Voting rules as statistical estimators
Voting rules as statistical estimators
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作为统计估计器的投票规则
DOI：
10.1007/s00355-011-0619-1
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发表时间：
2013
影响因子：
0.9
通讯作者：
M. Pivato
中科院分区：
文献类型：
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作者：
M. Pivato
我们对社会决策采用“认识论”的解释：有一个客观正确的选择，每个选民都会收到一个正确选择的“嘈杂信号”，社会目标是汇总这些信号，以对正确选择做出最好的猜测。一种认知方法是确定一个概率模型，并根据选民提供的数据计算最大似然估计器（MLE）、最大后验估计器（MAP）或期望效用最大化器（EUM）。我们首先证明，当且仅当抽象投票规则是评分规则时，可以将其解释为MLE或MAP。然后，我们专门研究基于距离的投票规则的情况，特别是在判断聚合中使用中位数规则。最后，我们展示了几种常见的“准功利主义”投票规则如何被解释为EUM。
We adopt an ‘epistemic’ interpretation of social decisions: there is an objectively correct choice, each voter receives a ‘noisy signal’ of the correct choice, and the social objective is to aggregate these signals to make the best possible guess about the correct choice. One epistemic method is to fix a probability model and compute the maximum likelihood estimator (MLE), maximum a posteriori (MAP) estimator or expected utility maximizer (EUM), given the data provided by the voters. We first show that an abstract voting rule can be interpreted as MLE or MAP if and only if it is a scoring rule. We then specialize to the case of distance-based voting rules, in particular, the use of the median rule in judgement aggregation. Finally, we show how several common ‘quasiutilitarian’ voting rules can be interpreted as EUM.