The Computational Complexity of Random Serial Dictatorship

TL;DR

This paper proves that computing the probabilities generated by the random serial dictatorship mechanism in social choice and assignment problems is #P-complete, indicating computational intractability despite its strategic and efficiency properties.

Contribution

It establishes the computational complexity of RSD, showing that calculating its outcome probabilities is #P-complete, a significant theoretical limitation.

Findings

Computing RSD probabilities is #P-complete.

RSD retains strategyproofness and ex post efficiency.

Intractability holds in voting and assignment contexts.

Abstract

In social choice settings with linear preferences, random dictatorship is known to be the only social decision scheme satisfying strategyproofness and ex post efficiency. When also allowing indifferences, random serial dictatorship (RSD) is a well-known generalization of random dictatorship that retains both properties. RSD has been particularly successful in the special domain of random assignment where indifferences are unavoidable. While executing RSD is obviously feasible, we show that computing the resulting probabilities is #P-complete and thus intractable, both in the context of voting and assignment.