Preference aggregation in a multiagent setting is a central issue in both human and computer contexts. In this paper, we study in terms of complexity the vulnerability of preference aggregation to destructive control. That is, we study the ability of an election's chair to, through such mechanisms as voter/candidate addition/suppression/partition, ensure that a particular candidate (equivalently, alternative) does not win. And we study the extent to which election systems can make it impossible, or computationally costly (NP-complete), for the chair to execute such control. Among the systems we study--plurality, Condorcet, and approval voting--we find cases where systems immune or computationally resistant to a chair choosing the winner nonetheless are vulnerable to the chair blocking a victory. Beyond that, we see that among our studied systems no one system offers the best protection against destructive control. Rather, the choice of a preference aggregation system will depend closely on which types of control one wishes to be protected against. We also find concrete cases where the complexity of or susceptibility to control varies dramatically based on the choice among natural tie-handling rules.

翻译：在多智能体环境中进行偏好聚合是人类与计算机领域的核心议题。本文从计算复杂性角度研究了偏好聚合在破坏性控制下的脆弱性。具体而言，我们探讨了选举主持人通过选民/候选人添加/删除/分区等机制确保特定候选人（即替代方案）无法获胜的能力。同时，我们研究了选举制度能在何种程度上使此类控制无法实施或计算成本高昂（NP完全问题）。在我们研究的选举制度（多数制、孔多塞制、赞同投票制）中，我们发现某些对主持人选择获胜者具有免疫力或计算抵抗力的制度，在主持人阻止特定候选人获胜方面仍存在脆弱性。此外，研究显示这些制度中没有任何单一系统能对破坏性控制提供最佳防护。实际上，偏好聚合系统的选择将密切取决于需要防范的控制类型。我们还发现若干具体案例，其中控制的复杂性或易受性会因自然平局处理规则的选择而产生显著差异。