  Bribery in an election is one of the well-studied control problems in
computational social choice. In this paper, we propose and study the safe
bribery problem. Here the goal of the briber is to ask the bribed voters to
vote in such a way that the briber never prefers the original winner (of the
unbribed election) more than the new winner, even if the bribed voters do not
fully follow the briber's advice. Indeed, in many applications of bribery,
campaigning for example, the briber often has limited control on whether the
bribed voters eventually follow her recommendation and thus it is conceivable
that the bribed voters can either partially or fully ignore the briber's
recommendation. We provide a comprehensive complexity theoretic landscape of
the safe bribery problem for many common voting rules in this paper.
