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A Taxonomy of Non-dictatorial Unidimensional Domains

Author

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  • Shurojit Chatterji
  • Huaxia Zeng
Abstract
A preference domain is called a non-dictatorial domain if it allows the design of unanimous social choice functions (henceforth, rules) that are non-dictatorial and strategy-proof. We study a class of preference domains called unidimensional domains and establish that the unique seconds property (introduced by Aswal, Chatterji, and Sen (2003)) characterizes all non-dictatorial domains. The principal contribution is the subsequent exhaustive classification of all non-dictatorial, unidimensional domains and canonical strategy-proof rules on these domains, based on a simple property of two-voter rules called invariance. The preference domains that constitute the classification are semi-single-peaked domains (introduced by Chatterji, Sanver, and Sen (2013)) and semi-hybrid domains (introduced here) which are two appropriate weakenings of single-peaked domains and are shown to allow strategy-proof rules to depend on non-peak information of voters' preferences; the canonical rules for these domains are the projection rule and the hybrid rule 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 voters' preference peaks.

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  • Shurojit Chatterji & Huaxia Zeng, 2022. "A Taxonomy of Non-dictatorial Unidimensional Domains," Papers 2201.00496, arXiv.org, revised Oct 2022.
    • Handle: RePEc:arx:papers:2201.00496
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    References listed on IDEAS

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