The impossibility of extending random dictatorship to weak preferences

•Random dictatorship (RD) is efficient and strategyproof for strict preferences.•It is the only social decision scheme satisfying both properties (Gibbard, 1977).•We show that no extension of RD to weak preferences satisfies both properties.•This holds even when significantly weakening the required degree of strategyproofness.

Random dictatorship has been characterized as the only social decision scheme that satisfies efficiency and strategyproofness when individual preferences are strict. We show that no extension of random dictatorship to weak preferences satisfies these properties, even when significantly weakening the required degree of strategyproofness.