The Query Complexity of Scoring Rules

Pablo Azar, S. Micali
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引用次数: 1

Abstract

Proper scoring rules are crucial tools to elicit truthful information from experts. A scoring rule maps X, an expert-provided distribution over the set of all possible states of the world, and ω, a realized state of the world, to a real number representing the expert’s reward for his provided information. To compute this reward, a scoring rule queries the distribution X at various states. The number of these queries is thus a natural measure of the complexity of the scoring rule. We prove that any bounded and strictly proper scoring rule that is deterministic must make a number of queries to its input distribution that is a quarter of the number of states of the world. When the state space is very large, this makes the computation of such scoring rules impractical. We also show a new stochastic scoring rule that is bounded, strictly proper, and which makes only two queries to its input distribution. Thus, using randomness allows us to have significant savings when computing scoring rules.
评分规则查询复杂度
适当的评分规则是从专家那里获得真实信息的关键工具。评分规则将X(专家提供的世界所有可能状态集合上的分布)和ω(世界的实现状态)映射为一个实数,表示专家对其提供的信息的奖励。为了计算这个奖励,评分规则查询不同状态下的分布X。因此,这些查询的数量是评分规则复杂性的自然度量。我们证明了任何确定的有界严格适当的评分规则都必须对其输入分布进行多次查询,该输入分布是世界状态数的四分之一。当状态空间非常大时,这使得这种评分规则的计算变得不切实际。我们还展示了一个新的随机评分规则,它是有界的,严格正确的,并且只对其输入分布进行两次查询。因此,使用随机性可以让我们在计算得分规则时节省大量时间。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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