真正难以操作的问题在哪里？操纵否决权规则的阶段性转变
Where are the really hard manipulation problems? The phase transition in manipulating the veto rule
摘要：
投票是一种简单的机制，可以聚合代理人的偏好。许多投票规则被证明是NP难操纵的。然而，最近的一些理论结果表明，这种复杂性可能只是在最坏的情况下，因为操纵往往是很容易在实践中。在本文中，我们表明，实证研究是有用的，在提高我们对这个问题的理解。我们证明，有一个平稳过渡的概率，联盟可以选出一个所需的候选人使用否决权规则的规模的操纵联盟的增加。我们表明，重新标度的概率曲线显示一个简单的和普遍的形式独立的问题的大小。我们认为，操纵的否决权规则是渐近容易许多独立和同分布的选票，即使在联盟的操纵者是关键的大小。基于这一论点，我们确定了一种情况下，操纵是计算困难的。这是当选票高度相关，选举是“挂”。然而，我们表明，即使是一个不相关的选民也足以使操纵再次变得容易。
英文摘要：
Voting is a simple mechanism to aggregate the preferences of agents. Many voting rules have been shown to be NP-hard to manipulate. However, a number of recent theoretical results suggest that this complexity may only be in the worst-case since manipulation is often easy in practice. In this paper, we show that empirical studies are useful in improving our understanding of this issue. We demonstrate that there is a smooth transition in the probability that a coalition can elect a desired candidate using the veto rule as the size of the manipulating coalition increases. We show that a rescaled probability curve displays a simple and universal form independent of the size of the problem. We argue that manipulation of the veto rule is asymptotically easy for many independent and identically distributed votes even when the coalition of manipulators is critical in size. Based on this argument, we identify a situation in which manipulation is computationally hard. This is when votes are highly correlated and the election is "hung". We show, however, that even a single uncorrelated voter is enough to make manipulation easy again.
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。
