多党竞选

摘要：

我们研究了一个社会选择设置的操纵选举和扩展通常的模型在两个主要方面：第一，而不是考虑一个单一的操纵代理，在我们的设置有几个，可能竞争的;第二，而不是评估选举后的第一个操纵行动，我们允许几个来回轮发生。我们表明，在某些情况下，如在选举中只有几个候选人，每个操纵代理的最佳策略可以有效地计算。我们的算法结果依赖于制定的问题，找到一个最佳的策略，Presburger算法的句子是短的，只涉及小系数，我们表明是固定参数的易处理性-事实上，我们的贡献之一是一个一般的结果，关于固定参数的易处理性Presburger算法，可能是有用的，在其他设置。根据我们的一般定理，我们设计相当一般的算法，特别是，我们描述了如何设计有效的算法，为各种设置，包括设置在其中，我们模型的意见在社会网络中的扩散，复杂的预算方案提供给操纵代理，和各种现实的限制对手的行动。

英文摘要：

We study a social choice setting of manipulation in elections and extend the usual model in two major ways: first, instead of considering a single manipulating agent, in our setting there are several, possibly competing ones; second, instead of evaluating an election after the first manipulative action, we allow several back-and-forth rounds to take place. We show that in certain situations, such as in elections with only a few candidates, optimal strategies for each of the manipulating agents can be computed efficiently. Our algorithmic results rely on formulating the problem of finding an optimal strategy as sentences of Presburger arithmetic that are short and only involve small coefficients, which we show is fixed-parameter tractable -- indeed, one of our contributions is a general result regarding fixed-parameter tractability of Presburger arithmetic that might be useful in other settings. Following our general theorem, we design quite general algorithms; in particular, we describe how to design efficient algorithms for various settings, including settings in which we model diffusion of opinions in a social network, complex budgeting schemes available to the manipulating agents, and various realistic restrictions on adversary actions.

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