180px|Daniel Kahneman, who won the 2002 Nobel Memorial Prize in Economics for his work developing prospect theory . These two examples are thus in contradiction with the expected utility theory, which only considers choices with the maximum utility. Note also that the concavity for gains and convexity for losses implies diminishing marginal utility with increasing gains/losses. In other words, someone who has more money has a lower desire for a fixed amount of gain (and lower aversion to a fixed amount of loss) than someone who has less money. The theory continues with a second concept, based on the observation that people attribute excessive weight to events with low probabilities and insufficient weight to events with high probability. For example, individuals may unconsciously treat an outcome with a probability of 99\% as if its probability was 95\%, and an outcome with probability of 1\% as if it had a probability of 5\%. Under- and over-weighting of probabilities is importantly distinct from under- and over-estimating probabilities, a different type of cognitive bias observed for example in the overconfidence effect. However  if and either or , then: As , , but since , it would imply that must be linear , however dominated alternatives are brought to the evaluation phase since they are eliminated in the editing phase. Although direct violations of dominance never happen in prospect theory, it is possible that a prospect A dominates B, B dominates C but C dominates A. Probability distortion is that people generally do not look at the value of probability uniformly between 0 and 1. Lower probability is said to be over-weighted (that is  a person is over concerned with the outcome of the probability) while medium to high probability is under-weighted (that is  a person is not concerned enough with the outcome of the probability). The exact point in which probability goes from over-weighted to under-weighted is arbitrary, however a good point to consider is probability = 0.33. A person values probability = 0.01 much more than the value of probability = 0 (probability = 0.01 is said to be over-weighted). However, a person has about the same value for probability = 0.4 and probability = 0.5. Also, the value of probability = 0.99 is much less than the value of probability = 1, a sure thing (probability = 0.99 is under-weighted). A little more in depth when looking at probability distortion is that π(p) + π(1 − p) < 1 (where π(p) is probability in prospect theory). An important implication of prospect theory is that the way economic agents subjectively frame an outcome or transaction in their mind affects the utility they expect or receive. Narrow framing is a derivative result which has been documented in experimental settings by Tversky and Kahneman, whereby people evaluate new gambles in isolation, ignoring other relevant risks. This phenomenon can be seen in practice in the reaction of people to stock market fluctuations in comparison with other aspects of their overall wealth; people are more sensitive to spikes in the stock market as opposed to their labor income or the housing market. It has also been shown that narrow framing causes loss aversion among stock market investors. And their work , that of Tversky and Kahneman , is largely responsible for the advent of behavioral economics, and is used extensively in mental accounting.Pesendorfer, Wolfgang. 2006. "Behavioral Economics Comes of Age: A Review Essay on Advances in Behavioral Economics." Journal of Economic Literature, 44 (3): 712-721.
180px|Daniel Kahneman, who won the 2002 Nobel Memorial Prize in Economics for his work developing prospect theory These two examples are thus in contradiction with the expected utility theory, which only considers choices with the maximum utility. Also, the concavity for gains and convexity for losses implies diminishing marginal utility with increasing gains/losses. In other words, someone who has more money has a lower desire for a fixed amount of gain (and lower aversion to a fixed amount of loss) than someone who has less money. The theory continues with a second concept, based on the observation that people attribute excessive weight to events with low probabilities and insufficient weight to events with high probability. For example, individuals may unconsciously treat an outcome with a probability of 99\% as if its probability were 95\%, and an outcome with probability of 1\% as if it had a probability of 5\%. Under- and over-weighting of probabilities is importantly distinct from under- and over-estimating probabilities, a different type of cognitive bias observed for example in the overconfidence effect. However , if and either or , then: As , , but since , it would imply that must be linear ; however, dominated alternatives are brought to the evaluation phase since they are eliminated in the editing phase. Although direct violations of dominance never happen in prospect theory, it is possible that a prospect A dominates B, B dominates C but C dominates A. Probability distortion is that people generally do not look at the value of probability uniformly between 0 and 1. Lower probability is said to be over-weighted (that is , a person is overly concerned with the outcome of the probability) while medium to high probability is under-weighted (that is , a person is not concerned enough with the outcome of the probability). The exact point in which probability goes from over-weighted to under-weighted is arbitrary, but a good point to consider is probability = 0.33. A person values probability = 0.01 much more than the value of probability = 0 (probability = 0.01 is said to be over-weighted). However, a person has about the same value for probability = 0.4 and probability = 0.5. Also, the value of probability = 0.99 is much less than the value of probability = 1, a sure thing (probability = 0.99 is under-weighted). A little more in depth when looking at probability distortion is that π(p) + π(1 − p) < 1 (where π(p) is probability in prospect theory). An important implication of prospect theory is that the way economic agents subjectively frame an outcome or transaction in their mind affects the utility they expect or receive. Narrow framing is a derivative result which has been documented in experimental settings by Tversky and Kahneman, whereby people evaluate new gambles in isolation, ignoring other relevant risks. This phenomenon can be seen in practice in the reaction of people to stock market fluctuations in comparison with other aspects of their overall wealth; people are more sensitive to spikes in the stock market as opposed to their labor income or the housing market. It has also been shown that narrow framing causes loss aversion among stock market investors. And the work of Tversky and Kahneman is largely responsible for the advent of behavioral economics, and is used extensively in mental accounting.Pesendorfer, Wolfgang. 2006. "Behavioral Economics Comes of Age: A Review Essay on Advances in Behavioral Economics." Journal of Economic Literature, 44 (3): 712-721.
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