The complexity of online bribery in sequential elections

Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all votes. However, in many real-world settings votes come in sequentially, and the briber may have a use-it-or-lose-it moment to decide whether to alter a given vote, and when making that decision the briber may not know what votes remaining voters will cast. We introduce a model for, and initiate the study of, bribery in such an online, sequential setting. We show that even for election systems whose winner-determination problem is polynomial-time computable, an online, sequential setting may vastly increase the complexity of bribery, jumping the problem up to completeness for high levels of the polynomial hierarchy or even PSPACE. But we also show that for some natural, important election systems, such a dramatic complexity increase does not occur, and we pinpoint the complexity of their bribery problems.