We investigate the results of Kreps (1979), dropping his completeness axiom. As an added generalization, we work on arbitrary lattices, rather than a lattice of sets. We show that one of the properties of Kreps is intimately tied with representation via a closure operator. That is, a preference satis es Kreps' axiom (and a few other mild conditions) if and only if there is a closure operator on the lattice, such that preferences over elements of the lattice coincide with dominance of their closures. We tie the work to recent literature by Richter and Rubinstein (2015). Finally, we carry the concept to the theory of path-independent choice functions.

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关闭和偏好

我们调查了 Kreps (1979) 的结果，放弃了他的完整性公理。作为额外的概括，我们研究任意格，而不是集合格。我们表明 Kreps 的属性之一与通过闭包运算符的表示密切相关。也就是说，当且仅当格子上存在闭包算子时，偏好才满足 Kreps 公理（以及一些其他温和条件），使得对格子元素的偏好与其闭包的优势一致。我们将这项工作与 Richter 和 Rubinstein (2015) 的近期文献联系起来。最后，我们将该概念引入路径无关选择函数理论。