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.

本文从统计决策论的视角出发，提出了基于决策规则的社会选择机制，比较了Bayesian估计器、Mallows模型、Condorcet模型和Kemeny规则等各种类型的机制，并探讨了其规范性能、计算复杂度和渐近行为等方面的性质。其中，对于Condorcet模型，本文证明了Bayesian估计器满足匿名性、中立性和单调性等期望性能，能够在多项式时间内计算，并在一定条件下与其他两种决策规则渐近不同。

社会选择的统计决策理论框架