Utility

Implicit in the decision tree above is the notion that $100,000 is 100,000 times as valuable as $1. This is simply not true. Given a limited amount of money, an individual would spend the first dollar on the item that provides the greatest value for money. The next dollar would be spent on the next most valuable. And so on. The result is that every dollar has slightly less value than the previous dollar.

Companies often face the same decreasing value of money. A company generally has available a limited number of projects in which to invest. The projects with the highest returns get the first dollars. The second best projects get the next dollars. And so on. Also, a company's cost of capital (the interest rate paid for money) shows this same non-linear relationship. A company will raise money from the least expensive sources first.

To compensate for this effect, you need to replace monetary outcome values with another measure that is often called utility.

Utility is simply a measure of the usefulness of an outcome. If you were to plot an individual's perception of utility as a function of money, you would get a curve similar to this:

This curve tends to level off as the monetary outcome increases; meaning that each dollar is worth less than the previous.

By controlling the shape of the utility curve, you can model a decision-maker's risk behavior. A downward-cupped curve represents risk-adverse behavior. A straight-line represents risk neutral behavior. And, an upward-cupped curve represents risk-seeking behavior.

Risk-seeking behavior might seem to be a bit ridiculous. However, it is quite common. Just consider how much money is spent gambling in casinos.

Mathematically, utility is often implemented using an exponential or logarithmic function. DecisionPro uses the function

where k is a constant reflecting the decision-maker's risk-averse (or risk-seeking) behavior, and x is the monetary value.

Now let’s revisit the real estate decision tree presented at the beginning of this section and replace all monetary values with utilities. By convention, utility generally ranges from zero (no value) to one (all wealth available to the decision-maker). The actual range and scale of the utility curve are not important. This example will use the function graphed below.

Without Utility With Utility

Notice that now the chosen option has switched from Option 1 to Option 2. In fact, the expected value for Option 2 is now significantly higher than that for Option 1. This result is more in keeping with our expectations.