In Yaari's (1987) dual theory of choice under risk, risks preferences are based on a functional that epends on a subjective function called distortion. In the context of Wang's (1996) premium principle, Wang and Young (1998) considered a sequence of classes of partial orderings of risk distributions characterizing the preferences of groups of risk averse agents that base decisions on this functional. Under this approach, if a distribution is perceived as less risky than another, the mean of the former is smaller or equal to the latter's, making some risk distributions of interest non-comparable. In this paper, we study a sequence of partial orders of risk distributions based on comparisons of successive integrals of TVaR curves that characterize the preferences of groups of agents exclusively concerned with large risks higher than the expected values. [This version: September 3, 2022]We acknowledge support received from the Ministerio de Ciencia e Innovación (Spain) under grant PID2020-116216GB-I00
