Authors: Shurojit Chatterji, Souvik Roy, Soumyarup Sadhukhan, Arunava Sen and Huaxia Zeng
We study Random Social Choice Functions (or RSCFs) in a standard ordinal mechanism design model.
We introduce a new preference domain called a hybrid domain which includes as special cases as the complete domain and the single-peaked domain. We characterize the class of unanimous and strategy-proof RSCFs on these domains and refer to them as restricted probabilistic fixed ballot rules (RPFBR). These RSCFs are not necessarily decomposable, i.e., cannot be written as a convex combination of their deterministic counterparts. We then pin down the necessary and sufficient condition under which decomposability holds on anonymous RPFBRs. Finally, we provide an axiomatic justification of hybrid domains and show that every connected domain satisfying some richness conditions is a hybrid domain, and moreover shares the same strategy-proof random voting rules with the hybrid domain.
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