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arXiv 2005.04037cs.SI
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基于社会影响力的多赢家选举控制

Multi-Winner Election Control via Social Influence

Mohammad Abouei Mehrizi, Gianlorenzo D'Angelo

摘要:

在选举中,我们有一组选民,每个人都有一个偏好列表,这些列表分布在社交网络上。我们考虑的情况下,选民可能会改变他们的偏好列表的结果,他们的邻居在社交网络中收到的消息。具体来说,我们考虑一个政治运动,在社会网络中传播的消息,支持或反对一个给定的候选人和传播遵循一个动态模型的信息扩散。当消息到达投票者时,后者根据更新规则改变其偏好列表。选举控制问题要求找到一个有界的节点集是支持(建设性问题)或反对(破坏性问题)一个给定的目标候选人$c$的政治运动的启动器,以这样的方式,$c$的胜利幅度w.r.t.它的最大投票对手被最大化。已经证明,这个问题的几个变体可以在最优的常数因子近似值内得到解决,这表明通过社交网络控制选举是可行的,并构成了现代民主国家的一个真正问题。然而,大多数文献都集中在单一赢家选举的情况下。在本文中,我们定义了社交网络中的选举控制问题的“多赢家选举”的目的是建模的候选人选举。从单赢家的情况下,我们表明,多赢家选举控制问题是NP-难的近似在任何因素的建设性和破坏性的情况下。然后,我们研究了一个放松的问题,其中选票汇总的基础上的政党(而不是单一的候选人),这是一个变化的所谓的“直党投票”在一些真正的选举。我们发现,后者的问题仍然是NP难的,但可以近似在一个常数因子。

英文摘要:

In an election, we are given a set of voters, each having a preference list over a set of candidates, that are distributed on a social network. We consider a scenario where voters may change their preference lists as a consequence of the messages received by their neighbors in a social network. Specifically, we consider a political campaign that spreads messages in a social network in support or against a given candidate and the spreading follows a dynamic model for information diffusion. When a message reaches a voter, this latter changes its preference list according to an update rule. The election control problem asks to find a bounded set of nodes to be the starter of a political campaign in support (constructive problem) or against (destructive problem) a given target candidate $c$, in such a way that the margin of victory of $c$ w.r.t. its most voted opponents is maximized. It has been shown that several variants of the problem can be solved within a constant factor approximation of the optimum, which shows that controlling elections by means of social networks is doable and constitutes a real problem for modern democracies. Most of the literature, however, focuses on the case of single-winner elections. In this paper, we define the election control problem in social networks for "multi-winner elections" with the aim of modeling parliamentarian elections. Differently from the single-winner case, we show that the multi-winner election control problem is NP-hard to approximate within any factor in both constructive and destructive cases. We then study a relaxation of the problem where votes are aggregated on the basis of parties (instead of single candidates), which is a variation of the so-called "straight-party voting" used in some real parliamentarian elections. We show that the latter problem remains NP-hard but can be approximated within a constant factor.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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