偏好的对子态可分性

Pairwise Separability of Preferences

本文提出了消费者偏好的对子态可分性概念，并用来揭示一般选择集合上偏好的效用函数表示的特征，证明了偏好关系可用效用函数表示的充分必要条件是该偏好具有对子态可分性和可数满足性，还证明了偏好关系具有长直线ｗ１—表示的充分必要条件是该偏好具有对子态可分性．这两个结果，使得对子态可分性成为用直线上的序来表示消费偏好序之本质所在．

In this paper the pairwise separability of a preference is presented and studied. It is showed that a preferences on a general set has utility functions if and only if it is pairwise separable and countably satiable.It is also showed that the pairwise separability is the sufficient and necessary condition for a preference to berepresented by the long line R(w1).