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 an important diversity of contexts into the fold, amongst which choice between horse lottery options, I pay special attention to the case where these linear spaces don't 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 for, amongst many other choice methods, Levi's E-admissibility and Walley-Sen maximality.
翻译:我介绍并研究一种新概念,即对于生活在抽象的Banach空间的二进制和非二进制选择,通过一种非常一般的选择模式,即所谓的一套理想的选择模式。 为了能够将各种环境(包括马乐乐选项之间的选择)引入折叠中,我特别关注这样的情况:这些线性空间不包括所有“稳妥”选项。 我认为与Archimede(和连贯的)选择模式相关的保守推论框架,并且非常关注一般(非二进制)选择模式在简单、二进制选择模式中的代表性。 这里所证明的代表为Lev的“E-容许性”和Walley-Sen 最高性等许多其他选择方法提供了一种不言理的特征。