先验信息公平选择
Impartial selection with prior information
摘要：
我们研究的问题{ \em公正的选择}，一个话题，在计算的社会选择和机制设计的交叉点。目标是在一组社区成员中选择最受欢迎的个人。输入可以被建模为有向图，其中每个节点表示一个个体，并且有向边指示社区成员对另一个的提名或批准。{ \em公正机制}对个体的潜在自私行为是鲁棒的，并且通过确保节点成为赢家的机会不取决于其传出边来向投票者提供适当的激励以报告他们的真实偏好。我们的目标是设计一个公平的机制，选择一个节点的程度是尽可能接近最高的程度。我们通过这些入度的差异来衡量这种机制的效率，称为其{ \em加法}近似。特别是，我们研究了在何种程度上选民的偏好先验信息可能是有用的，在设计高效的确定性公平的选择机制，具有良好的添加剂近似保证。我们考虑三种模型的先验信息，我们称之为{ \em民意测验}，{ \em一个先验流行}，和{ \em统一}模型。我们分析了自然选择机制，我们称之为{ \em批准投票与默认}（AVD）的性能，并表明它实现了$O(\sqrt{n\ln{n}})$添加剂保证民意调查和$O(\ln^2n)$的先验流行输入，其中$n$是个人的数量。我们认为这是我们的主要技术贡献polylogarithmic约束。我们补充这最后一个结果表明，我们的分析是接近紧，显示了一个$Ω(\ln{n})$下限。这在统一模型中成立，它是三个模型中最简单的。
英文摘要：
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 $Ω(\ln{n})$ lower bound. This holds in the uniform model, which is the simplest among the three models.
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