IRRATIONALITY CANNOT PERSIST FOREVER
(Rodrigo Peñaloza, jan. 2016)

The basic theoretical framework for the Homo Oeconomicus is rationality. Many people, however, criticize this framework on the ground of observed irrationality in many controlled experiments. The question then arises as to the epistemic relevance of these criticisms with respect to what rationality really means. In order to approach this problem properly, let me first define what rationality is.

Suppose Adam faces a finite set X of alternative courses of action. In the economic realm, Adam has to make choices. His decision criterium is given by a relation R over X. The relation R has to be interpreted in the following manner: xRy means “x is preferred to y”. For simplicity, let us assume that this ordering is strict and denote it by >. Therefore, x>y means that Adam strictly prefers x to y. If Adam is a homo oeconomicus, then he is rational. By rationality we mean that > satisfies two properties. Firstly, it is complete. It means that, given any two alternatives, Adam is able to decide which one he prefers the most: either x>y or y>x. If Adam has to choose between apple and pear, he is able to give a straight answer. Since we assumed preferences to be strict, indifference is precluded at the outset. This is no loss of generality, it is only a didactical simplification to make the argument easier and shorter. Secondly, > is transitive, that is, if x>y and y>z, then x>z. If Adam strictly prefers apple to pear, and also strictly prefers pear to orange, then he strictly prefers apple to orange.

So, what if Adam is irrational? He will be irrational if his preferences (a) are not complete or (b) are not transitive or (c) are neither complete nor transitive. In order to argue that he cannot be irrational forever, it suffices to understand the consequences that will fall upon him should his preferences be either incomplete (a) or intransitive (b). Case (c) will then yield the same consequences.

What criticizers in general do not understand about rationality is that valuation depends on the whole set of alternatives available to the decision-taker. Indeed, marginal utility is decreasing because total resources are scarce. Criticizers do not understand either that, from the economic point of view, errors of decisions bring about losses of available resources, otherwise errors would not be that bad after all. When they do recognize losses, they barely give any thought to what it means in terms of restructuring of preferences. To fit this remark into our example, let us assume that Adam’s available resources are given by \$10, that is, 10 units of money. Let me just mention that it does not matter if his resources are expressed in terms of money or in terms of physical goods. They could be the area where he gathers fruits, the field he plows, the river where he fishes, whatever, even his own health or his family’s. We could also assume that Adam’s resources are given by a certain amount of apples, pears and oranges. The important thing is that, should Adam make a mistake, the feeling of pain caused by realizing the error is translated into loss of resources.

So let us begin by assuming that Adam’s preferences are not complete. This means that there are two alternatives x and y about which Adam cannot say anything, that is, he cannot decide.

Before proceeding, let me explain it a bit further. Suppose Adam is taking a walk in the fields after arguing with Eve. He suddenly sees a lion right in front of him, ready to attack. If Adam is rational, he will try to save his life at whatever costs. If he just freezes, he will be certainly dead. If he runs away, he at least has a small chance to survive. He then has to choose between running rightwards or leftwards. What if he just cannot decide wich side to run to? This is equivalent to freezing, hence death. I gave this extreme example to make clear that irrationality brings about losses. In economics, incompleteness of preferences means that Adam may eventually face a choice between two alternatives and will just freeze. If he does so, he will lose something. This is the whole meaning of considering errors as harmful to the man. If nothing harmful happens to Adam after his not being able to decide when life brings him to a crossroad, then how could Nature select the best species to survive? When people criticize rationality, they focus on the preference structure alone and do not conceive of its relation to the available resources in terms of losses.

Let us get back to Adam’s irrationality in terms of incomplete preferences. Suppose x=apple and y=pear. Here Eve will play the role of mother Nature with all her wisdom. She will personify the instrument of punishment from Nature for the mistakes made. You can think of Nature as the Market, if you wish. This is the way Eve will give Adam true knowledge. Eve offers Adam a choice: apple or pear. Since he is unable to decide, Eve takes \$1 from him. If the choice were between apple and orange, maybe Adam would give a straight answer. However, sometimes Life offers Adam the choice between apple and pear. If he is irrational, he will lose something. Eve may proceed, every now and then, offering Adam the choice between apple and pear, but if Adam does not learn from his mistakes, as Eve has been trying to tell him in the first place, he will eventually lose all his resources and will die. He will be deleted from the face of the Earth as a species not fit enough to survive. You can also think that the Homo Oeconomicus named Adam will eventually be taken out of the Market for being so stupid all the time.

Criticizers only observe that sometimes Adam is irrational in the sense that he cannot decide between apple and pear and hence conclude that rationality is not pervasive and not a good framework. What they do not realize is that this kind of irrationality cannot persit forever, they are eventual, not essential. People can make mistakes out of irrationality sometimes, but they cannot be irrational all the time.

Now suppose that Adam is irrational in terms of intransitivity of preferences. For instance, say that he ranks apple, pear and orange in the following way:

apple>pear > orange > apple

(In)transitivity is the property by which Eve teaches Adam about trade. In this case, let us assume that Adam’s resources, in addition to his initial \$10, are also given by certain amounts of apple, pears, and oranges. Eve offers him an apple in exchange for one pear and \$1. Since Adam strictly perfers apple to pear, we may assume that \$1 is a small enough amount of money for Adam to think he is still getting better off from this transaction, so he gives in his pear to Eve for an apple and loses \$1. Assume this happens likewise for the other pairs of goods as well. He has now one pear less, one apple more, and \$1 less. Eve now offers him a pear in exchange for an orange and \$1. Given his preferences, Adam agrees to it. He gets back his initial amount of pears, loses one orange and loses \$1 more. Then Eve offers him an orange in exchange for an apple and \$1. He again agrees to it. He gets back his initial amount of oranges and loses that first extra apple. Besides, he loses \$1 once more. In the end, after three rounds of transactions with Eve, he keeps the same initial amounts of goods, but he is \$3 poorer. Eve can proceed this way until Adam loses all his money. When he realizes it, he can sell his goods to get money. However, if Adam does not learn to correct his intransitivity, everything will eventually happen again and again until he dies. Once again, criticizers overlook the the full consequences of irrationality because they only focus on the preference structure.

The overall lesson from this mental experiment is that Adam cannot be irrational forever. If he is, he will eventually die. This evolutionary argument explains after all why we, modern human beings, are still on Earth and why we are economically better off today than the Neanderthals ever were or the socialists want us to be. Adam can only survive Nature, or Market for that matter, if he accepts the fact that Eve is trying to give him knowledge about his irrationality, in the hope that he will correct his wrong preferences before it is too late.

In the end, people can be irrational sometimes, but most of the time, at the least for the relevant crossroads in the economic realm, people will be rational. In the evolutionary process of a market economy, the Homo Oeconomicus cannot consistently commit himself with irrationality, otherwise he will be excluded from the market. Sooner or later, the irrational agent must correct his preference structure and start to behave in the most rational way possible to survive. It is not necessary to get into the details of how this inner enlightment comes to be. It suffices to say that pain caused by losses is the trigger to think about ourselves. Once Adam eats the fruit of knowledge Eve is offering him, he will become rational and progress.

Criticisms on the whole framework of rationality make absolutely no sense. Of course Homo Oeconomicus is a fictional character, but it is not correct to say that his rationality is departed from reality. It is a model that captures very well the specific difference that makes Adam differ from his genus proximus, the animalia. Throwing away this framework on the ground of punctual violations is nothing more than hypermetromory.

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