Random Utility Theory for Social Choice

TL;DR

This paper advances random utility models for social choice by establishing conditions for fast Bayesian inference, demonstrating scalability and model selection capabilities through empirical and simulated data.

Contribution

It develops conditions enabling efficient Bayesian inference for general random utility models, including Plackett-Luce, with proven concavity and bounded solutions.

Findings

Supports scalability on real-world data

Demonstrates effective model selection

Provides fast inference methods

Abstract

Random utility theory models an agent's preferences on alternatives by drawing a real-valued score on each alternative (typically independently) from a parameterized distribution, and then ranking the alternatives according to scores. A special case that has received significant attention is the Plackett-Luce model, for which fast inference methods for maximum likelihood estimators are available. This paper develops conditions on general random utility models that enable fast inference within a Bayesian framework through MC-EM, providing concave loglikelihood functions and bounded sets of global maxima solutions. Results on both real-world and simulated data provide support for the scalability of the approach and capability for model selection among general random utility models including Plackett-Luce.