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).
Generalized random dictatorships, Top-separable domains, Connected domains, Multidimensional single-peaked domains, Constrained voting
Behavioral Economics | Economic Theory
CHATTERJI, Shurojit and ZENG, Huaxia.
Random mechanism design on multidimensional domains. (2017). 1-54. Research Collection School Of Economics.
Available at: http://ink.library.smu.edu.sg/soe_research/2108
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