Towards a Characterization of Random Serial Dictatorship
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913425735548928 |
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| author | Brandt, Felix Greger, Matthias Romen, René |
| author_facet | Brandt, Felix Greger, Matthias Romen, René |
| contents | Random serial dictatorship (RSD) is a randomized assignment rule that - given a set of $n$ agents with strict preferences over $n$ houses - satisfies equal treatment of equals, ex post efficiency, and strategyproofness. For $n \le 3$, Bogomolnaia and Moulin (2001) have shown that RSD is characterized by these axioms. Extending this characterization to arbitrary $n$ is a long-standing open problem. By weakening ex post efficiency and strategyproofness, we reduce the question of whether RSD is characterized by these axioms for fixed $n$ to determining whether a matrix has rank $n^2 n!^n$. We provide computer-generated counterexamples to show that two other approaches for proving the characterization (using deterministic extreme points or restricted domains of preferences) are inadequate. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_11976 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Towards a Characterization of Random Serial Dictatorship Brandt, Felix Greger, Matthias Romen, René Theoretical Economics Random serial dictatorship (RSD) is a randomized assignment rule that - given a set of $n$ agents with strict preferences over $n$ houses - satisfies equal treatment of equals, ex post efficiency, and strategyproofness. For $n \le 3$, Bogomolnaia and Moulin (2001) have shown that RSD is characterized by these axioms. Extending this characterization to arbitrary $n$ is a long-standing open problem. By weakening ex post efficiency and strategyproofness, we reduce the question of whether RSD is characterized by these axioms for fixed $n$ to determining whether a matrix has rank $n^2 n!^n$. We provide computer-generated counterexamples to show that two other approaches for proving the characterization (using deterministic extreme points or restricted domains of preferences) are inadequate. |
| title | Towards a Characterization of Random Serial Dictatorship |
| topic | Theoretical Economics |
| url | https://arxiv.org/abs/2303.11976 |