# Consistent Probabilistic Social Choice

arXiv: https://arxiv.org/abs/1503.00694 · HTML: https://mlsanity.com/paper/1503.00694/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Feb 2015.

## Built on by (most cited first, 4 of 4)

- [A Minimaximalist Approach to Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2401.04056/) (2024)
- [Is RLHF More Difficult than Standard RL?](https://mlsanity.com/paper/2306.14111/) (2023)
- [AI Alignment From Social Choice Perspectives](https://mlsanity.com/paper/2606.21550/) (2026)
- [Robust AI Evaluation through Maximal Lotteries](https://mlsanity.com/paper/2602.21297/) (2026)

## Abstract (arXiv)

Two fundamental axioms in social choice theory are consistency with respect to a variable electorate and consistency with respect to components of similar alternatives. In the context of traditional non-probabilistic social choice, these axioms are incompatible with each other. We show that in the context of probabilistic social choice, these axioms uniquely characterize a function proposed by Fishburn (Rev. Econ. Stud., 51(4), 683--692, 1984). Fishburn's function returns so-called maximal lotteries, i.e., lotteries that correspond to optimal mixed strategies of the underlying plurality game. Maximal lotteries are guaranteed to exist due to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming.