Optimality as a prescriptive tool

This paper examines the strengths and weaknesses of one of science's most pervasive and flexible metaprinciples; optimality is used to explain utility maximization in economics, least effort principles in physics, entropy in chemistry, and survival of the fittest in biology. Fermat's principle of least time involves both teleological and causal considerations, two distinct modes of explanation resting on poorly understood psychological primitives. The rationality heuristic in economics provides an example from social science of the potential biases arising from the extreme flexibility of optimality considerations, including selective search for confirming evidence, ex post rationalization, and the confusion of prediction with explanation. Commentators are asked to reflect on the extent to which optimality is (1) an organizing principle of nature, (2) a set of relatively unconnected techniques of science, (3) a normative principle for rational choice and social organization, (4) a metaphysical way of looking at the world, or (5) something else still. Keywords-, adaptation; biases; causality; control theory; economics; entropy; evolution; explanation; heuristics; homeostasis; optimization; rationality; regulation; sociobiology; variational principles Most scientists seek to explain as well as describe and predict empirical regularities. Often such explanations involve optimality arguments, ranging from "least effort" principles in physics to "survival of the fittest" in biology or economics. This paper suggests that the use of optimality in science is a powerful heuristic (i.e., a mental shortcut) for describing existing phenomena as well as predicting new ones. As with any heuristic (Tversky & Kahneman 1974), however, the optimality approach is prone to systematic biases, which the paper identifies. First, a brief review is offered of the pervasiveness of optimality arguments in various sciences. The concept of optimality is then examined as a model bound notion, involving intentional and teleological perspectives. Fermat's principle of least time is used to examine the difference between teleological and causal theories, followed by a discussion of modes of scientific explanation. The paper closes with an examination of the rationality assumption underlying economics. Both the power of the optimality heuristic and its inherent biases are highlighted. 1. Optimality principles Whenever a behavior or other empirical phenomenon is explained as maximizing or minimizing some objective function (subject to well-defined constraints), an optimality principle is implicitly or explicitly adduced. This paper examines the scientific use of such optimality principles, a key characteristic of which is that the empirical phenomenon of interest is viewed as a necessary consequence of optimizing some well-specified objective function. The following are examples of such optimality principles in various fields of inquiry. To develop the argument, we will equate extremum principles with optimality principles (although some readers may find this objectionable). 1.1. Economics. Among the social sciences, economics is most closely wedded to the optimality approach, especially at the microlevel. Individual consumers as well as business organizations are presumed to be maximizing entities who calculate with lightning speed their optimal consumption patterns and output levels. Cournot (1838), Pareto (1897), and others (such as Edgeworth, Slutsky, Walras, and Marshall) introduced mathematics with great vigor (and controversy) into economics, and Paul Samuelson (1946) set the standard for subsequent generations regarding the use of formal analysis. Today optimality models abound in economics, ranging from Pareto optimality to the optimal designs of incentive structures and contracts in firms. Current theories of finance, as a branch of microeconomics, offer a good example of the approach (Fama 1976). Firms are presumed to issue stock and debt in ratios that minimize the total cost of capital. Investors assess stock prices by rationally projecting dividends and discounting them for time and risk. The latter concerns only the so-called systematic risk component (i.e., covariance with the market) as most firm-specific risk can be diversified away via portfolios. Investors are assumed to hold only efficient portfolios, that is, those having minimum risk for a given level of expected return. New information immediately gives rise to new expectations concerning dividends (via Bayes' theorem), so that stock prices follow Martingale distributions or random walks (see Fama & Miller 1972). Although no claim is made that 1991 Cambridge University Press 0140^525X191 $5.00+,00 205 Schoemaker: Optimality anyone actually solves the complex equations involved, it is nonetheless argued (in the tradition of positivism) that such "as if" assumptions closely predict aggregate realworld behavior. Several authors have examined optimality parallels between economics and physics (Magill 1970; Samuelson 1970; Tinbergen 1928) as well as economics and biology (Alchian 1950; Cooper 1987; Ghiselin 1974; Hirshleifer 1977; Houthakker 1956; Maynard Smith 1978). In economics, either expected utility or economic profit is maximized; in biology, mean fitness or reproductive survival of genes or organisms (Lewontin 1974). In the latter case (as in physics and chemistry), the optimization argument is clearly advanced "as if," since biological entities lack the conscious striving and foresight characteristic of humans. Thus, the justification for the optimality heuristic seems, a fortiori, stronger in economics than in the life or physical sciences, although some consider even economic rationality no more than "as if" (Friedman 1953). 1.2. Physics. Maupertuis's (1744) principle of least action is perhaps the first major use of a formal optimality argument in science (see von Helmholtz 1886). It holds that a mechanical system moves along the path of least resistance (i.e., minimal mechanical action). In optics, this law was known earlier (ca. 1657) as Fermat's principle of least time (assuming total energy remains constant). Both principles were later generalized, following Euler (1744) and Lagrange (1788), by Hamilton (1834; 1835) to systems without conservation of energy. Hamilton's principle of least action has become one of the major unifying concepts of theoretical physics. The application of Hamilton's principle involves the calculus of variations and can be illustrated by considering the trajectory a ball will follow when thrown away in the air. In a constant gravitational field, without other forces operating, the trajectory of the ball will be a parabola. This is derivable from the least action principle as follows. Let imv(x) be the kinetic energy at a given point x along the trajectory and mgx its potential energy (where m is mass, v velocity and g the gravitational constant). If we "sum" the differences between kinetic and potential energy along the trajectory, the following function obtains: Action = [-mv(t) mgx{t)]dt where x = f(t) J Z