论文标题
偏好空间的最终拓扑
Final Topology for Preference Spaces
论文作者
论文摘要
我们说，如果实用程序功能的小扰动（分别，偏好）会在模型的输出中产生小变化，则模型在实用程序（分别，偏好）中是连续的。虽然相似，但这两个问题是不同的。它们仅在以下两组是同构时才等效的：从偏好到模型输出的连续映射集，以及从实用程序到模型输出的连续映射集。在本文中，我们研究了由这种同构定义的偏好空间的拓扑结构。这项研究实际上很重要，因为连续性分析主要是通过实用性函数而不是基本偏好空间进行的。我们的发现使研究人员能够推断出实用性的连续性，以表明潜在偏好的连续性。
We say a model is continuous in utilities (resp., preferences) if small perturbations of utility functions (resp., preferences) generate small changes in the model's outputs. While similar, these two questions are different. They are only equivalent when the following two sets are isomorphic: the set of continuous mappings from preferences to the model's outputs, and the set of continuous mappings from utilities to the model's outputs. In this paper, we study the topology for preference spaces defined by such an isomorphism. This study is practically significant, as continuity analysis is predominantly conducted through utility functions, rather than the underlying preference space. Our findings enable researchers to infer continuity in utility as indicative of continuity in underlying preferences.
