Is it Rational Behavior or is it Risk Aversion?

As I was struggling with a “medical” decision as to whether to continue a “mode” of treatment that has run its course and is no longer viable or alternatively embark on a new treatment with a new technology, I read a most interesting and to the point write up in THE WEEK. It goes without saying that the “old” is familiar; the new is approached with apprehension if not suspicious. Hence, anything that makes the “new” a bit “old” helps. In the June 18th issue of THE WEEK, under the heading of “Author of the Week” , a story unfolds about a medical choice made quite a few years back by Dan Ariely who has written a couple of books using this choice to facilitate the understanding of a relatively new theory of economics.
Dan Ariely is a fellow economist, a “behavioral economist”, who according to THE WEEK has written a 2008 bestselling book: “The Upside of Irrationality”. Behavioral economists are a new breed of economists who are challenging the standard “textbook” notion of human “rationality”, a notion so fundamental to main stream economics. Rationality is a basic assumption economists use to analyze the individual decision, whether the choice is that of a consumption basket, a choice of occupation, and work versus leisure and so on. It is assumed that the individual knows the alternatives and chooses the one that “maximizes” his or her utility. This assumption is essential to our understanding of choice exercised in the market place in a setting which does not involve risk or uncertainty. When the individual is confronted with a choice that involves “RISK”, the choice is not as simple. In this situation we need to sort out individuals in terms of their “sensitivity” to risk taking.
Economists analyze three categories of risk taking exhibited by the individual: Risk averter, Risk lover and Risk neutral. The individual is said to be “risk averse” when he/she places a much higher weight to a choice that “minimizes” taking of risk; a risk lover goes for a risky choice while a risk neutral gives equal weight to risky and non-risky options.
That was more or less all we needed to know to decipher choices of the individual. But then, a group of economists mainly from the “Chicago School” revived a critique levied against the assumption of rationality and self control (See for example Schelling, T., (1978) Economics or the Art of Self Management, Am. Eco. Rev. pp. 290-94). The new group including Sunstein, Thaler, Laibson, O’Donoghue and Rabin to name but a few, earned the label: Behavioral economists for their contributions to the understanding of human decisions. In a nut shell, behavioral economists challenged the notion of rationality and maximization of utility. In effect, they argue that observed behavior is more likely to exhibit “irrational” rather than a rational decision making process. An example that is often cited has to do with the consumption of “sin” goods—cigarettes, alcohol, drugs and the like. Lack of self control is essential to the analysis, as well as the dimension of choice.
Back to the choice made by Dan Ariely, which THE WEEK Magazine uses in alluding to his book on the thesis of behavioral economics. As the magazine tells it (I have yet to read the book), Dan uses his own choice to explain one of the tenants of the behavioral economists’ theory—that people are less than perfectly rational in their choices. The author uses his own choice which he has made several years back to make the point. The choice involved two types of “medical intervention”. According to the write up, at the age of 18, the author suffered burns on 70% of his body. Two medical options were put before him: Amputate his right arm and replace it with a “hook”, or retain the arm after an excruciating surgery and endure severe pain and partial use of the arm for the rest of his life. At the time, at the age of 18, the choice he made was to retain the arm. Was this a rational or irrational decision?
At the time the decision was made, the author, in my view, exhibited what traditional economists label as “risk aversion”. As he put it: I was “incredibly attached to my hand—in multiple ways”. On backward reflection on such decision, Dan Ariely posits that the decision made at the time was “irrational”. When revisiting the decision about his own arm, as it is retold by THE WEEK, he admits that IRRATIONALITY may have led him astray. On revisiting the decision, at least for the book’s benefit Dan Ariely speculated about whether “prosthesis might have been more functional—that keeping my arm was, in a cost-benefit sense, a mistake”.
This reflection on a past decision causes me to revisit in this blog the assumption of rational choice not in terms of one period horizon but intertemporally. In simple terms, a choice with consequences lasting more than one period, for example, a choice involving one period can be depicted by the consumption of an ice cream cone, a cup of tea or a glass of mineral water. An intertemporal choice is a choice with consequences beyond the period when the item is consumed. As an example, cigarette smoking in one period gives satisfaction in that period but carries with it undesirable consequences in subsequent periods.
A great deal has been written about this type of choice. Traditional economists have advanced theories explaining intertemporal choice. The add-on by behavioral economists is that the individual may exhibit what is called “bounded rationality”—that the individual lacks self control when it comes to consumption of sin goods. Accepting this proposition has led some behavioral economists to advocate “paternalism”. Government or some higher authority would override individuals’ preferences for society’s preferences (the ban on smoking in public places, restaurants and bars is an example). For more on this point and references see Bae and Ott “The Public Economics of Self Control”, Journal of Economics and Finance (October 2008. Pp. 356-367).
Let us contemplate a decision at time t, involving two courses of action: An action A and action B. If one knows with “certainty” the outcomes of both, then the standard economist model applies. That is if a choice of A gives pleasure or satisfaction equal to X utiles, and B gives satisfaction equal to Y utiles (discounted if it were to materialize in a future period), then if A is chosen rather than B, then X utiles are greater than Y’s and vice versa. The individual choice maximizes his/her utility. Two problems arise in this scenario: first, a choice with outcome extending beyond the one period (future period(s)), involves uncertainty or unmeasured risk. Secondly, what discount rate to apply to future outcomes?
Back in the late 1940’s, Milton Friedman and T. J. Savage put this issue before us in their seminal article “The Utility Analysis of Choice Involving Risk” in the Journal of Political Economy (August 1948, pp. 279-304). In order to get as close as possible to explaining the individual temporal choice—a choice involving one period when faced with risky choice, they use the categorization of individuals as risk averter, risk lover and risk neutral. In their example the choice involved two options: a “certain sum of money”, and a chance (game) with two outcomes: losing with a high probability a small sum of money and winning with a very small probability a very large sum of money. Depending on the threshold of risk a choice is made among the two options. If the individual is risk averse he is likely to choose the “certain outcome”, if risk lover he will choose the “bet”. Nothing in the second choice is said to exhibit irrational behavior even if the individual were to bet the house and looses it.
Fundamental to the analysis of choice involving risk, is not only the computation of the expected value of the bet so that it can be compared with the “certain” option, but also the expected utility of the uncertain outcome. The expected utility depends on the shape of the utility function of the individual exercising the choice. Such utility is a function of the individual tolerance of risk. Unfortunately, this is a subjective value that can only be assigned by the individual. Which brings me back to Dan Ariety’s choice, and to a choice I am contemplating.
To illustrate:
Using the example of medical intervention, let option X be current treatment mode which has lost most of its effectiveness in the face of the disease progression. Staying with option X is given a probability Pr. =0.2 that it will have some effect. Let individual A be designated as “risk averter”. He/she assigns a utility value to this option as equal to 100 utiles (some scale of value). Hence:
Pr* Ux= 0.2(100) +0.8(0) =20 is the expected utility.
Option Y has the probability of success of 0.7 that it will be effective, (1-0.7) it will not be. If effective, the utility is 1,000. Accordingly:
Pr*Uy=0.7(1,000) + (1-0.7) (0) =700.
Comparing the expected utility of the two options clearly indicates that option Y will be chosen.
This however is not the complete story. If the new technology carries with it, in addition to the failure probability, a probability of adverse side effects then such probability has to be incorporated to arrive at the expected utility of this option. This complicates the analysis as one needs to know, in addition, something about the risk tolerance of the individual.
Let the side effects (usually ascertained from clinical trials) to have a low probability equals (0.007) such that if it materialized will have severe consequences, even death. To calculate the expected utility of option Y one needs to account for this second component.
But there the problem with the optimal choices lies: one needs to know the risk profile of the individual.
As I have mentioned earlier, the individual can be a risk averter, risk lover or risk neutral (this last category is not likely to be prevalent in the population). Hence, I focus on the risk averter.
Suppose that the risk of side effect was evaluated as equal to -100,000 utiles and a probability of occurrence equals to 0.007. The calculation of the expected utility of option Y is: 0.7(1,000) + (1-0.7) (0) +0.007(-100,000) =0. Option Y will be rejected. For it to win over option X the evaluation of the risk has to be lowered. The equivalent value of the option Y to X requires a risk evaluation equals -97,142 utiles. With this value the individual would be indifferent between the two options. For Y to be chosen over X the risk tolerance has to be reduced so that the expected value of the loss is below the threshold of -97,142 utiles.
This is a problem a concerned physician is likely to face: First, he/she has to ascertain the risk tolerance of the patient (that can be done with a full review of the patient medical history a time consuming process to be sure), and secondly, how to induce the patient to lower the evaluation of risk as the probability of occurrence of the side effects is not subject to change without new information. The solution of this problem is not easy, not for the physician or for the patient.
It needs to be emphasized that at the time one is contemplating a choice involving risk, risk assessment has to be made so that the appropriate discount rate can be applied (the discount rate is used to convert future values to the present. This is ignored in this presentation). The choice Dan Ariely faced was a choice involving risk. His first option, keeping the arm may be viewed as the “sure bet” or the “certain” option. The second option is the uncertain option or the risky choice. The uncertainty about the outcome of the second option with all its ramifications would suggest that at the time the decision was made a very high discount rate was applied to the utility derived from choosing the second option to tip the scale in favor of the first option. In my view, that decision has nothing to do with being “IRRATIONAL”.
In a dynamic world, the discount rate does not remain constant. The discount rate that one would use at the age of 20, 30 versus 50, 60 or 70 is not likely to be the same. Accordingly, many years after the fact the author may have denigrated the discount rate he has used when he was at the age of 18. The traditional theory still holds in that intertemporal choices are made at the beginning of the period. However, nothing is irrational about revising the choice in subsequent periods when more information becomes available.
Having cleared up in my own mind as to how my own choice of the two medical options is likely to come down to, I maintain that “given the information at hand whatever option I choose”, my choice will be a “RATIONAL” choice. A fundamental lesson I have learned during my studies, teaching and research is the value of information and the quality of said information. Without good information the discount rate will be faulty and the choice “suboptimal” although “not irrational.”
A final note to reflect upon:
In a decision involving medical intervention, with an option that has an uncertain outcome, a physician uses his/her expertise to calculate the probability of a successful outcome of the option so that it can be compared with the status quo or some other less uncertain options. This probability when communicated to the patient would help the patient to calculate the discount rate that must be applied to obtain the expected value (and utility) of the uncertain mode of intervention, which can then be compared with the outcome of other options including the status quo. It is worth emphasizing at this juncture that the discount rate computed by the patient reflects his/her type, whether, he/she is risk averter, risk lover or risk neutral. As only the individual can put himself/herself in one of these three categories, a choice that may appear “irrational” is in effect completely “rational.”
In my next blog I shall review some of the literature on risky choice and some of the contributions of the behavioral economics especially as some aspects of the theory pits individual choice against societal choice.