A taxonomy of non-dictatorial unidimensional domains
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...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
2023
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| 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 |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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. |
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