使用比较函数激发单峰偏好
Eliciting Single-Peaked Preferences Using Comparison Queries
摘要：
投票是聚合多个代理人偏好的通用方法。每个代理对所有可能的备选方案进行排名，并基于此，产生备选方案（或至少是获胜的备选方案）的综合排名。然而，当有许多选择时，简单地要求代理人报告他们的完整偏好是不切实际的。相反，代理人的偏好，或至少其相关部分，需要被引出。这是通过向代理询问（希望是少量的）关于其偏好的简单查询来完成的，例如比较查询，其要求代理比较两个备选方案。以前的工作偏好诱导投票的情况下，集中在无限制的偏好。它已被证明，在这种情况下，有时需要问每个代理（几乎）尽可能多的查询，将需要确定一个任意排名的替代品。相比之下，在本文中，我们专注于单峰偏好。我们表明，这样的偏好可以引起只使用线性数量的比较查询，如果相对于偏好是单峰的顺序是已知的，或至少有一个其他代理人完整的偏好是已知的。我们表明，使用次线性数量的查询是不够的。我们也考虑基数单峰偏好的情况。对于这种情况下，我们表明，如果替代品的基数位置是已知的，那么代理商的偏好，可以引起只使用对数数量的查询，但是，我们也表明，如果基数位置是未知的，那么次线性数量的查询是不够的。我们目前的实验结果，所有启发式算法。我们还考虑的问题，只引出足够的信息，以确定聚合排名，并表明，即使是这个更温和的目标，每个代理的查询的次线性数量不足以为已知的序数或未知的基数位置。最后，我们讨论了这些技术是否以及如何可以应用时，偏好几乎是单峰。
英文摘要：
Voting is a general method for aggregating the preferences of multiple agents. Each agent ranks all the possible alternatives, and based on this, an aggregate ranking of the alternatives (or at least a winning alternative) is produced. However, when there are many alternatives, it is impractical to simply ask agents to report their complete preferences. Rather, the agents preferences, or at least the relevant parts thereof, need to be elicited. This is done by asking the agents a (hopefully small) number of simple queries about their preferences, such as comparison queries, which ask an agent to compare two of the alternatives. Prior work on preference elicitation in voting has focused on the case of unrestricted preferences. It has been shown that in this setting, it is sometimes necessary to ask each agent (almost) as many queries as would be required to determine an arbitrary ranking of the alternatives. In contrast, in this paper, we focus on single-peaked preferences. We show that such preferences can be elicited using only a linear number of comparison queries, if either the order with respect to which preferences are single-peaked is known, or at least one other agents complete preferences are known. We show that using a sublinear number of queries does not suffice. We also consider the case of cardinally single-peaked preferences. For this case, we show that if the alternatives cardinal positions are known, then an agents preferences can be elicited using only a logarithmic number of queries; however, we also show that if the cardinal positions are not known, then a sublinear number of queries does not suffice. We present experimental results for all elicitation algorithms. We also consider the problem of only eliciting enough information to determine the aggregate ranking, and show that even for this more modest objective, a sublinear number of queries per agent does not suffice for known ordinal or unknown cardinal positions. Finally, we discuss whether and how these techniques can be applied when preferences are almost single-peaked.
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。
