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Coherent and Archimedean choice in general Banach spaces

lib:9e875797c384062b (v1.0.0)

Authors: Gert de Cooman
ArXiv: 2002.05461
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Abstract URL: https://arxiv.org/abs/2002.05461v2


I introduce and study a new notion of Archimedeanity for binary and non-binary choice between options that live in an abstract Banach space, through a very general class of choice models, called sets of desirable option sets. In order to be able to bring horse lottery options into the fold, I pay special attention to the case where these linear spaces do not include all `constant' options. I consider the frameworks of conservative inference associated with Archimedean (and coherent) choice models, and also pay quite a lot of attention to representation of general (non-binary) choice models in terms of the simpler, binary ones. The representation theorems proved here provide an axiomatic characterisation of, amongst other choice methods, Levi's E-admissibility and Walley-Sen maximality.

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