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arXiv 1410.7856cs.AIcs.MA
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社会选择的统计决策理论框架

A Statistical Decision-Theoretic Framework for Social Choice

Google Research(谷歌研究院);Harvard University(哈佛大学);Rensselaer Polytechnic Institute(伦斯勒理工学院)

Hossein Azari Soufiani, David C. Parkes, Lirong Xia

摘要:

在本文中,我们采取统计决策理论的社会选择的观点,把重点放在决策代表一个系统的代理。在我们的框架中,我们给出了一个统计排名模型,决策空间,和(参数,决策)对定义的损失函数,并制定社会选择机制的决策规则,最大限度地减少预期损失。这为设计和分析新的社会选择机制提供了一个总体框架。我们比较贝叶斯估计,最大限度地减少贝叶斯预期损失,马洛模型和孔多塞模型分别,和Kemeny规则。我们考虑各种规范的属性,除了计算复杂性和渐近行为。特别是,我们证明了贝叶斯估计的孔多塞模型满足一些所需的属性,如匿名性,中立性和单调性,可以在多项式时间计算,是渐近不同的其他两个规则时,数据从孔多塞模型的一些地面真理参数。

英文摘要:

In this paper, we take a statistical decision-theoretic viewpoint on social choice, putting a focus on the decision to be made on behalf of a system of agents. In our framework, we are given a statistical ranking model, a decision space, and a loss function defined on (parameter, decision) pairs, and formulate social choice mechanisms as decision rules that minimize expected loss. This suggests a general framework for the design and analysis of new social choice mechanisms. We compare Bayesian estimators, which minimize Bayesian expected loss, for the Mallows model and the Condorcet model respectively, and the Kemeny rule. We consider various normative properties, in addition to computational complexity and asymptotic behavior. In particular, we show that the Bayesian estimator for the Condorcet model satisfies some desired properties such as anonymity, neutrality, and monotonicity, can be computed in polynomial time, and is asymptotically different from the other two rules when the data are generated from the Condorcet model for some ground truth parameter.

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。

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