舒尔茨规则的联盟操纵
Coalitional Manipulation for Schulze's Rule
摘要：
Schulze的规则被用于包括Wikimedia和Debian在内的大量组织的选举中。其流行的部分原因是大量的公理性质，如单调性和孔多塞一致性，它满足。我们确定了一个潜在的缺点舒尔茨的规则：它是计算容易受到操纵。特别是，我们证明了计算未加权联盟操纵（UCM）是多项式的任何数量的机械手。这一结果适用于UCM的唯一获胜者和共同获胜者版本。这解决了Parkes and Xia（2012）提出的一个未决问题。我们还证明了计算一个加权联盟操纵（WCM）是多项式的有限数量的候选人。最后，我们讨论了唯一赢家UCM问题和共同赢家UCM问题之间的关系，并认为他们有实质上不同的充分必要条件存在一个成功的操纵。
英文摘要：
Schulze's rule is used in the elections of a large number of organizations including Wikimedia and Debian. Part of the reason for its popularity is the large number of axiomatic properties, like monotonicity and Condorcet consistency, which it satisfies. We identify a potential shortcoming of Schulze's rule: it is computationally vulnerable to manipulation. In particular, we prove that computing an unweighted coalitional manipulation (UCM) is polynomial for any number of manipulators. This result holds for both the unique winner and the co-winner versions of UCM. This resolves an open question stated by Parkes and Xia (2012). We also prove that computing a weighted coalitional manipulation (WCM) is polynomial for a bounded number of candidates. Finally, we discuss the relation between the unique winner UCM problem and the co-winner UCM problem and argue that they have substantially different necessary and sufficient conditions for the existence of a successful manipulation.
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