Representing preorders with injective monotones
| Autor: | Pedro Hack, Daniel A. Braun, Sebastian Gottwald |
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| Přispěvatelé: | European Union (EU), Horizon 2020 |
| Rok vydání: | 2022 |
| Předmět: |
FOS: Computer and information sciences
Richter-Peleg function Information Theory (cs.IT) Computer Science - Information Theory Mathematics::General Topology General Social Sciences General Decision Sciences Maximum entropy method Maximum-Entropie-Methode Computer Science Applications Uncertainty preorder Arts and Humanities (miscellaneous) Developmental and Educational Psychology Majorization DDC 004 / Data processing & computer science ddc:004 Multi-utility representation General Economics Econometrics and Finance Applied Psychology |
| Zdroj: | Theory and Decision. 93:663-690 |
| ISSN: | 1573-7187 0040-5833 |
| DOI: | 10.1007/s11238-021-09861-w |
| Popis: | We introduce a new class of real-valued monotones in preordered spaces, injective monotones. We show that the class of preorders for which they exist lies in between the class of preorders with strict monotones and preorders with countable multi-utilities, improving upon the known classification of preordered spaces through real-valued monotones. We extend several well-known results for strict monotones (Richter-Peleg functions) to injective monotones, we provide a construction of injective monotones from countable multi-utilities, and relate injective monotones to classic results concerning Debreu denseness and order separability. Along the way, we connect our results to Shannon entropy and the uncertainty preorder, obtaining new insights into how they are related. In particular, we show how injective montones can be used to generalize some appealing properties of Jaynes' maximum entropy principle, which is considered a basis for statistical inference and serves as a justification for many regularization techniques that appear throughout machine learning and decision theory. publishedVersion |
| Databáze: | OpenAIRE |
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