We consider choice correspondences that assign a subset to every choice set of alternatives, where the total set of alternatives is an arbitrary finite or infinite set. We focus on the relations between several extensions of the condition of independence of irrelevant alternatives on one hand, and conditions on the revealed preference relation on sets, notably the weak axiom of revealed preference, on the other hand. We also establish the connection between the condition of independence of irrelevant alternatives and so-called strong sets; the latter characterize a social choice correspondence satisfying independence of irrelevant alternatives.

中文翻译：

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设置并显示多值选择的偏好公理

我们考虑将每个选择集的子集分配给子集的选择对应关系，其中总选择集是任意有限或无限集。我们一方面着眼于无关选择的独立性条件的几种扩展之间的关系，另一方面着眼于集合上显性偏好关系的条件之间的关系，特别是显性偏好的弱公理。我们还建立了无关选择的独立性条件和所谓的强集之间的联系；后者的特征是满足不相关选择的独立性的社会选择对应。