Formal Power Series Representations in Probability and Expected Utility Theory
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913969488265216 |
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| author | Pedersen, Arthur Paul Alexander, Samuel Allen |
| author_facet | Pedersen, Arthur Paul Alexander, Samuel Allen |
| contents | We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it satisfies a certain coherence requirement analogous to the one de Finetti advanced for his foundations of probability. Unlike de Finetti's theory, the one we set forth requires neither transitivity nor Archimedeanness nor boundedness nor continuity of preference. This theory also enjoys the property that any complete preference system meeting the standard of coherence can be represented by utility in an ordered field extension of the reals. Representability by utility is a corollary of this paper's central result, which at once extends Hölder's Theorem and strengthens Hahn's Embedding Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00294 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Formal Power Series Representations in Probability and Expected Utility Theory Pedersen, Arthur Paul Alexander, Samuel Allen Probability Artificial Intelligence Theoretical Economics Logic Statistics Theory 60A05 We advance a general theory of coherent preference that surrenders restrictions embodied in orthodox doctrine. This theory enjoys the property that any preference system admits extension to a complete system of preferences, provided it satisfies a certain coherence requirement analogous to the one de Finetti advanced for his foundations of probability. Unlike de Finetti's theory, the one we set forth requires neither transitivity nor Archimedeanness nor boundedness nor continuity of preference. This theory also enjoys the property that any complete preference system meeting the standard of coherence can be represented by utility in an ordered field extension of the reals. Representability by utility is a corollary of this paper's central result, which at once extends Hölder's Theorem and strengthens Hahn's Embedding Theorem. |
| title | Formal Power Series Representations in Probability and Expected Utility Theory |
| topic | Probability Artificial Intelligence Theoretical Economics Logic Statistics Theory 60A05 |
| url | https://arxiv.org/abs/2508.00294 |