Bounded Rationality and Politics by Jonathan Bendor

Author:Jonathan Bendor [Bendor, Jonathan]
Language: eng
Format: epub
ISBN: 978-0-520-94551-7
Publisher: University of California Press
Published: 2010-08-14T16:00:00+00:00

Optimizing Is Difficult

It is virtually a folk conjecture among formally inclined political scientists that in a stationary environment, many kinds of sensible adaptation converge to optimal behavior. Theorem 1 indicates that this view is overconfident: adaptive schemes that satisfy (A1)—a sensible property—fall short of optimality even in the long run. We suspect that this overconfidence arises from a failure to appreciate how hard it is to optimize when the effectiveness of different options is unknown. This uncertainty creates a fundamental tension between exploration and (wise) persistence; resolving this tension optimally is, in general, difficult.25 To give a sense of how hard it is, reconsider the famous Bush-Mosteller rule. Because the speed of learning in this rule is a fixed parameter (i.e., it is independent of time), the canonical Bush-Mosteller rule satisfies (A1). Hence, a person who adapts via this scheme will not settle on his or her optimal action if it is imperfect. As with any (A1)-type rule, the culprit is relentless learning, driven by an implicit refusal to tolerate any error. A natural question arises: is it possible to dampen this restlessness of the Bush-Mosteller approach by making the speed of learning time dependent? (Note that corollary 1 tells us that we must do so since optimality requires violating [A1].) The answer is yes—but it is easy to overdo this dampening and make the scheme too sluggish. Specifically, one can show that performance is improved if αt, the (now time-dependent) speed of learning, (Robbins and Monro 1951). However, α is overkill. It is not intuitively obvious why αt is just right, whereas is too much dampening.26 Thus, we see that getting the trade-off between exploration and search just right is no mean feat. (This is why Robbins and Monro’s paper was considered a major breakthrough.) Indeed, it is a delicate matter. There is no compelling reason to believe that many garden-variety heuristics have this unusual property.

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