Egalitarianism and Utilitarianism in Multiple Criteria Decision Problems with Partial Information

Abstract

Egalitarianism and utilitarianism can be viewed as two opposed axiomatic principles from where to begin the search of appropriate solutions to multi-criteria problems. When a vector of criterion weights is provided, these two principles yield respectively to weighted maxmin solutions, and to weighted utilitarian solutions. However, if only partial information about the importance of the criteria is available, the situation becomes more complex and a variety of solutions which extend the utilitarian and the maxmin solution arise. In this paper we explore some of these solutions and their axiomatic properties. If a utilitarian principle is first considered and a pessimistic or an optimistic rule applied afterwards, then two new solution concepts arise. Utilitarian solutions based on the pessimistic rule are inequality averse, and therefore can be viewed as a compromise between the egalitarian and utilitarian solutions. We also explore the solutions obtained when an egalitarian principle with respect to the criteria is considered and a pessimistic or an optimistic rule is applied to select criterion weights.