Mathematics Commons. Advanced Search. Privacy Copyright. Skip to main content ScholarWorks at University of Montana. Maureen and Mike Mansfield Library. Authors Manfred Borovcnik. Abstract Risk is a hot topic. Included in Mathematics Commons. Companies can benefit from using both probability and research in decision-making. A writer since , Christian Fisher is an author specializing in personal empowerment and professional success.
From to , he wrote true stories of human triumph for "Woman's World" magazine. Since , he has also helped launch businesses including a music licensing company and a music school. By Christian Fisher. When Odds Are Good Basing a decision solely on probability involves analyzing possible outcomes of your decision and the odds that each particular outcome will occur. When Factors Are Unclear Research studies can be essential for decisions requiring larger company investments.
How much higher? The expected value calculation is simple in these kinds of cases. Even though P stiffed is not 0, V stiffed is; if we get stiffed, our investment is worth nothing. So when calculating expected value, we can ignore the second term in the sum. All we have to do is multiply P paid by V paid.
Considerations like these are apparently the spark that lit the fuse on the financial crisis of late On September 15th of that year, the financial services firm Lehman Brothers filed for bankruptcy—the largest bankruptcy filing in history. The stock market went into a free-fall, and the economy ground to a halt.
What does it mean to be a good, rational economic agent? How should a person, generally speaking, invest money? As we mentioned earlier, a plausible rule governing such decisions would be something like this: always choose the investment for which expected value is maximized. The value of choice a can be easily calculated:. But in real life, most people who are offered such a choice go with the sure-thing, b. Are people who make such a choice behaving irrationally?
Not necessarily. The tendency of people to accept a sure thing over a risky wager, despite a lower expected value, is referred to as risk aversion. This is the consequence of an idea first formalized by the mathematician Daniel Bernoulli in the diminishing marginal utility of wealth.
The money would add very little utility for Gates, but much more for the college student. Utility rises quickly at first, but levels out at higher amounts. Computing the expected utility of the coin-flip wager gives us this result:. The utility of 70 for the sure-thing easily beats the expected utility from the wager. It is possible to get people to accept risky bets over sure-things, but one must take into account this diminishing marginal utility.
It has long been accepted economic doctrine that rational economic agents act in such a way as to maximize their utility, not their value. It is a matter of some dispute what sort of utility function best captures rational economic agency. Different economic theories assume different versions of ideal rationality for the agents in their models. Recently, this practice of assuming perfect utility-maximizing rationality of economic agents has been challenged.
Psychologists—especially Daniel Kahneman and Amos Tversky— have conducted a number of experiments that demonstrate pretty conclusively that people regularly behave in ways that, by the lights of economic theory, are irrational. For example, consider the following two scenarios go slowly; think about your choices carefully :. Which would you choose? For this and many other examples, see Kahneman
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