Random mechanism design on multidimensional domains

• Main Authors: CHATTERJI, Shurojit, ZENG, Huaxia
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2019
• Subjects: Generalized random dictatorships; Top-separability; Separability; Multidimensional single-peakedness; Connected+ domains; Voting under constraints; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2259; https://ink.library.smu.edu.sg/context/soe_research/article/3258/viewcontent/Random_Mechanism_Design_on_Multidimensional_Domains.pdf
• Institution: Singapore Management University

We study random mechanism design in an environment where the set of alternatives has a Cartesian product structure. We first show that all generalized random dictatorships are strategy-proof on a minimally rich domain if and only if the domain is a top-separable domain. We next generalize the notion of connectedness (Monjardet, 2009) to establish a particular class of top-separable domains: connected domains, and show that in the class of minimally rich and connected domains, the multidimensional single-peakedness restriction is necessary and sufficient for the design of a flexible random social choice function that is unanimous and strategy-proof. Such a flexible function is distinct from generalized random dictatorships in that it allows for a systematic notion of compromise. Our characterization remains valid (under an additional hypothesis) for a problem of voting with constraints where not all alternatives are feasible (Barbera et al., 1997).