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Notes and Comments: Utility Theory without the Completeness Axiom: A Correction

Robert J. Aumann

Abstract

Theorem B of [1] is false as it stands (Section 1). It is true if the preference order is defined by a finite number of linear functions (Section 2) or alternatively, if the archimidean assumption [1, (1.2)] is replaced by either of the stronger forms [1, (4.1)] or [1, (4.2)] (Section 3). A corresponding correction must be made for Theorem C of [1] (Section 4).