“Rationality” isn’t always Rational

by Mario Rizzo

Over the past two years I have been reading more than I ever dreamed about rationality in economics, especially in the standard neoclassical theory of choice. I have done this because I want to get at the root of the controversies concerning whether people’s behavior is, in particular contexts, rational or not.  Claims about the rationality of individual behavior are very closely linked to important policy questions about state paternalism. The highly abstract is working its way down the line to practical policy issues.

In all of this I am well-aware of the argument that “rationality” is the result of market processes and of decisionmaking institutions. I have nothing per se against this line of reasoning. Nevertheless, I want to approach the issue on the terms espoused by many choice theorists and behavioral economists themselves. This is the idea that the axioms of rational choice have a normative importance in and of themselves. By and large, behavioral economists accept the normativity of standard rational choice even as they reject the descriptive reality of rational choice.

The funny thing about all of this is that, initially, the axioms of rational choice were supposed to shed light on how people actually made choices. Then a sleight of hand occurred. It was claimed that they shed light on how rational individuals would choose – without addressing the issue of whether people were in fact rational in the sense of the axioms. Finally, it was alleged – in the face of empirical evidence that people often did not choose rationally – that the axioms defined the norms of choice. They told us how rational individuals should choose. More than that. Since being rational is taken as “good,” they show us how people should behave – full stop.

What are these axioms? One can multiply them, depending on the problem at hand. For our purposes, however, the most important ones are: (1) the transitivity of preferences and (2) the closely related idea of the independence of irrelevant alternatives. I’ll give one example of each.

Suppose I choose an apple over an orange when each is available to me. And I choose an orange over a pear when each is available. Transitivity demands that I must choose an apple over a pear when each of these is available. If I don’t, then I am “irrational.”

Independence is a related idea. Suppose I choose an apple instead of an orange when each is available.  If I am offered an apple or an orange or a pear, I will not choose an orange (although I may now choose the pear). The offer of a pear is irrelevant to the choice between an apple and an orange. It must not make a difference – if I am rational.

It may seem as if these axioms are indeed consistent with rational choice. They can but need not be.  They are not necessitated by rationality more broadly considered. In other words, we can easily come up with counter-examples that are also consistent with broad rationality. Even more significantly, the counter-examples reveal the inadequacy of the narrow, more technical version of rationality.

Counter-example to transitivity: Let us imagine a dinner party of polite people. Your preferences for fruit are as follows:  A large apple is preferred to an orange. An orange is preferred to a small apple.  The host is out of oranges. So he offers you either a large apple or a small apple. Transitivity requires that you choose the large apple. Politeness seems to require that you choose the small apple. And so you do. Are you irrational? Most people would say no.

What has happened?  The binary option itself changed the meaning of the choice. The choice now means more than just getting the apple; it means revealing something about your character as well. Note that if you had been offered the ternary option (large apple or orange or small apple) it would have been plausibly acceptable to choose the large apple.

What this means is that it is not irrational for an individual to choose intransitively. If a large apple is preferred to an orange which is preferred to a small apple, then the individual “should” have chosen the large apple in the binary case. But he did not.  Nevertheless, he is rational in the broad sense.

Counter-example to independence (from Amartya Sen):  Suppose a well-mannered and rather conservative lady has the following preferences. She would prefer to have tea with her cousin to not having tea with him. Suppose now he gives her an additional alternative, that is, to have tea and some cocaine with him. The new option itself tells her more about him. With such a person she would now prefer not to have even a simple tea. Thus while a simple tea is preferred to no tea when the third option is not available, this preference is reversed when given all three options. She chooses no tea at all. But the lady is nevertheless rational in the broad sense.

It is not hard to imagine that the proponents of the normativity of the standard axioms would have a response. The response is essentially to re-describe the behavior and thus save the axioms. In the first counter-example the proponents might say that the preferences were conditional on the demands of politeness being served or not being at issue. They would say that we sneaked a new object of choice into the mix: displaying politeness. In the second counter-example the proponents would say that we have introduced new information. The initial binary preference was conditional on the cousin being a conventional-type while the new option alters that conditional.

These responses, however, do not work as a consistent strategy. They are seriously ad hoc. We can see this for a number of reasons. First, the analyst only worries about these counter-examples because they are consistent with a higher or more basic notion of rationality. They show the technical notions in a bad light. Thus, the urge to re-describe effectively concedes that the technical axioms are deficient both descriptively and normatively. Second, the counter-examples show that objectively (that is, analyst) defined or characterized options do not capture either the meaning or the knowledge-context of choices.  Third, the logic of transitivity and independence is static. In other words, this logic strictly applies to preferences at a single instant in time when meaning and knowledge are unchanged.  In the counter-examples given, however, the addition or subtraction of options produces a change in meaning or knowledge. So the previously-defined options have changed.  The agent cannot choose the initial small apple or simple tea. They no longer exist.  Thus we cannot make inferences from the initial choices to the “subsequent” choices.

What are we to conclude from this? Are we to say that the behavioralists are right after all? The behavior illustrated here is not rational. It certainly is not rational in the sense meant by those who espouse the standard axiomatic version of rationality. But since it is quite plausibly rational in a broader sense of the term why should the failure to conform to the axioms bother us?  It might bother us if our only task were to explain or predict behavior. The model does not do the job.

On the other hand, there is no basis for claiming that the transitivity or independence axioms are general norms of rationality. The behavior of individuals need not be “corrected” by policy. To attempt to do so would seem quite arbitrary.

The behavioralists may well be correct that people do not act in accordance with these rationality axioms. But they are surely wrong in claiming that they ought to behave in this way. The problem is not with deficient individuals. It is a problem of deficient rationality standards.