Question

1. Under what conditions is a decision tree preferable to a decision/payoff table?

2. In what types of situations would it be more appropriate to use a utility framework for decision making rather than an expected monetary value framework? Give an example.

Answer 1

A decision tree is preferable to a decision table when
a. a number of sequential decisions are to be made.
b. probabilities are available.
c. the maximax criterion is used.
d. the objective is to maximize regret.

Expected utility theory is used as a tool for analyzing situations where individuals must make a decision without knowing which outcomes may result from that decision, i.e., decision making under uncertainty.

A point comes where we need to realize that decision tree analysis methodology and the tools that implement it do not require the use of EMV. Decision trees can be solved based on an expected utility (E(U)) of the project to the performing organization. There is no requirement that utility is measured by EMV. In fact, non-linear utility functions can be substituted for linear EMV in most decision tree software packages, and E(U) is then substituted for EMV as the decision criterion.

There is a trick to analyzing the E(U) of the choices, of course. How do we know the organization's utility function? We know how to calculate the EMV of alternative bets and their values: multiply the alternative values by their probabilities. However, if utility is not equal to the economic value of the outcome, how do we identify the utility of each scenario to the organization in order to take its expected value? We substitute utility for value and decide on E(U) rather than on EMV.

This theory helps explains why people may take out insurance policies to cover themselves for a variety of risks. The expected value from paying for insurance would be to lose out monetarily. But, the possibility of large-scale losses could lead to a serious decline in utility because of diminishing marginal utility of wealth.