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Unformatted text preview: Von Neumann-Morgenstern - Proof I: Lecture XII Charles B. Moss September 16, 2010 I. A:A If u v then < implies (1 ) u + v (1 ) u + v (1) 1. The direction of the assertion is that if u v and < , then the preference ordering must follow. 2. To demonstrate this we start with axiom 3:B:a given 0 1 u v u u + (1 ) v u (1 ) + v (2) 3. Intuitively, this axiom states that if u is the inferior bundle, then any bundle constructed with any combination of v must be pre- ferred to u . 4. bf Axiom 3:B:b reverses this axiom by saying that if u is the pre- ferred bundle then it must also be preferred to a bundle containing any amount of v . u v u u + (1 ) v (3) 5. We start from the first equation, replace with and by replacing the first in the right-hand side with preceding equation yields (1 ) u + v ((1 ) u + v ) + (1 ) v (4) 1 AEB 6182 Agricultural Risk Analysis and Decision Making...
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- Fall '08