Parametrized algorithms for random serial dictatorship

Voting and assignment are two of the most fundamental settings in social choice theory. For both settings, random serial dictatorship (RSD) is a well-known rule that satisfies anonymity, ex post efficiency, and strategyproofness. Recently, it was shown that computing the resulting probabilities is #P-complete both in the voting and assignment setting. In this paper, we present efficient parametrized algorithms to compute the RSD probabilities for the parameters the number of agent types, alternatives, or objects. When the parameters are small, then the respective algorithms are considerably more efficient than the naive approach of going through all permutations of agents.