Local Diversity of Condorcet Domains

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Tác giả: Alexander Karpov, Klas Markström, Søren Riis, Bei Zhou

Ngôn ngữ: eng

Ký hiệu phân loại: 342.15 Constitutional and administrative law

Thông tin xuất bản: 2024

Mô tả vật lý:

Bộ sưu tập: Metadata

ID: 201330

Several of the classical results in social choice theory demonstrate that in order for many voting systems to be well-behaved the set domain of individual preferences must satisfy some kind of restriction, such as being single-peaked on a political axis. As a consequence it becomes interesting to measure how diverse the preferences in a well-behaved domain can be. In this paper we introduce an egalitarian approach to measuring preference diversity, focusing on the abundance of distinct suborders one subsets of the alternative. We provide a common generalisation of the frequently used concepts of ampleness and copiousness. We give a detailed investigation of the abundance for Condorcet domains. Our theorems imply a ceiling for the local diversity in domains on large sets of alternatives, which show that in this measure Black's single-peaked domain is in fact optimal. We also demonstrate that for some numbers of alternatives, there are Condorcet domains which have largest local diversity without having maximum order.
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