Stable Manipulation in Voting

We introduce the problem of {\em stable manipulation} where the manipulators need to compute if there exist votes for the manipulators which make their preferred alternative win the election even if the manipulators' knowledge about others' votes are little inaccurate, that is, manipulation remains successful even under small perturbation of the non-manipulators' votes. We show that every scoring rule, maximin, Bucklin, and simplified Bucklin voting rules are stably manipulable in polynomial time for single manipulator. In contrast, stable manipulation becomes intractable for the Copeland$^\alpha$ voting rule for every $\alpha\in[0,1]$ even for single manipulator. However for a constant number of alternatives, we show that the stable manipulation problem is polynomial time solvable for every anonymous and efficient voting rules. Finally we empirically show that the probability that a uniformly random profile is stably manipulable decreases drastically even if manipulator possess little uncertainty about others' votes.