The Role of Risk in Decision Making

In his article “Decision-Making in the Presence of Risk”, Machina discusses the role that risk plays in making decisions, and what factors affect how risk is supposed to be managed. He begins by saying that if the probability of an event can be predicted, the expected results will be shown as the number of trials converges to infinity. However, if a single trial is run, risk plays a much larger role which will subsequently affect the way decisions are made. He uses the example of the game St. Petersburg Paradox in which the expected value of an outcome was infinity because of the possibly extremely high payoffs, but since the most likely payoffs were closer to a dollar this has a very strong effect on how much an individual would be willing to pay to participate in the game.
The article goes on to discuss how Gabriel Cramer and Daniel Bernoulli developed a utility function that is adjusted for risk. Using this function decision makers can determine whether it is a better deal to take a payoff with no risk attached or a larger payout with a certain degree of risk. Over the last two hundred years, there has been a large number of studies that have shown the validity of this theory if it used appropriately. However, evidence has also shown that people often do not use these models when making a decision and often ignore the results they get when actually making the decision.
The Expected Utility Model for most people can take four different forms: concave utility, convex utility, steep indifference and flat indifference curves. Since most people are reluctant to take risk, the required expected value is a function of risk, requiring a greater return for increased risk. In the concave function, the expected return begins to level off, meaning that the decision maker will not require a much higher rate of return for additional risk. On the other hand, a convex function reaches a point where a much higher rate of return is required for a small amount of risk. In both of these situations, the risk-return relationship varies depending on the amount of risk. In the indifference curves however, the change in expected return is constant, regardless of the amount of risk observed.
In order to determine how an individual feels about risk by experimentally determining what choices they would make in three different situations, each of which has a set of returns each with their respective probabilities. Evidence of using these tests has shown that the choices that decision makers often make decisions that do not follow the logic that they would otherwise make. A simpler approach of determining an individual’s risk aversion preferences to determine what definite return the individual would take instead of taking a risk that would involve a certain payoff or receive nothing at all. Interestingly, decision makers frequently depart from the expected value of the utility function in making this determination.
Researchers have arrived at several theories that explain why decision makers may make these seemingly irrational choices. First of all, they may simply not be very experienced at making decisions where the outcomes could not be easily predicted. Secondly, when someone pointed out to these individuals that their strategies for making decisions were not consistent with the expected outcomes of a utility function. Finally, the decisions made in an experiment may not reflect how decision makers would behave in a real world situation with real risks.
Since so many individuals do not follow the expected model approach, models have been created which take the unique preferences of the decision makers into account as well. Unfortunately, there are limitations to these models as well. One problem is that these models require a unique set of conditions since the incremental change in risk has a different effect on behavior and preferences at different stages. There are also still restrictions based on the variables that go into the function. Therefore, while the preference may better explain individuals decisions they are still not without their own limitations.
While it has been clear that there is not usually a linear relationship between risk and return of decision makers with different risk preferences, there are also other problems with the expected return hypothesis. One problem is that subjects in experiments often will change their preferences and decisions after being made to reconsider them. Another problem is that the way a problem is stated or presented also has a profound effect on how a decision maker will respond. Finally, if probabilities are not clear, it is difficult for decision makers to make a decision that is consistent with the expected utility function.