Robert Frank on expected utility theory

4 Aug, 2014 at 13:43 | Posted in Economics | 2 Comments

Although the expected utility theory is obviously both theoretically and descriptively inadequate, colleagues and microeconomics textbook writers all over the world gladly continue to use it, as though its deficiencies were unknown or unheard of.

Not even Robert Frank — in one of my favourite intermediate textbooks on microeconomics — manages to get it quite right on this issue:

As a general rule, human nature obviously prefers certainty to risk. At the same time, however, risk is an inescapable part of the environment. People naturally want the largest possible gain and the smallest possible risk, but most of the time we are forced to trade risk and gain off against one another. When choosing between two risky alternatives, we are forced to recognize this trade-off explicitly. In such cases, we cannot escape the cognitive effort required to reach a sensible decision. But when one of the alternatives is riskless, it is often easier simply to choose it and not waste too much effort on the decision. What this pattern of behavior fails to recognize, however, is that choosing a sure win of $30 over an 80 percent chance to win $45 does precious little to reduce any of the uncertainty that really matters in life.

On the contrary, when only small sums of money are at stake, a compelling case can be made that the only sensible strategy is to choose the alternative with the highest expected value. The argument for this strategy … rests on the law of large numbers. Here, the law tells us that if we take a large number of independent gambles and pool them, we can be very confident of getting almost exactly the sum of their expected values. As a decision maker, the trick is to remind yourself that each small risky choice is simply part of a much larger collection. After all, it takes the sting out of an occasional small loss to know that following any other strategy would have led to a virtually certain large loss.

To illustrate, consider again the choice between the sure gain of $30 and the 80 percent chance to win $45, and suppose you were confronted with the equivalent of one such choice each week. Recall that the gamble has an expected value of $36, $6 more than the sure thing. By always choosing the “risky” alternative, your expected gain — over and beyond the gain from the sure alternative — will be $312 each year. Students who have had an introductory course in probability can easily show that the probability you would have come out better by choosing the sure alternative in any year is less than 1 percent. The long-run opportunity cost of following a risk-averse strategy for decisions involving small outcomes is an almost sure LOSS of considerable magnitude. By thinking of your problem as that of choosing a policy for dealing with a large number of choices of the same type, a seemingly risky strategy is transformed into an obviously very safe one.

What Frank — and other mainstream textbook authors — tries to do in face of the obvious behavioural inadequacies of the expected utility theory, is to marginally mend it. But that cannot be the right attitude when facing scientific anomalies. When models are plainly wrong, you’d better replace them! As Matthew Rabin and Richard Thaler have it in Risk Aversion:

It is time for economists to recognize that expected utility is an ex-hypothesis, so that we can concentrate our energies on the important task of developing better descriptive models of choice under uncertainty.

If a friend of yours offered you a gamble on the toss of a coin where you could lose €100 or win €200, would you accept it? Probably not. But if you were offered to make one hundred such bets, you would probably be willing to accept it, since most of us see that the aggregated gamble of one hundred 50–50 lose €100/gain €200 bets has an expected return of €5000 (and making our probabilistic calculations we find out that there is only a 0.04% risk of losing any money).

Unfortunately – at least if you want to adhere to the standard neoclassical expected utility maximization theory – you are then considered irrational! A neoclassical utility maximizer that rejects the single gamble should also reject the aggregate offer.

Daniel Kahneman writes in Thinking, Fast and Slow that expected utility theory is seriously flawed since it doesn’t take into consideration the basic fact that people’s choices are influenced by changes in their wealth. Where standard microeconomic theory assumes that preferences are stable over time, Kahneman and other behavioural economists have forcefully again and again shown that preferences aren’t fixed, but vary with different reference points. How can a theory that doesn’t allow for people having different reference points from which they consider their options have an almost axiomatic status within economic theory?

The mystery is how a conception of the utility of outcomes that is vulnerable to such obvious counterexamples survived for so long. I can explain it only by a weakness of the scholarly mind … I call it theory-induced blindness: once you have accepted a theory and used it as a tool in your thinking it is extraordinarily difficult to notice its flaws … You give the theory the benefit of the doubt, trusting the community of experts who have accepted it … But they did not pursue the idea to the point of saying, “This theory is seriously wrong because it ignores the fact that utility depends on the history of one’s wealth, not only present wealth.”

What the works of people like Rabin, Thaler and Kahneman, show is that expected utility theory is an “ex-hypothesis” that transmogrifies truth. And as such it shouldn’t just be marginally mended. It should be replaced!