Consistent Probabilistic Social Choice Revisited

2026-06-09

AI Summary

This study addresses the challenge of reproducing the maximal lotteries outcome—originally derived within the framework of fractional preference profiles—in the standard finite-voter model of social choice. By introducing a weaker continuity condition, the authors extend prior results, which were restricted to rational-valued probabilities, to the full space of real-valued probabilities. This extension reestablishes the existence and consistency of maximal lotteries within classical social choice settings. Integrating insights from probabilistic social choice theory, preference modeling, and axiomatic analysis, the work not only bridges the gap between abstract theoretical models and practical voting scenarios but also substantially enhances the theoretical robustness and applicability of the maximal lotteries mechanism.

Abstract

Brandt et al. (2016) characterized a probabilistic social choice function known as maximal lotteries within a framework based on fractional preference profiles, which abstracts away from individual voters. While this modeling assumption enables a more elegant and transparent proof, it complicates comparison with other results in the literature. The purpose of this note is to transfer their results to the standard model of social choice, where each preference profile is defined for a finite number of voters. Along the way, we prove a slightly stronger version of their main theorem that uses a weaker continuity condition and allows for real-valued (rather than only rational-valued) probabilities.

Problem

• probabilistic social choice
• maximal lotteries
• preference profiles
• social choice theory
• continuity condition

Innovation

• maximal lotteries
• probabilistic social choice
• fractional preference profiles
• continuity condition
• real-valued probabilities