# Do a group of economic agents really act as if they are rational?

When questioning the rational choice hypothesis, I often get responses that are similar to the followings:

"Individuals may sometimes make irrational decisions, but a large group of economic agents would act as if each of them is making rational decisions when you look at their choices in aggregate."

Questions:

1. Can you explain the rationale behind the above statement in further details?
2. How does the above statement hold up against empirical evidences?
• Do you mean "a group of people" rather than "a group of economic agents"? Or are you trying to generalise from humans to corporations? Once you drop the unifying "rational self interest" assumption you have to start talking about the kind of agents, since different kinds of agents may be irrational in different ways. Oct 22 '21 at 10:58

The literature is full of examples in which either

1. individual rationality leads to aggregate rationality
2. individual rationality does not yield aggregate rationality (when public goods or externalities are considered; Arrow's impossibility theorem also falls into this case)
3. lack of individual rationality yields lack of aggregate rationality
is obvious and not very interesting, but the case you mention in your post is the more fascinating:
4. Lack of individual rationality yield aggregate rationality

1. Can you explain the rationale behind the above statement in further details?

In my view, there is a statistical law behind many "regularity through aggregation results", which is best illustrated by these equations (in standard notations):

\begin{align} y_n &= f_n(p) + u_n \\ \frac{1}{N}\sum_n^N y_n &= F(p) + \frac{1}{N}\sum_n^N u_n \end{align}

The disaggregate error term $$u_n$$ represents a gap wrt rational behavior. If this term is iid, then the variance of the aggregate "mean" term is much smaller than the variance of $$u_n$$. So, while "irrationality" can be large empirically at the individual level, there is hope for a smaller importance of "irrationality" in the aggregate (due to compensations by summation). The "rational" (demand or supply) function $$F(p) \equiv \frac{1}{N} \sum_n^N f_n(p)$$ may become the driving force for explaining the aggregate "mean" level $$Y$$, whereas rationality may be a small component in disaggregate behaviors.

If economic structure (for instance a simple budget constraints, or market equilibrium condition) is added to the above statistical explanation, then some properties can be reinforced in the aggregate. For a reference illustrating this type of reasoning, see:

Becker, G. S., 1962, “Irrational Behavior and Economic Theory,” Journal of Political Economy, 70, 1-13.
Heiner, R. A., 1982, "Theory of the Firm in Short-Run Industry Equilibrium," American Economic Review, 72, 555-62.

1. How does the above statement hold up against empirical evidences?

Well, there are many aggregate results which are not "rational" (because they fall into category 2 above). Regarding non-experimental evidence for category 4, there is:

Hildenbrand, W., 1994, Market Demand: Theory and Empirical Evidence, Princeton University Press.

• Finally: this is a personal opinion, but my esteem for Becker dropped noticably when I read “Irrational Behavior and Economic Theory.” Seems to me that his examples rely on the "middle of budget line consumption" type of assumption very heavily, making the paper a slight of hand. Oct 23 '21 at 13:04
• @Giskard: Yes, point 1. is finally not so obvious, you are right, I made your suggested changes. Regarding Becker's paper, his finding can be generalized and still holds under weaker assumptions. I think that there are not many other (non-experimental) references that can be added here. Oct 23 '21 at 13:20
1. Can you explain the rationale behind the above statement in further details?

This is an example of an emergent property or sometimes called just emergence. Emergence in layman's terms denotes situations where the whole is more than just a sum of its parts. For example, individual molecules of $$\text{H}_2\text{O}$$ (water) are not wet themselves, but if you put billions of such molecules together you get something that gives you the sensation of wetness. Neurons that form our brains lack any intelligence or consciousness but if you put a lot of neurons together in the right order somehow that can give you consciousness. These are just some examples, in a very large number of complex systems you will find emergent properties. In fact, this is so common that even thinking that something that is true of a part must be true of a whole is considered a fallacy of composition.

Similarly, it is possible that, in some situations, individual humans would not act rationally, but a sufficiently large group of humans would. Rationality can emerge due to human interaction, for example, trading on a market can lead to rational behavior thanks to prices that emerge in the market by supply-demand interactions, people bidding etc. You can see an overview of theoretical discussions of group rationality in Sarkar (2007).

1. How does the above statement hold up against empirical evidences?

There is solid empirical evidence that there are situations where people or heck even animals act rationally as a group even if they could possibly, in the same situation, act irrationally as individuals. For example, even beings so simple as ants can be shown to behave fully rationally in groups (see Sasaki & Pratt 2011). In fact, you might be surprised but even plants can 'behave' rationally and not just in groups but also individually (Schmid, 2016; Khalil; 2010), heck there is even argument to be made they behave rationally more often than animals.

When it comes to the subject of humans, there is a lot of evidence that there are cases where humans can act irrationally individually but will act rationally in a group. For example, Bornstein & Yaniv (1998), show that in an ultimatum game experiments groups act rationally more often than individuals. Rubinstein (2019) discusses rationality that arises in the financial markets even if individuals themselves might not necessarily be rational. There are many other cases where group rationality emerges, even when individually people are not rational. Empirically this has to be tested every time since you can also encounter cases where individuals do act rationally but groups don't or cases when both individuals and groups act rationally or cases where neither do. Going over all empirical examples is beyond the scope of stack exchange answer, but you can have look at works cited in the referenced listed above.

However, note an important caveat is that in economics and other related sciences, word rational does not have the same meaning as in common English. In common English, rational just means smart, in scientific jargon rational behavior is behavior that follows some basic axioms such as transversality axiom (if you prefer A to B and B to C you automatically prefer A to C) or completeness axiom (you can rank all your options given your preference and being indifferent between options is also allowed). So someone can be completely rational but still exhibit behavior we would consider stupid (e.g. being anti-vaxer, trying to prove earth is flat, throwing yourself into a volcano and so on can be completely rational in the jargon of decision theory).

• It seems to me that you are blurring the lines between "rational" and "rationalizable". Oct 23 '21 at 12:56
• Off topic - a heuristic if mine: 1. Is the answer somewhat long? 2. Does it have several academic references? 3. Does it contain the word "heck"? If the answer to all three is "yes", then it is a 1muflon1 answer with 99% probability. (I usually reach this conclusion before scrolling down to see your username.) Oct 23 '21 at 12:59
• @Giskard thanks for the remark, well I do not try to intentionally blurry the line, rationalizability, if I remember correctly my game theory classes, requires also common knowledge assumption. But I guess lines there are a bit blurry since most examples of rational behavior will overlap with examples of rationalizable strategies
– 1muflon1
Oct 23 '21 at 13:59
• It seems I am using the term in an imprecise manner. What I meant: models usually assume that X agent is "rational" and has goal function Y. Empirical testing usually tests if there is any possible goal function Y that can possibly "rationalize" the observed behavior of X. These kind of tests can of course only falsify, not prove, that the agent is indeed rational. Oct 23 '21 at 15:04

This paper describes the distinction between implicit, tacit, and explicit knowledge:

http://www.mkdavies.net/Martin_Davies/Recent_files/KnowledgeExpImpTacit.pdf

If utility functions are tacit and implicit there is no secondary explicit description of whether or not behavior motivated by such utility functions is "rational" or "irrational".

The reference posted by 1muflon1 has this opening sentence:

In its original economic setting, rational choice theory predicts behavior under the assumption that humans act to maximize utility, an implicit measure of net benefit (von Neumann and Morgenstern 1944).

In Artificial Intelligence applications we may program a machine with explicit code to behave according to some utility function; or we may attempt to build a neural network which learns its own utility functions. In the first case we recognize an explicit utility function such as would be discussed and described by a model among economists; and in the second case we do not know the implicit utility function so we are forced to invent an explicit model.

Knowledge is implicit in the respective body and mind of an animal or human being. This knowledge is only explicit when human beings communicate to evoke the knowledge implicit in the respective members of a group.

To compare rational action to irrational action requires a counterfactual model in which the agent takes an action which fails to maximize utility but in theory the agent could have taken action that would maximize utility. The model for action and payoffs must be explicit or there is no way to detect "irrationality" via the use of counterfactual reasoning.

The phrase "maximize utility, an implicit measure of net benefit" is interpreted to mean that a rational individual and/or rational group knows what outcome gives maximum utility, knows how to act to cause maximum utility, and acts to cause maximum utility. If no one knows the model for maximum utility versus the alternatives then there is no model for rational or irrational behavior there are just actions and consequences with no utility rank.

So if the group is rational despite the presence of some or many irrational agents this requires a body and mind that decides the meaning of implicit measure of net benefit in the context of observing the behavior of individuals and the group as a whole.

• (-1) > The phrase "maximize utility, an implicit measure of net benefit" is interpreted to mean that a rational individual and/or rational group knows what outcome gives maximum utility, knows how to act to cause maximum utility, and acts to cause maximum utility. < This is not the interpretation of the word rational in economics, it is not an epistemic category. Oct 23 '21 at 12:54
• If the economist denies that utility functions are epistemic experiences and/or models of the mind then the economist is a person who is out of their mind. Oct 23 '21 at 13:26
• Transcend moral and ethical judgments, concerning good or bad outcomes, and there is no basis to judge whether an action or interaction is "rational" or "irrational". In the physical sciences no one pretends to be the authority on whether nature is rational or irrational. The social sciences evoke the experience of minds and there is the debate over whether actions are rational or irrational. Oct 23 '21 at 13:28