A duality between utility transforms and probability distortions
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866929282416115712 |
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| author | Chambers, Christopher P. Liu, Peng Wang, Ruodu |
| author_facet | Chambers, Christopher P. Liu, Peng Wang, Ruodu |
| contents | In this paper, we establish a mathematical duality between utility transforms and probability distortions. These transforms play a central role in decision under risk by forming the foundation for the classic theories of expected utility, dual utility, and rank-dependent utility. Our main results establish that probability distortions are characterized by commutation with utility transforms, and utility transforms are characterized by commutation with probability distortions. These results require no additional conditions, and hence each class can be axiomatized with only one property. Moreover, under monotonicity, rank-dependent utility transforms can be characterized by set commutation with either utility transforms or probability distortions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_05816 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | A duality between utility transforms and probability distortions Chambers, Christopher P. Liu, Peng Wang, Ruodu Theoretical Economics 91B70 In this paper, we establish a mathematical duality between utility transforms and probability distortions. These transforms play a central role in decision under risk by forming the foundation for the classic theories of expected utility, dual utility, and rank-dependent utility. Our main results establish that probability distortions are characterized by commutation with utility transforms, and utility transforms are characterized by commutation with probability distortions. These results require no additional conditions, and hence each class can be axiomatized with only one property. Moreover, under monotonicity, rank-dependent utility transforms can be characterized by set commutation with either utility transforms or probability distortions. |
| title | A duality between utility transforms and probability distortions |
| topic | Theoretical Economics 91B70 |
| url | https://arxiv.org/abs/2309.05816 |