The computational study of election problems generally focuses on questions related to the winner or set of winners of an election. But social preference functions such as Kemeny rule output a full ranking of the candidates (a consensus). We study the complexity of consensus-related questions, with a particular focus on Kemeny and its qualitative version Slater. The simplest of these questions is the problem of determining whether a ranking is a consensus, and we show that this problem is coNP-complete. We also study the natural question of the complexity of manipulative actions that have a specific consensus as a goal. Though determining whether a ranking is a Kemeny consensus is hard, the optimal action for manipulators is to simply vote their desired consensus. We provide evidence that this simplicity is caused by the combination of election system (Kemeny), manipulative action (manipulation), and manipulative goal (consensus). In the process we provide the first completeness results at the second level of the polynomial hierarchy for electoral manipulation and for optimal solution recognition.

中文翻译：

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Kemeny共识复杂性

选举问题的计算研究通常集中于与选举获胜者或一组获胜者有关的问题。但是诸如Kemeny规则之类的社会偏好功能会输出候选人的完整排名（共识）。我们研究了与共识相关的问题的复杂性，特别关注了Kemeny及其定性版本Slater。这些问题中最简单的是确定排名是否是共识的问题，并且我们证明此问题是coNP完全的。我们还研究了以特定共识为目标的操纵行为的复杂性这一自然问题。尽管确定排名是否为Kemeny共识很困难，但对于机械手而言，最佳操作是简单地投票给他们期望的共识。我们提供的证据表明，这种简单性是由选举系统（Kemeny），操纵性行为（操纵性）和操纵性目标（共识）的组合引起的。在此过程中，我们在多项式层次结构的第二级提供第一完整性结果，以进行选举操作和最佳解决方案识别。