Arrow's Theorem for Economic Domains and Edgeworth Hyperboxes
证明当备选方案集为埃奇沃思超盒且个体具有经典经济偏好(连续性、严格凸性、严格单调性和自私性)时,阿罗不可能定理仍然成立,并发展了将两商品不可能性推广到多商品的一般技术。
Kenneth J. Arrow's theorem holds when the set of alternatives is an Edgeworth hyperbox and the individuals have classical economic preferences over their consumption sets. (Free disposability is not assumed.) By classical individual preferences the authors mean preorders satisfying continuity, strict convexity, strict monotonicity, and selfishness. A minor, but noteworthy, accomplishment is the development of a general technique for extending two-commodity impossibility theorems to the general m-commodity counterpart. Copyright 1995 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.