Abstract Aggregations and Proximity Preservation: An Impossibility Result

An impossibility result for completely abstract social aggregation rules is presented. It is shown that non-imposition and a new no-veto property (two properties in the spirit of the Pareto principle and non-dictatorship respectively) are incompatible with an inter-profile consistency condition formulated in terms of proximity preservation.The result in this paper has been presented in the Staff Seminar at the University of Graz and at the 2001 Meeting of the Public Choice Society in San Antonio. We are grateful to all participants, especially Hannu Nurmi and Don Saari, and to an anonymous referee for helpful comments.