The classification of preordered spaces in terms of monotones: complexity and optimization

Pedro Hack (), Daniel A. Braun () and Sebastian Gottwald ()
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Pedro Hack: Ulm University
Daniel A. Braun: Ulm University
Sebastian Gottwald: Ulm University

Theory and Decision, 2023, vol. 94, issue 4, No 6, 693-720

Abstract: Abstract The study of complexity and optimization in decision theory involves both partial and complete characterizations of preferences over decision spaces in terms of real-valued monotones. With this motivation, and following the recent introduction of new classes of monotones, like injective monotones or strict monotone multi-utilities, we present the classification of preordered spaces in terms of both the existence and cardinality of real-valued monotones and the cardinality of the quotient space. In particular, we take advantage of a characterization of real-valued monotones in terms of separating families of increasing sets to obtain a more complete classification consisting of classes that are strictly different from each other. As a result, we gain new insight into both complexity and optimization, and clarify their interplay in preordered spaces.

Keywords: Multi-utility representation; Richter–Peleg function; Injective monotone; Majorization; Uncertainty preorder (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11238-022-09904-w

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