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.

翻译：选举中的贿赂是计算社会选择学中一个被充分研究的控制问题。本文提出并研究了安全贿赂问题。在此问题中，贿赂者的目标是要求被贿赂的选民以某种方式投票，使得即使在被贿赂的选民未完全遵循其建议的情况下，贿赂者也永远不会比新胜出者更偏爱未贿赂选举的原始胜出者。实际上，在许多贿赂应用场景中（例如竞选活动），贿赂者往往对被贿赂选民是否最终遵循其建议的控制能力有限，因此可以合理假设被贿赂选民可能部分或完全忽视贿赂者的建议。本文针对多种常见投票规则，为安全贿赂问题提供了完整的计算复杂性理论图景。