Local Diversity of Condorcet Domains
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866916101501222912 |
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| author | Karpov, Alexander Markström, Klas Riis, Søren Zhou, Bei |
| author_facet | Karpov, Alexander Markström, Klas Riis, Søren Zhou, Bei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_11912 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Local Diversity of Condorcet Domains Karpov, Alexander Markström, Klas Riis, Søren Zhou, Bei Theoretical Economics Discrete Mathematics 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. |
| title | Local Diversity of Condorcet Domains |
| topic | Theoretical Economics Discrete Mathematics |
| url | https://arxiv.org/abs/2401.11912 |