A taxonomy of non-dictatorial unidimensional domains

• Main Authors: CHATTERJI, Shurojit, ZENG, Huaxia
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2023
• Subjects: Strategy-proofness; Invariance; Unidimensional domains; Semi-single-peaked preference; Semi-hybrid preference; Economic Theory
• Online Access: https://ink.library.smu.edu.sg/soe_research/2648; https://ink.library.smu.edu.sg/context/soe_research/article/3647/viewcontent/2201.00496.pdf
• Institution: Singapore Management University

Non-dictatorial preference domains allow the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof. On a class of preference domains called unidimensional domains, we show that the unique seconds property characterizes all non-dictatorial domains. Subsequently, we provide an exhaustive classification of all non-dictatorial, unidimensional domains, based on a simple property of two-voter rules called invariance. The domains constituting the classification are semi-single-peaked domains and semi-hybrid domains (introduced here) which are two appropriate weakenings of single-peaked domains and shown to allow strategy-proof rules to depend on non-peak information of voters' preferences; the canonical strategy-proof rules for these domains are projection rules and hybrid rules respectively. As a refinement of the classification, single-peaked domains and hybrid domains emerge as the only unidimensional domains that force strategy-proof rules to be determined completely by preference peaks.