Non-dictatorial Social Choice Rules Are Safely Manipulable

When a number of like-minded voters vote strategically and have limited abilities to communicate the under and overshooting may occur when too few or too many of them vote insincerely. In this paper we discuss this phenomenon and define the concept of a safe strategic vote. We prove that for any onto and non-dictatorial social choice rule there exist a profile at which a voter can make a safe strategic vote. This means that on occasion a voter will have an incentive to make a strategic vote and know that he will not be worse off regardless of how other voters with similar preferences would vote, sincerely or not. We also extend the Gibbard-Satterthwaite theorem. We prove that an onto, non-dictatorial social choice rule which is employed to choose one of at least three alternatives is safely manipulable by a single voter. We discuss new problems related to computational complexity that appear in this new framework.