关于效用函数及阿罗不可能定理的一个猜想

Conjecture in Utility Function and Arrow's Impossibility Theorem

这是一篇关于效用函数是否存在,及阿罗不可能定理是否成立的研究性论文。文章讨论了"阿罗不可能定理"的逻辑问题。并且指出,如果将效用函数放在非欧空间里考察,则"投票悖论"可以解决。文章给出了效用函数在空间里的一个猜想模型,并证明了这种可能性。以及如何利用模型,求"Edgeworth盒"的契约曲线及无差异函数。

This paper discusses the Logic of Arrow＇s Impossibility Theorem. It indicates that the Condorcet Paradox can be worked out ff the Utility function is introduced into the Non-Euclidean space. The paper gives a conjectural model of utility function on Non-Euclidean space, and proves this possibility, as well as a solution to Edgeworth contract curve and indifference function by utilizing the proposed model.