Indifferences and Domain Restrictions

Abstract

Abstract The purpose of this paper is to discuss the extent to which allowing for individuals to be indifferent among alternatives may alter the qualitative results that are obtained in social choice theory when domain restrictions are defined on profiles of linear orders. The general message is that indifferences require attention and careful treatment, because the translation of results from a world without indifferences to another where agents may be indifferent among some alternatives is not always a straightforward exercise. But the warning is not one-directional: sometimes indifferences complicate the statement of results, but preserve their essential message. Sometimes, they help to create domains where some rules work better than in the presence of linear orders. In other cases, however, their presence destroys the positive results that would apply in their absence. I provide examples of these three situations.