We study the problem of {\em impartial selection}, a topic that lies at the intersection of computational social choice and mechanism design. The goal is to select the most popular individual among a set of community members. The input can be modeled as a directed graph, where each node represents an individual, and a directed edge indicates nomination or approval of a community member to another. An {\em impartial mechanism} is robust to potential selfish behavior of the individuals and provides appropriate incentives to voters to report their true preferences by ensuring that the chance of a node to become a winner does not depend on its outgoing edges. The goal is to design impartial mechanisms that select a node with an in-degree that is as close as possible to the highest in-degree. We measure the efficiency of such a mechanism by the difference of these in-degrees, known as its {\em additive} approximation. In particular, we study the extent to which prior information on voters' preferences could be useful in the design of efficient deterministic impartial selection mechanisms with good additive approximation guarantees. We consider three models of prior information, which we call the {\em opinion poll}, the {\em a prior popularity}, and the {\em uniform} model. We analyze the performance of a natural selection mechanism that we call {\em approval voting with default} (AVD) and show that it achieves a $O(\sqrt{n\ln{n}})$ additive guarantee for opinion poll and a $O(\ln^2n)$ for a priori popularity inputs, where $n$ is the number of individuals. We consider this polylogarithmic bound as our main technical contribution. We complement this last result by showing that our analysis is close to tight, showing an $\Omega(\ln{n})$ lower bound. This holds in the uniform model, which is the simplest among the three models.

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事先选择公正的信息

我们研究{\ em公正选择}的问题，这是一个计算社会选择与机制设计的交集。目标是从一组社区成员中选择最受欢迎的个人。输入可以建模为有向图，其中每个节点代表一个人，有向边表示社区成员向另一个成员的提名或批准。{\ em公正机制}对个人的潜在自私行为具有鲁棒性，并通过确保节点成为获胜者的机会不依赖于其外向优势，从而为选民提供了适当的激励机制，以报告其真实偏好。目标是设计一种公正的机制，以选择与最大in-degree尽可能接近的in-degree的节点。我们通过这些度数之差（称为其{\ em加法器}近似值）来测量这种机制的效率。尤其是，我们研究了有关选民偏好的先验信息在设计有效的确定性公正选择机制（具有良好的加法近似保证）方面的有用程度。我们考虑了三种先验信息模型，分别称为{\ em民意测验}，{\ em先验流行度}和{\ em统一}模型。我们分析了一种自然选择机制的性能，该机制称为{\ em带有默认投票批准}（AVD），并表明它为民意调查和$ O（\ ln ^ 2n）$用于先验受欢迎度输入，其中$ n $是个人数量。我们认为这种对数界限是我们的主要技术贡献。我们通过显示我们的分析接近严格，对$ \ Omega（\ ln {n}）$下界进行了补充，对最后一个结果进行了补充。这适用于统一模型，这是三个模型中最简单的一个。