Probabilistic Social Choice: New Proof Unlocks Fair, Efficient Decision Lotteries

Two fundamental axioms in social choice theory—consistency with respect to a variable electorate and consistency with respect to components of similar alternatives—have long been known to be incompatible in deterministic (non-probabilistic) settings. A new proof by Florian Brandl, Felix Brandt, and Hans Georg Seedig shows that in the context of probabilistic social choice, these axioms are not only compatible but uniquely characterize a function first proposed by Fishburn in 1984. Fishburn's function returns what are called maximal lotteries—lotteries that correspond to optimal mixed strategies in the underlying plurality game.

Maximal lotteries are guaranteed to exist thanks to von Neumann's Minimax Theorem, are almost always unique, and can be efficiently computed using linear programming. This means that for any set of alternatives and voter preferences, there is a well-defined, axiomatically justified probability distribution that respects both consistency criteria. The result has deep implications for multi-agent decision systems, AI alignment, and any domain where group decisions need to be both fair and computationally tractable. The paper is available on arXiv under the title 'Consistent Probabilistic Social Choice.'