This research explores optimal preferences in compact spaces, highlighting implications on utility representations.
The search for maximal elements of preference relations has been recently related to the optimization of one-way utilities on compact topological spaces. In this paper, we deepen this study by referring to upper semicontinuous finite Richter–Peleg multi-utility representations of preorders. We provide necessary and sufficient conditions for the existence of representations of this kind and then, under the assumption of near-completeness, we characterize the identification of all maximal elements by maximizing all functions in an appropriate representation under compactness.
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Bosi et al. (2026) studied this question.
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