Gonzales C
LIP6, Université Paris 6, Paris, France
J Math Psychol. 2000 Jun;44(2):285-309. doi: 10.1006/jmps.1998.1248.
This paper addresses conditions for the existence of additive separable utilities. It considers mainly two-dimensional Cartesian products in which restricted solvability holds w.r.t. one component, but some results are extended to n-dimensional spaces. The main result shows that, in general, cancellation axioms of any order are required to ensure additive representability. More precisely, a generic family of counterexamples is provided, proving that the (m+1)st order cancellation axiom cannot be derived from the mth order cancellation axiom when m is even. However, a special case is considered in which the existence of additive representations can be derived from the independence axiom alone. Unlike the classical representation theorems, these representations are not unique up to strictly positive affine transformations, but follow Fishburn's (1981) uniqueness property. Copyright 2000 Academic Press.
本文探讨了可加可分效用存在的条件。它主要考虑二维笛卡尔积，其中关于一个分量满足受限可解性，但一些结果被扩展到了n维空间。主要结果表明，一般来说，需要任意阶的消去公理来确保可加表示性。更确切地说，给出了一个通用的反例族，证明当m为偶数时，第(m + 1)阶消去公理不能从第m阶消去公理推导出来。然而，考虑了一种特殊情况，其中可加表示的存在性可以仅从独立性公理推导出来。与经典表示定理不同，这些表示在严格正仿射变换下不是唯一的，而是遵循菲什伯恩（1981）的唯一性性质。版权所有2000年学术出版社。
