Continuous Social Decision Procedures

Classical social decision procedures are supposed to map lists of preference orderings into binary relations which describe society's "preferences." But when there are infinitely many alternatives the resulting plethora of possible preference orderings make it impossible to differentiate "nearby" preference relations. If the preference information used to make social decisions is imperfect, society may wish to implement a continuous social decision procedure (SDP) so that nearby preference configurations will map into nearby social preference relations. It is shown here that a continuity requirement can severely restrict the admissible behavior of a social decision procedure. Furthermore a characterization of continuous SDPs is presented which facilitates the examination of such procedures and their relation to various voting mechanisms.