一维非独裁Domain的分类
A Taxonomy of Non-dictatorial Unidimensional Domains
摘要：
如果一个偏好域允许设计一致的社会选择函数（以下简称规则），这些函数是非独裁的和防策略的，那么这个偏好域就被称为非独裁域。我们研究了一类称为一维域的偏好域，并建立了唯一的秒性质（由Aswal，Chatterji和Sen（2003）引入），它刻画了所有非独裁域。主要贡献是随后的所有非独裁，一维域和规范的策略证明规则，这些域上的详尽分类，基于一个简单的属性的两个选民规则称为不变性。构成分类的偏好域是半单峰域（由Chatterji，Sanver和Sen（2013）介绍）和半混合域（这里介绍），这是两个适当的单峰域的削弱，并允许策略证明规则依赖于非峰值信息的选民的喜好;这些领域的规范规则分别是投影规则和混合规则。作为分类的细化，单峰域和混合域成为唯一的一维域，迫使策略证明规则完全由选民的偏好峰值决定。
英文摘要：
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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