Aggregation of Preferences in Infinite Setting. Social Welfare Functions

A.V. Vladimirov

Institute of Control Sciences, Russian Academy of Sciences, Profsoyusnaya,

65, Moscow, 117806, Russia

e-mail: avv@ins.ru

Abstract

This paper characterizes social welfare functions (SWFs) satisfying Arrow's ``binary independence`` in the case where both the set of agents and the set of alternatives are not assumed to be finite. Consistent combinations of axioms imposed on the SWFs induce a distribution of individuals' power. In particular, power structure such as ``dictatorship`` corresponds to an ultrafilter. Our main result shows that any neutral to alternatives SWF can be uniquely represented as a linearly ordered subset of ultrafilters on Boolean algebra of coalition structure. We prove the above result without such axioms as monotonicity and various forms of the Pareto principle. Under more severe version of binary independence this result is equivalent to the known fact that ''absolutely dictatorial'' SWF is represented by an ultrafilter.