This paper investigates the number of profiles at which a social choice function is manipulable. It is found that there is a lower bound on this number when the social choice function is assumed non-dictatorial. Also, any number between this lower bound and the maximal number of profiles may be...

A well-known impossibility theorem in social choice theory states that every non-dictatorial social choice function, assigning a unique alternative from a set of at least three to every profile of individual preferences, can be manipulated. In this paper we examine a particular family of social...