Hans Herzberger's 1973 essay 'Ordinal Preference and Rational Choice' is a classic milestone in the erosion of the idea that rational agents are maximizers of utility. By the time Herzberger wrote, many authors had replaced this claim with the thesis that rational agents are maximizers of preference. That is to say, it was assumed that at the moment of choice a rational agent has a weak ordering representing his or her preferences among the options available to the agent for choice and that the rational agent restricts choice to one of the optimal options. Such an option is an available option judged at least as good as any other.
Herzberger explored the prospects of weakening this ordinalist view of maximizing rationality still further. Herzberger considered the possibility that preferences fail to impose a weak ordering over a decision-maker's options or over the domain of potential options of which the set of available options is a subset. The decision maker may judge some pair of available options as noncomparable so that the preference over the options is not connected.
Herzberger does not elaborate in much detail on his reasons for wishing to provide for noncomparability or incompleteness in the preference ranking. But it seems fairly clear that he understood theories of rational choice to be idealized descriptive and explanatory theories addressing the choices of decision makers. Advocates of such a theory of decision making might concede that flesh and blood decision making fails to fit the specifications of the theory perfectly. The theory, however, serves as a default standard in the sense that insofar [End Page 1] as decision making behaviour conforms to its conditions, the behaviour requires no further explanation. Only failures to satisfy the specifications call for explanation.
Herzberger seemed to think that the assumption that rational agents have preferences that weakly order their options and that they choose options that are optimal with respect to such preferences (if such optima exist) is not to be expected even as a default idealization of the behaviour of consumers, producers, and other decision makers. Consequently, he explored the possibility of abandoning the weak-ordering assumption and weakening the thesis that consumers, producers, or other agents maximize preferences at least ideally in the sense that on average they do so to a good degree of approximation or that failures to do so can be explained away. Idealized theories of the types he wished to consider retain the assumption that a rational agent's goals, values, or preferences are representable by some binary relation of weak preference and the asymmetric and symmetric factors of this relation that serve as relations of strict and equipreference. And rational agents choose options according a principle of 'liberal maximization.' Given a set S of available options, x in S is a liberal maximum if and only if it is not strictly dispreferred to any other member of S. (Liberal maximization is called 'maximality' by Sen and Walley, among many others.)
My own approach to rational choice shares with Herzberger's the view that rational preference need not be a weak ordering (see Levi 1974; 1986). Unlike Herzberger, I focus on prescriptive accounts of rationality. I am inclined to think that good explanatory and predictive models of human behaviour are more likely to come from biologically based models and not from theories of the psychology of belief and desire. If there is any value at all in the study of models of deliberate and intentional behaviour, such models should be understood to be ineliminably suffused with normativity. Decision makers do, indeed, fail to have preference structures that weakly order their options and fail to choose options that maximize their preferences. But the concept of preference involved in this factual claim is characterized by principles of rational preference that serve as a standard of rational health. Failures to satisfy the requirements may be explicable as due to unhealthy circumstances. But not all failures are of this kind. The central claim I have advanced in the past and continue to insist upon is that in many contexts of choice rational agents may remain [End Page 2] coherent (rationally healthy) even though their coherent preferences...