Daniel Kahneman and Amos Tversky called their studies of how people manage risk and uncertainty Prospect Theory for no other reason than that it is a catchy, attention-getting name. This is much like Richard Bellman calling his algorithm of multistage decision-making Dynamic Programming because programming was a hot topic at the time he was choosing a label. Kahneman and Tversky's theory, developed over a thirty year period, is however highly important in economics and especially in financial economics. In 2002 Daniel Kahneman shared the Nobel Prize in Economics but unfortunately Amos Tversky had died by that time and did not get his share of the fame.
Kahneman and Tversky started their research investigating apparent anomalies and contradictions in human behavior. Subjects when offered a choice formulated in one way might display risk-aversion but when offerred essentially the same choice formulated in a different way might display risk-seeking behavior. For example, as Kahneman says, people may drive across town to save $5 on a $15 calculator but not drive across town to save $5 on a $125 coat.
One very important result of Kahneman and Tversky work is demonstrating that people's attitudes toward risks concerning gains may be quite different from their attitudes toward risks concerning losses. For example, when given a choice between getting $1000 with certainty or having a 50% chance of getting $2500 they may well choose the certain $1000 in preference to the uncertain chance of getting $2500 even though the mathematical expectation of the uncertain option is $1250. This is a perfectly reasonable attitude that is described as risk-aversion. But Kahneman and Tversky found that the same people when confronted with a certain loss of $1000 versus a 50% chance of no loss or a $2500 loss do often choose the risky alternative. This is called risk-seeking behavior. This is not necessarily irrational but it is important for analysts to recognize the asymmetry of human choices.
Peter Bernstein cites an experiment by Richard Thaler in which student were told to assume they had just won $30 and were offered a coin-fip upon which they would win or lose $9. Seventy percent of the students opted for the coin-flip. When other students were offered $30 for certain versus a coin-flip in which they got either $21 or $39 a much smaller proportion, 43%, opted for the coin-flip.
Some of the problems of interpreting human behavior in the face of risk has to do with the problem of people making decisions on the basis of subjective assessments of probabilities which may be quite different from the objective or true probabilities. Events of small probability that have never occured before may be assessed as having a probability of zero in decision-making, but this is leads to tragedies in which people find they have been playing Russian roulette without even knowing they are doing so. Small probabilities add up when chances are taken repeatedly. A calculator is provided here to show the probability of avoiding a danger given the probability and the number of repetitions of the risk. A notable phenomenon is what happens to the probability of avoiding a small risk event when the probability is increased, say doubled. For example, suppose the probability of being involved in an automobile accident on any one trip is 0.0001. In 2000 trips the probability of not being involved in an accident is about 0.82. If the probability of being involved in an accident is doubled to 0.0002, perhaps as a result of driving behavior, the probability not being involved in a accident in 2000 trips falls to 0.67. If the probability of being involved in an accident on one trip were tripled to 0.0003 the probability of avoiding an accident in 2000 trips falls from 0.82 to 0.55. The point is that while probabilities of 0.0001 and 0.0003 seems so small as to be insignificant there are not really zero and there is a lot of difference between 0.0001 and 0.0003.
The Kennedy family seems plagued by tragedy but any review of their behavior indicates that they are significantly higher than average risk-takers and that while most of the time they are unscathed by the risks the odds are that the frequent repetitions of the trials will result in tragedies for the family.
Peter Bernstein reports some interesting results from a Tversky study of people's, in this case 120 Stanford graduates, estimates of the probability of dying from various causes.
|Estimates of Probabilities of Death From Various Causes|
|Cause||Subject Estimates||Statistical Estimates|
|Other Natural Causes||0.33||0.35|
|All Natural Causes||0.73||0.92|
|Other Unnatural Causes||0.11||0.02|
|All Unnatural Causes||0.53||0.08|
The above represent the probability estimate of one group in the study. Another group was not asked to estimate the probabilities for separate causes but only the probability of death by natural versus unnatural causes. The probability estimate of a natural death by this second group was 0.58, significantly lower than when the subjects considered each cause separately. The second group's estimate of an unnatural death was 0.32, again significantly lower than for the first group. The most notable aspect of the estimates is that the subjects significantly underestimated the probabilities for natural causes and vastly overestimated the probabilities for unnatural causes. This indicates that probably people give more attention to worrying about the unnatural dangers and not enough to the natural dangers.
Peter Bernstein, Against the Gods: The Remarkable Story of Risk, John Wiley & Sons, New York, 1996.
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