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تسجيل مستخدم جديدThe Complexity of Controlling Candidate-Sequential Elections
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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 paper develops a model for studying online control for elections where the structure is sequential with respect to the candidates, and in which the decision regarding adding and deleting must be irrevocably made at the moment the candidate is presented. We show that great complexity---PSPACE-completeness---can occur in this setting, but we also provide within this setting polynomial-time algorithms for the most important of election systems, plurality.
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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 sequentiall
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ework, in which manipulators can see the past votes but not the future ones, to model online coalitional manipulation of sequential elections, and we show that in this setting manipulation can be extremely complex even for election systems with simple winner problems. Yet we also show that for some of the most important election systems such manipulation is simple in certain settings. This suggests that when using sequential voting, one should pay great attention to the details of the setting in choosing ones voting rule. Among the highlights of our classifications are: We show that, depending on the size of the manipulative coalition, the online manipulation problem can be complete for each level of the polynomial hierarchy or even for PSPACE. We obtain the most dramatic contrast to date between the nonunique-winner and unique-winner models: Online weighted manipulation for plurality is in P in the nonunique-winner model, yet is coNP-hard (constructive case) and NP-hard (destructive case) in the unique-winner model. And we obtain what to the best of our knowledge are the first PNP[1]-completeness and PNP-completeness results in the field of computational social choice, in particular proving such completeness for, respectively, the complexity of 3-candidate and 4-candidate (and unlimited-candidate) online weighted coalition manipulation of veto elections.
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