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Inductive Reasoning and Bounded Rationality (Arthur, 1994)

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W. Brian Arthur

In: American Economic Review 84

"How do humans reason in situations that are complicated or ill-defined?"

"to deal with complication: we construct plausible, simpler models that we can cope with. It enables us to deal with ill-definedness: where we have insufficient definition, our working models fill the gap."

JLJ - Mr. complexity himself, W. Brian Arthur. One of the early "prophets" of complexity science - we could learn a thing or two from him if we would only read what he has written... tell us Brian, how do humans reason in situations that are complicated or ill-defined - we want to know. You told us in 1994, but we did not listen...

p.1 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.

p.2 How do humans reason in situations that are complicated or ill-defined?

p.3 to deal with complication: we construct plausible, simpler models that we can cope with. It enables us to deal with ill-definedness: where we have insufficient definition, our working models fill the gap. It is not antithetical to "reason," or to science for that matter. In fact, it is the way science itself operates and progresses.

p.4 A key question remains. Where do the hypotheses or mental models come from? [JLJ - I suspect that we as humans, in order to survive, are constantly creating them, and disposing of them if they are not an improvement on our current models] How are they generated? Behaviorally, this is a deep question in psychology, having to do with cognition, object representation, and pattern recognition. I will not go into it here. But there are some simple and practical options for modeling. Sometimes we might endow our agents with focal models - patterns or hypotheses that are obvious, simple and easily dealt with mentally.

p.7 If predictors do not "work" they will not be used; if they do work they will come to the fore.

p.8 Predictors need to "cover" the available prediction space to some modest degree.

p.9 The inductive-reasoning system I have described above consists of a multitude of "elements" in the form of belief-models or hypotheses that adapt to the aggregate environment they jointly create. Thus it qualifies as an adaptive complex system. After some initial learning time, the hypotheses or mental models in use are mutually co-adapted.

p.9 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.