Most Expected Winner: An Interpretation of Winners over Uncertain Voter Preferences

TL;DR

This paper introduces the Most Expected Winner (MEW) as a new method for determining election winners under uncertain voter preferences, providing theoretical insights and practical algorithms for various probabilistic models.

Contribution

It proposes the MEW concept, analyzes its computational hardness, and develops efficient solvers and pruning strategies for practical election scenarios.

Findings

MEW is computationally hard in general but tractable in specific models.

Developed customized solvers for different voter preference distributions.

Practical algorithms perform well on real and synthetic data.

Abstract

It remains an open question how to determine the winner of an election when voter preferences are incomplete or uncertain. One option is to assume some probability space over the voting profile and select the Most Probable Winner (MPW) -- the candidate or candidates with the best chance of winning. In this paper, we propose an alternative winner interpretation, selecting the Most Expected Winner (MEW) according to the expected performance of the candidates. We separate the uncertainty in voter preferences into the generation step and the observation step, which gives rise to a unified voting profile combining both incomplete and probabilistic voting profiles. We use this framework to establish the theoretical hardness of \mew over incomplete voter preferences, and then identify a collection of tractable cases for a variety of voting profiles, including those based on the popular Repeated Insertion Model (RIM) and its special case, the Mallows model. We develop solvers customized for various voter preference types to quantify the candidate performance for the individual voters, and propose a pruning strategy that optimizes computation. The performance of the proposed solvers and pruning strategy is evaluated extensively on real and synthetic benchmarks, showing that our methods are practical.