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Unformatted text preview: Economics 206 Spring 2007 (Prof. G. Loury) A Note on Stochastic Dominance (February 8, 2007) Here are a few observations on stochastic dominance that may help with the material in yesterdays lecture. We will study the partial orderings of probability distributions i.e., when one distribution can be taken to be at least as good as another, from the viewpoint of expected utility maximizing decision makers. Throughout these notes, to keep the mathematics simple, I restrict attention to money outcomes, y , from some risky situation which are bounded above and below. Given this, as explained in class, we can always make our units such that an outcome is measured by its distance from the worst outcome as a percentage of the distance between the best and worst outcome. This linear shift of units can have no affect on risk preferences. So, having assumed that money outcomes are bounded above and below, we can without any further loss of generality take these outcomes to lie in the unit interval: y Y [0 , 1]. So, consider Bernoulli utility functions and probability distributions whose do- mains that are the unit interval, Y [0 , 1]. Of course, Bernoulli utility functions can be subjected to a postive linear transformation without changing how they rep- resent an agents preferences, So we can with no loss of generality take the utility of the worst outcome ( y = 0) to be zero, and the utility of the best outcome (...
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