Minimal Manipulable: Unanimity and Nondictatorship

This paper is concerned with the number of profiles at which a nondictatorial social choice function is manipulable. For three or more alternatives the lower bound is found for unanimous social choice functions. In the case of three alternatives the lower bound is found for surjective social choice functions. In both cases all social choice functions reaching the lower bound are characterized for more than two agents. In the case of two agents the characterized social choice functions form a subset of the set of all social choice functions reaching the minimum