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Prior work on the complexity of bribery assumes that the bribery happens simultaneously, and that the briber has full knowledge of all voters votes. But neither of those assumptions always holds. 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 bribe/alter a given vote, and at the time of making that decision, the briber may not know what votes remaining voters are planning on casting. In this paper, 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, in fact jumping the problem up to completeness for high levels of the polynomial hierarchy or even PSPACE. On the other hand, we 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 in the online, sequential setting.
Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We introduce a fram
Previous work on voter control, which refers to situations where a chair seeks to change the outcome of an election by deleting, adding, or partitioning voters, takes for granted that the chair knows all the voters preferences and that all votes are
Candidate control of elections is the study of how adding or removing candidates can affect the outcome. However, the traditional study of the complexity of candidate control is in the model in which all candidates and votes are known up front. This
Most work on manipulation assumes that all preferences are known to the manipulators. However, in many settings elections are open and sequential, and manipulators may know the already cast votes but may not know the future votes. We introduce a fram
The bribery problem in election has received considerable attention in the literature, upon which various algorithmic and complexity results have been obtained. It is thus natural to ask whether we can protect an election from potential bribery. We a