# Random mechanism design on multidimensional domains

*Shurojit Chatterji* and
*Huaxia Zeng*

*Journal of Economic Theory*, 2019, vol. 182, issue C, 25-105

**Abstract:**
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 sd-strategy-proof on a minimally rich domain if and only if all preferences are top-separable. We call a domain satisfying top-separability a multidimensional domain, and furthermore generalize the notion of connectedness (Monjardet, 2009) to a broad class of multidimensional domains: connected+domains. We 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 sd-strategy-proof. Such a flexible random social choice function allows for a systematic notion of compromise. We prove an analogous result for deterministic social choice functions satisfying anonymity. Our characterization remains valid for a problem of voting under constraints where not all alternatives are feasible (Barberà et al., 1997).

**Keywords:** Generalized random dictatorships; Top-separability; Separability; Multidimensional single-peakedness; Connected+ domains; Voting under constraints (search for similar items in EconPapers)

**JEL-codes:** D71 (search for similar items in EconPapers)

**Date:** 2019

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:jetheo:v:182:y:2019:i:c:p:25-105

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