A hard choice is a situation in which an agent is unable to make a justifiable choice from a given menu of alternatives. Our objective is to present a systematic treatment of the axiomatic structure of such situations. To do so, we draw on and contribute to the study of choice functions that can be indecisive, i.e., that may fail to select a non-empty set for some menus. In this more general framework, we present new characterizations of two well-known choice rules, the maximally dominant choice rule and the top-cycle choice rule. Together with existing results, this yields an understanding of the circumstances in which hard choices arise.

中文翻译：

---

选择函数和硬选择

艰难选择是一种代理无法从给定的备选菜单中做出合理选择的情况。我们的目标是对这种情况的公理结构进行系统的处理。为此，我们借鉴并致力于研究可能优柔寡断的选择功能，即可能无法为某些菜单选择非空集。在这个更一般的框架中，我们提出了两个众所周知的选择规则的新特征，即最大优势选择规则和顶部循环选择规则。连同现有的结果，这产生了对出现艰难选择的情况的理解。