Restricted probabilistic fixed ballot rules and hybrid domains

• Main Authors: CHATTERJI, Shurojit, ROY, Souvik, SADHUKHAN, Soumyarup, SEN, Arunava, ZENG, Huaxia
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2020
• Subjects: Strategy-proofness; hybrid domain; restricted probabilistic fixed ballot rule; decomposability; connectedness; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2342; https://ink.library.smu.edu.sg/context/soe_research/article/3341/viewcontent/RPFBR_Jan_9_.pdf
• Institution: Singapore Management University

We study Random Social Choice Functions (or RSCFs) in a standard ordinal mech-anism 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 (or RPFBRs). These RSCFs are not necessarily decomposable, i.e., cannot be written as a convex combina-tion of their deterministic counterparts. We identify a necessary and sufficient condition under which decomposability holds for anonymous RPFBRs. Finally, we provide an axiomatic justification of hybrid domains and show that every connected domain satis-fying some mild conditions is a hybrid domain where the RPFBR characterization still prevails.