We restrict permissible probabilities only to decimal ell ary in general fractions of finite depths up to a given cognitive bound. L x probability of single draw original ellsberg thought experiment l 1 x probability of repeated draws within the meta experiment the choices described by ellsberg become consistent with standard risk and expected utility calculations.
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Introduction bayesian statistical techniques are applicable when the information and uncertainty with respect to the parameters or hypotheses in question can be expressed by a probability distribution.
Probability distribution expected utility. In such events an individual calculates probability of expected outcomes and weighs them against the expected. The expected utility hypothesis is a popular concept in economics game theory and decision theory that serves as a reference guide for judging decisions involving uncertainty. Maxmin expected utility how should we think about this.
The central point is that for a single draw the ellsberg case the distribution of winnings are. In this case the function u is called an expected utility function and the function u is call a von neumann morgenstern utility function. Comonotonic independence uncertainty aversion expected utility subjec tive probability.
If preferences over lotteries happen to have an expected utility representation its as if consumer has a utility function over consequences and chooses among lotteries so as to maximize 12. Decisions involving expected utility are decisions involving uncertain outcomes. Rather than their being a single probability distribution there is a range of possible distributions after you chose your act you evaluate it using the worst of these distributions this is maxmin expected utility you maximize the minimum utility that you can get across.
Ux is the expected utility of an amount moreover marginal utility should be decreasing the value of an additional dollar gets lower the more money you have for example u0 0 u499999 10 u1000000 16. Allais 1952 was one of the first to propose an outcome dependent probability weighting function to characterize probability distortions that explain violations of the linear probability model for expected utility theory eut. We reformulate expected utility theory from the viewpoint of bounded rationality by introducing probability grids and a cognitive bound.
The theory recommends which option a rational individual should choose in a complex situation based on his tolerance for risk and personal preferences.
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