certain assumptions, such as weakly decreasing consumption-specific risk aversion, it is never desirable to use randomized incentive schemes. It concludes that the concept of i-premium specific risk aversion is useful for studying differences in risk attitudes when ordinal preferences over the underlying outcome space are not identical. However, it warns that in situations involving differences in ordinal preferences, the comparative assessment of risk attitudes through the concept of i-premium specific risk aversion depends on the commodity in which risk premia are paid. The paper also introduces the notion of uniformly greater risk aversion, which is independent of how risk premia are paid.