El Farol Problem – Inductive Reasoning and Bounded Rationality

Very important paper outlining the importance of inductive reasoning.

Introduction (Via Brian Arthur @ Santa Fe Institute)

The type of rationality we assume in economics–perfect, logical, deductive rationality–is extremely useful in generating solutions to theoretical problems. But it demands much of human behavior–much more in fact than it can usually deliver. If we were to imagine the vast collection of decision problems economic agents might conceivably deal with as a sea or an ocean, with the easier problems on top and more complicated ones at increasing depth, then deductive rationality would describe human behavior accurately only within a few feet of the surface. For example, the game Tic-Tac-Toe is simple, and we can readily find a perfectly rational, minimax solution to it. But we do not find rational “solutions” at the depth of Checkers; and certainly not at the still modest depths of Chess and Go.

There are two reasons for perfect or deductive rationality to break down under complication. The obvious one is that beyond a certain complicatedness, our logical apparatus ceases to cope–our rationality is bounded. The other is that in interactive situations of complication, agents can not rely upon the other agents they are dealing with to behave under perfect rationality, and so they are forced to guess their behavior. This lands them in a world of subjective beliefs, and subjective beliefs about subjective beliefs. Objective, well-defined, shared assumptions then cease to apply. In turn, rational, deductive reasoning–deriving a conclusion by perfect logical processes from well-defined premises–itself cannot apply. The problem becomes ill-defined.

As economists, of course, we are well aware of this. The question is not whether perfect rationality works, but rather what to put in its place. How do we model bounded rationality in economics? Many ideas have been suggested in the small but growing literature on bounded rationality; but there is not yet much convergence among them. In the behavioral sciences this is not the case. Modern psychologists are in reasonable agreement that in situations that are complicated or ill-defined, humans use characteristic and predictable methods of reasoning. These methods are not deductive, but inductive.

In this paper I will argue that as economists we need to pay great attention to inductive reasoning; that it makes excellent sense as an intellectual process; and that it is not hard to model. In the main part of this paper, I will present a decision problem–the “bar problem”–in which inductive reasoning is assumed and modeled, and its implications are examined. The system that emerges under inductive reasoning will have connections both with evolution and complexity.

Additional Excerpt (Via Brian Arthur @ Santa Fe Institute)

Economists have long been uneasy with the assumption of perfect, deductive rationality in decision contexts that are complicated and potentially ill-defined. The level at which humans can apply perfect rationality is surprisingly modest. Yet it has not been clear how to deal with imperfect or bounded rationality. From the reasoning given above, I believe that as humans in these contexts we use inductive reasoning: we induce a variety of working hypotheses, act upon the most credible, and replace hypotheses with new ones if they cease to work. Such reasoning can be modeled in a variety of ways. Usually this leads to a rich psychological world in which agents’ ideas or mental models compete for survival against other agents’ ideas or mental models–a world that is both evolutionary and complex.

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08. September 2009 by Miguel Barbosa
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