Societies and social decision functions

Antonio Camacho

pp. 217-253

in: Werner Leinfellner, Eckehart Köhler (eds), Developments in the methodology of social science, Berlin, Springer, 1974

Abstract

In this paper a model of social choice is developed. And it is argued, in the context of the model, that cardinal utility indices have to be considered and used if we want to develop a useful type of analysis.A class of societies _Q is defined. Each society S of the class l is supposed to go through different states Sj ₁, s _j2,… The preferences of the individuals of S with regard to the possible actions {a_1..,am} available to them depend, it is assumed, on the state of S that occurs. Axioms describing how the individuals order the possible sequence of actions a _Ф1, a _Ф2,…, for any given possible sequence of states s _{j 1}, s _{j 2}… are introduced. From these axioms, cardinal utility indices are derived. Using these cardinal utility indices, social decision functions, that is, functions that determine for each state of S the action that society should take, are constructed. These functions, which are very simple to operate, are shown to be Pareto-optimal in a sense precisely defined in the paper. It is then proved, Theorem 5, that there is no social decision function which is based only on the orderings of the set of possible actions by the members of society at each of its different states (and that also satisfies a rather mild anonymity condition) and that is Pareto-optimal over the class of societies Q.