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A Unified Characterization of Randomized Strategy-proof Rules

Roy, Souvik and Sadhukhan, Soumyarup (2017): A Unified Characterization of Randomized Strategy-proof Rules.

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Abstract

This paper presents a unified characterization of the unanimous and strategy-proof random rules on a class of domains that are based on some prior ordering over the alternatives. It identifies a condition called top-richness so that, if a domain satisfies top-richness, then an RSCF on it is unanimous and strategy-proof if and only if it is a convex combination of tops-restricted min-max rules. Well-known domains like single-crossing, single-peaked, single-dipped etc. satisfy top-richness. This paper also provides a characterization of the random min-max domains. Furthermore, it offers a characterization of the tops-only and strategy-proof random rules on top-rich domains satisfying top-connectedness. Finally, it presents a characterization of the unanimous (tops-only) and group strategy-proof random rules on those domains.

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