Random dictatorship domains

• Main Authors: CHATTERJI, Shurojit, SEN, Arunava, ZENG, Huaxia
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2014
• Subjects: Strategy-proofness; Random social choice functions; Random dictatorship; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/1888; https://ink.library.smu.edu.sg/context/soe_research/article/2888/viewcontent/Random_Dictatorship_Domains_pp.pdf
• Institution: Singapore Management University

A domain of preference orderings is a random dictatorship domain if every strategy-proof random social choice function satisfying unanimity defined on the domain is a random dictatorship. Gibbard (1977) showed that the universal domain is a random dictatorship domain. We ask whether an arbitrary dictatorial domain is a random dictatorship domain and show that the answer is negative by constructing dictatorial domains that admit anonymous, unanimous, strategy-proof random social choice functions which are not random dictatorships. Our result applies to the constrained voting model. Lastly, we show that substantial strengthenings of linked domains (a class of dictatorial domains introduced in Aswal et al., 2003) are needed to restore random dictatorship and such strengthenings are "almost necessary".