In multiagent systems, we often have a set of agents each of which have a preference ordering over a set of items and one would like to know these preference orderings for various tasks, for example, data analysis, preference aggregation, voting etc. However, we often have a large number of items which makes it impractical to ask the agents for their complete preference ordering. In such scenarios, we usually elicit these agents' preferences by asking (a hopefully small number of) comparison queries --- asking an agent to compare two items. Prior works on preference elicitation focus on unrestricted domain and the domain of single peaked preferences and show that the preferences in single peaked domain can be elicited by much less number of queries compared to unrestricted domain. We extend this line of research and study preference elicitation for single peaked preferences on trees which is a strict superset of the domain of single peaked preferences. We show that the query complexity crucially depends on the number of leaves, the path cover number, and the distance from path of the underlying single peaked tree, whereas the other natural parameters like maximum degree, diameter, pathwidth do not play any direct role in determining query complexity. We then investigate the query complexity for finding a weak Condorcet winner for preferences single peaked on a tree and show that this task has much less query complexity than preference elicitation. Here again we observe that the number of leaves in the underlying single peaked tree and the path cover number of the tree influence the query complexity of the problem.

本研究探讨了对于多代理系统中的单峰树型偏好如何通过尽可能少的询问获取其偏好信息，并且发现查询复杂度与叶子数、路径覆盖数和路径距离等参数密切相关。在此基础上，还探讨了基于单峰树型偏好的弱Condorcet赢家查询复杂度相对较低的问题。

树上其单峰偏好的引导