This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Von NeumannMorgenstern  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 ....
View
Full
Document
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
 Weldon

Click to edit the document details