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Unformatted text preview: Von Neumann-Morgenstern - Proof II: Lecture XIII Charles B. Moss September 20, 2010 I. Separating Classes A. There must exist with 0 < < 1 which separates the classes. 1. Thus, will be such that for < the resulting bundle is in Class I, 2. And if > then the resulting set is in Class II. B. First consider in Class I. 1. Specifically, we start by trying to generate a new point such that > , but w w . 2. In this case (1- ) u + v w 3. Using 3:B:e u w v u + (1- ) v w for some ((1- ) u + v ) + (1- ) v w (1) since w v . 4. Therefore by the combining axiom ((1- ) u + v ) + (1- ) v u- u + v + v- v (1- ) u + (1- (1- )) v (2) 5. Hence = 1- (1- ) : 0 < < 1 belongs to I. 6. This forms the contradiction, so that w cannot be preferred to w if < . C. Second, consider in Class II. 1 AEB 6182 Agricultural Risk Analysis and Decision Making Professor Charles B. Moss Lecture XII Fall 2010 1. Like the scenario above, we begin by generating the counter point that < , but w w ....
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This note was uploaded on 02/01/2012 for the course AEB 6182 taught by Professor Weldon during the Fall '08 term at University of Florida.
- Fall '08