Three Welfare Orderings That are Fully Comparable Revisited

We are concerned with welfare orderings on the set of evaluation vectors. In our framework the number of agents, criteria or states of nature is fixed and an evaluation vector assigns a real valued evaluation to each criteria, agent or state of nature. Hence the space of evaluation vectors is a finite dimensional Euclidean space. In such a context we provide axiomatic characterizations of the utilitarian, maximin and leximin welfare orderings. The axiomatic characterization of the utilitarian welfare ordering is based on a quasi-linearity property. The axiomatic characterizations of the maximin and leximin welfare orderings are obtained by suitably modifying the axioms used by Barbera and Jackson (1988)