Sum of Us：来自选择器的战略性选择
Sum of Us: Strategyproof Selection from the Selectors
摘要：
我们考虑一组n个代理上的有向图，其中边（i，j）被认为意味着代理i支持或信任代理j。给定这样的图和整数k \leq n，我们希望选择k个代理的子集，其最大化度的和，即，k个最受欢迎或最受信任的代理的子集。同时，我们假设每个个体代理只对被选择感兴趣，并且可能为此误报其传出边缘。这个问题的表述捕捉了现实的场景，代理人在他们自己之间进行选择，这可以在互联网搜索，社交网络（如Twitter）或声誉系统（如Epperly）的背景下找到。我们的目标是设计无支付机制，将每个图映射到要选择的代理的k子集，并满足以下两个约束：代理不能从错误报告它们的外出边缘和近似最优性中获益，即，所选择的代理子集的度的总和总是接近最优。我们的第一个主要结果是一个令人惊讶的不可能性：对于k \in {1，.，n-1}，没有确定性防策略机制可以提供有限的近似比。我们的第二个主要结果是一个随机的strategyproof机制的近似比，是有界的，从上面的四个为任何值的k，并接近一个k的增长。
英文摘要：
We consider directed graphs over a set of n agents, where an edge (i,j) is taken to mean that agent i supports or trusts agent j. Given such a graph and an integer k\leq n, we wish to select a subset of k agents that maximizes the sum of indegrees, i.e., a subset of k most popular or most trusted agents. At the same time we assume that each individual agent is only interested in being selected, and may misreport its outgoing edges to this end. This problem formulation captures realistic scenarios where agents choose among themselves, which can be found in the context of Internet search, social networks like Twitter, or reputation systems like Epinions. Our goal is to design mechanisms without payments that map each graph to a k-subset of agents to be selected and satisfy the following two constraints: strategyproofness, i.e., agents cannot benefit from misreporting their outgoing edges, and approximate optimality, i.e., the sum of indegrees of the selected subset of agents is always close to optimal. Our first main result is a surprising impossibility: for k \in {1,...,n-1}, no deterministic strategyproof mechanism can provide a finite approximation ratio. Our second main result is a randomized strategyproof mechanism with an approximation ratio that is bounded from above by four for any value of k, and approaches one as k grows.
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。
