Dictatorial domains

• Main Authors: ASWAL, Navin, CHATTERJI, Shurojit, SEN, Arunava
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2003
• Subjects: social choice functions; strategyproof; dictatorship; Gibbard-Satterthwaite theorem; restricted domains; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/1883; https://ink.library.smu.edu.sg/context/soe_research/article/2883/viewcontent/DictatorialDomains_av.pdf
• Institution: Singapore Management University

In this paper, we introduce the notion of a linked domain and prove that a non-manipulable social choice function defined on such a domain must be dictatorial. This result not only generalizes the Gibbard-Satterthwaite Theorem but also demonstrates that the equivalence between dictatorship and non-manipulability is far more robust than suggested by that theorem. We provide an application of this result in a particular model of voting. We also provide a necessary condition for a domain to be dictatorial and use it to characterize dictatorial domains in the cases where the number of alternatives is three.