Rawlsian maximin, Dutch books, and non-additive expected utility

The utilitarian and Rawlsian principles for choosing between income distributions in society are usually considered as alternatives and to some degree opposite approaches to the problem of social ranking. However, if the utilitarian principle is considered in the broader perspective of non-additive probabilities, contradictions disappear and the Rawlsian maximin principle appears as a special case of generalized expected utility maximization. In this paper we consider a set of axioms for a preference relation defined on a set of n-vectors, describing the distribution of welfare among a population of n individuals, which gives a utility representation as expected utility with respect to a suitable non-additive measure as in the rank-dependent utility models. The specific approach taken in the present paper consists in (1) relating the notion of Dutch books, which has proved useful in other applications, to the problem of ranking income distribution, and (2) using ordinal invariance to obtain a characterization in the form of a so-called k-Rawlsian social utility function, which reduces to the standard Rawlsian function by way of the Gärdenfors principle.