词典学选择函数
Lexicographic choice functions
摘要：
我们研究了Seidenfeld等人（2010）考虑的一致选择函数的推广，坚持凸性公理，但不施加阿基米德条件。我们定义我们的选择功能向量空间的选项，这使我们能够将作为特殊情况下，Seidenfeld等人。的（2010）选择功能的马彩票和可取的赌博（Quaeghebeur，2014），并调查他们的联系。我们表明，选择功能的基础上设置的理想的选项（赌博）满足Seidenfeld的凸性公理，只有非常特殊类型的理想的选项，这是在一个一对一的关系与字典概率。我们称之为词典选择函数。最后，我们证明了这些选择函数可以用来确定与给定的二元关系相关联的最保守的凸选择函数。
英文摘要：
We investigate a generalisation of the coherent choice functions considered by Seidenfeld et al. (2010), by sticking to the convexity axiom but imposing no Archimedeanity condition. We define our choice functions on vector spaces of options, which allows us to incorporate as special cases both Seidenfeld et al.'s (2010) choice functions on horse lotteries and sets of desirable gambles (Quaeghebeur, 2014), and to investigate their connections. We show that choice functions based on sets of desirable options (gambles) satisfy Seidenfeld's convexity axiom only for very particular types of sets of desirable options, which are in a one-to-one relationship with the lexicographic probabilities. We call them lexicographic choice functions. Finally, we prove that these choice functions can be used to determine the most conservative convex choice function associated with a given binary relation.
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