Voting rules as statistical estimators

Pivato, Marcus (2011): Voting rules as statistical estimators.

Abstract

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 estimator (MAP) 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.

• Item Type: MPRA Paper
• Language: English
• Keywords: voting; maximum likelihood estimator; maximum a priori estimator; expected utility maximizer; statistics; epistemic democracy; Condorcet jury theorem; scoring rule
• Subjects: D - Microeconomics > D8 - Information, Knowledge, and Uncertainty > D81 - Criteria for Decision-Making under Risk and Uncertainty; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics > C44 - Operations Research ; Statistical Decision Theory

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