The domain of preference.

• Author: Kornhauser, Lewis A.
• Position: Preferences and Rational Choice: New Perspectives and Legal Implications

INTRODUCTION

The concept of preference is one of the central, perhaps the central, concept in microeconomic theory. It is also one of the most protean of concepts within economics where it assumes many forms. Its centrality derives from its ubiquity; almost every model in microeconomics specifies a preference ordering for each agent. This very ubiquity, however, explains its protean nature. The models in which these preferences appear have a multitude of purposes. Moreover, a given application for a particular purpose may deploy a very different interpretation or specification of preference than another application that pursues an identical purpose.

Recently, the concept of preference has come under attack in a variety of ways. In this Article, I focus on the most sustained and central attack on the concept--that developed by psychologists and behavioral economists. (1) In Parts I and II of this Article, I briefly characterize the concept of preference itself and the behavioral critique of this concept. I then partially evaluate this critique through two related inquiries.

First, in Part III, I seek a clearer understanding of the multiple uses of the concept within microeconomic theory. These uses fall into four categories: descriptive, explanatory, design, and normative. The behavioral critique of preference theory has different force against different uses across and within categories.

Second, I suggest two reasons why a critique of a particular use of preference apparently undermines the concept of preference in all its uses. In Part IV, I argue that economists have not succeeded in draining their interpretations of the concept of preference of its original psychological content. The critique of behavioral economics undermines the use of preferences in a psychological explanation of behavior. It does not, however, undermine a role for preference within a nonpsychological theory of explanation, or in its design and normative uses. Further, in Part V, I argue that the paradigmatic arena of application of microeconomics--markets for goods and services--is special, and its characteristics do not translate readily to other arenas of application. In the standard model, agents choose from some set of (feasible) options that constitutes a subset of the options over which the agents have (explanatory) preferences. In addition, the well-being of agents derives from the extent to which these explanatory preferences are satisfied. The structure of the standard model is thus special because explanatory, normatively rational, and evaluative preferences coincide. Some models sever the link between the domain of choice and the domain of explanatory preference or between the domain of explanatory preference and the domain of well-being. Once one understands that these domains are not identical, intransitive choices may no longer undermine explanations that rely on a psychological interpretation of the concept of preference.

1. THE FORMAL CONCEPT OF PREFERENCE AND ITS BASIC INTERPRETATIONS

   In the discussion of preference, one must distinguish between the formal concept and its interpretations. The formal concept consists of a simple mathematical structure that I discuss below. This mathematical structure, however, may be (and has been) interpreted in many different ways. In a particular application, an interpretation will define very concretely the content of the agent's preferences. These concrete interpretations, however, pass through one of three more general models--decision making under certainty, decision making under risk, and decision making under uncertainty--each of which provides a more abstract interpretation of the formal theory.

   The formal concept of preference is quite simple: A preference is a pair (D, R) where D is a specified domain and R is a linear order over D. The domain D is simply a set of "objects." The linear order R is a binary relation over the elements of D that satisfies three conditions: (i) it is complete; (ii) it is symmetric; and (iii) it is transitive. (2) Completeness requires that, for every x and y in D, either xRy ("x is at least as preferred as y") or yRx ("y is at least as preferred as x"). Symmetry requires that xRx for every x. Transitivity requires that if xRy and yRz, then xRz; in words, if x is at least as preferred as y and y is at least as preferred as z, then x is at least as preferred as z. (3)

   One may represent many everyday relations, both physical and social, with this formal concept. For example, let the set of objects be mountains on earth and the relation be "at least as tall as." Then this pair (D = {mountains on earth}, R = "at least as tall as") satisfies the requirements of a preference. Or let the set of objects be individuals in the United States and the relation be "at least as old as." This pair, too, satisfies the requirements of a preference. These "preferences," of course, have no economic content.

   The three distinct contexts of decision making in which economists deploy the formal concept of preference all use the identical formal concept, even though the terminology used in these contexts--decision making under certainty, decision making under risk, and decision making under uncertainty--differs in order to reflect the different interpretation of the formalism required by the context of application. Under certainty, the decision maker knows with certainty what outcomes will result from her actions. Preferences in this instance are over the domain of "consequences." Under risk, she knows the probability distribution over possible outcomes that is associated with each possible action she may take; economists usually describe the elements of the domain D of preference as "lotteries." Under uncertainty, she knows only the set of consequences that a given action may have; economists usually describe the elements of the domain D of preference here as "actions."

   Even the simple characterization of the domain of preference as "consequences," "lotteries," or "actions" begins the process of interpretation. Formally, the set D in models of decision making under certainty is simply a set of objects; in the standard market context, the objects are "consumption bundles." In decision making under risk, the domain of preference is formally the unit simplex (4) of some (finite) set s. In decision making under uncertainty, the domain D of preferences is a set of functions from a (finite) set s (generally interpreted as "states of the world") to a set X (generally interpreted as "consequences"). In each context, microeconomic theory then generally proceeds to identify a set of conditions that are necessary and sufficient for the representation of the preference by a "utility" function or by "expected utility." (5)

2. THE BEHAVIORAL CRITIQUE OF PSYCHOLOGICAL PREFERENCES

   Research in behavioral economics has demonstrated a number of ways in which individual decisions deviate from the dictates of rationality as understood in preference theories. I consider a small set of these results that bear directly on preference theory. (6)

   First, the initial allocation of property rights affects an individual's valuation of a good; an individual is willing to pay less to acquire a good than she is willing to accept to sell it. This endowment effect exists even when the wealth effect of a particular allocation is small. Kahneman, Knetsch, and Thaler, for example, found an endowment effect when the market value of a fungible good was roughly three dollars. (7) The endowment effect permits intransitive preferences. Consider some good X for which the agent has a willingness to accept of $510 and a willingness to pay of $490. Let bundle A consist of X and $500, bundle B of $1000, and bundle C of X + $500. Then if the agent has bundle A, she prefers A to B; if she does not own X but has $1000, she prefers B to C, but she should be indifferent between A and C. These pair-wise comparisons yield the judgments A preferred to B preferred to C which is as preferred as A. A violation of the transitivity requirement undermines each of the three interpretations of preference theory as decision making under certainty, risk, and uncertainty.

   The endowment effect leads to intransitivity and a violation of the assumptions of preference theory only under some descriptions of the domain over which the agent has preferences. The violation arises when we describe options within the domain solely in terms of the physical characteristics, date, and location of the goods at issue. If we supplement this physical description of the bundles with the ownership status of the goods, then the intransitivity disappears. The agent prefers A to B only if she owns; otherwise she prefers B to A. Ownership status is thus decision relevant.

   This strategy to rescue preference theory is unsatisfying. Such a redescription is always available but not every redescription is plausible. In the absence of a reason why a particular factor should influence the agent's valuations, the redescription seems merely ad hoc. To require a reason to justify treating a particular attribute of a situation as decision relevant suggests that some preferences are irrational. It thus apparently imposes substantive content on the idea of a preference. Appearances may deceive; the endowment effect poses a problem because agents systematically exhibit this behavior. It thus seems important to explain either causally or normatively why they exhibit this behavior. (8)

   Second, individuals do not choose under risk in a fashion consonant with the dictates of preference theory. (9) Their probability judgments are defective. For example, individuals generally exhibit hindsight bias; they overestimate the likelihood that what actually happened would happen. This bias may arise in any legal context that requires a fact-finder to assess ex post the reasonableness of ex ante conduct that led to undesirable results. Hindsight bias is, arguably, an...