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The workhorses of economic analysis are simple formal models that can explain naturally occurring phenomena. Reflecting this taste, economists often say they will incorporate more psychological ideas into economics if those ideas can parsimoniously account for field data better than standard theories do. Taking this statement seriously, this article describes 10 regularities in naturally occurring data that are anomalies for expected utility theory but can all be explained by three simple elements of prospect theory: loss aversion, reflection effects, and nonlinear weighting of probability; moreover, the assumption is made that people isolate decisions (or edit them) from others they might be grouped with (Read, Loewenstein, and Rabin 1999; cf. Thaler, 1999). I hope to show how much success has already been had applying prospect theory to field data and to inspire economists and psychologists to spend more time in the wild.
The 10 patterns are summarized in Table 16.1. To keep the article brief, I sketch expected utility and prospect theory very quickly. (Readers who want to know more should look elsewhere in this volume or in Camerer 1995 or Rabin 1998a). In expected utility, gambles that yield risky outcomes xi with probabilities pi are valued according to Σpiu(xi), where u(x) is the utility of outcome x. In prospect theory they are valued by Σπ(pi)v(xi - r), where π(p) is a function that weights probabilities nonlinearly, overweighting probabilities below.
ABSTRACT. This paper presents a critique of expected utility theory as a descriptive model of decision making under risk and develops an alternative model, called prospect theory. Choices among risky prospects exhibit several pervasive effects that are inconsistent with the basic tenets of utility theory. In particular, people underweight outcomes that are merely probable in comparison with outcomes that are obtained with certainty. This tendency, called the certainty effect, contributes to risk aversion in choices involving sure gains and to risk seeking in choices involving sure losses. In addition, people generally discard components that are shared by all prospects under consideration. This tendency, called the isolation effect, leads to inconsistent preferences when the same choice is presented in different forms. An alternative theory of choice is developed, in which value is assigned to gains and losses rather than to final assets and in which probabilities are replaced by decision weights. The value function is normally concave for gains, commonly convex for losses, and is generally steeper for losses than for gains. Decision weights are generally lower than the corresponding probabilities, except in the range of low probabilities. Overweighting of low probabilities may contribute to the attractiveness of both insurance and gambling.
INTRODUCTION
Expected utility theory has dominated the analysis of decision making under risk. It has been generally accepted as a normative model of rational choice (Keeney & Raiffa, 1976), and widely applied as a descriptive model of economic behavior, e.g. (Friedman & Savage, 1948; Arrow, 1971). Thus, it is assumed that all reasonable people would wish to obey the axioms of the theory (von Neumann & Morgenstern, 1944; Savage, 1954), and that most people actually do, most of the time.
Economics can be distinguished from other social sciences by the belief that most (all?) behavior can be explained by assuming that agents have stable, well-defined preferences and make rational choices consistent with those preferences in markets that (eventually) clear. An empirical result qualifies as an anomaly if it is difficult to “rationalize,” or if implausible assumptions are necessary to explain it within the paradigm. This column presents a series of such anomalies. Readers are invited to suggest topics for future columns by sending a note with some reference to (or better yet copies of) the relevant research. Comments on anomalies printed here are also welcome. The address is Richard Thaler, c/o Journal of Economic Perspectives, Johnson Graduate School of Management, Malott Hall, Cornell University, Ithaca, NY 14853.
After this issue, the “Anomalies” column will no longer appear in every issue and instead will appear occasionally, when a pressing anomaly crosses Dick Thaler's desk. However, suggestions for new columns and comments on old ones are still welcome. Thaler would like to quash one rumor before it gets started, namely that he is cutting back because he has run out of anomalies. Au contraire, it is the dilemma of choosing which juicy anomaly to discuss that takes so much time.
ABSTRACT. Recent research has documented an ‘endowment effect’ whereby people become more attached to objects they receive than would be predicted from their prior desire to possess the object. In two experiments, we test whether people are aware of the effect - whether they realise that they will become attached to an object once they receive it. In both experiments, subjects without an object underestimated how much they would value the object when they received it.
Although the standard economic theory of consumer preference assumes fixed tastes, the idea that tastes change over time is not controversial. Numerous ‘habit formation’ models have been proposed which assume that current consumption influences future tastes (Duesenberry, 1949; Pollak, 1970; Stigler and Becker, 1977). These models have been applied to such diverse phenomena as the development of tastes for music and food, substance addiction (Becker and Murphy, 1988), and the surprisingly high rate of return on equities relative to fixed-income securities (e.g. Constantinedes, 1990).
Although it is more complicated to model than fixed tastes, there is nothing intrinsically irrational about habit formation as long as economic agents can predict without bias the effect of their current behaviour on their own future tastes. If people are aware of the effect of their actions on their own future tastes, they can adjust their consumption in a rational manner - e.g. by desisting from crack based on anticipation of future disutility from addiction.
ABSTRACT. Participants in contingent valuation surveys and jurors setting punitive damages in civil trials provide answers denominated in dollars. These answers are better understood as expressions of attitudes than as indications of economic preference. Well-established characteristics of attitudes and of the core process of affective valuation explain several robust features of dollar responses: high correlations with other measures of attractiveness or aversiveness, insensitivity to scope, preference reversals, and the high variability of dollar responses relative to other measures of the same attitude.
KEY WORDS preferences, attitudes, contingent valuation, psychology and economics, utility assessment
JEL Classification D00, H00
INTRODUCTION
Economics and psychology offer contrasting perspectives on the question of how people value things. The economic model of choice is concerned with a rational agent whose preferences obey a tight web of logical rules, formalized in consumer theory and in models of decision making under risk. The tradition of psychology, in contrast, is not congenial to the idea that a logic of rational choice can serve double duty as a model of actual decision behavior. Much behavioral research has been devoted to illustrations of choices that violate the logic of the economic model. The implied claim is that people do not have preferences, in the sense in which that term is used in economic theory (Fischhoff, 1991; Slovic, 1995; Payne, Bettman and Johnson, 1992). It is therefore fair to ask: If people do not have economic preferences, what do they have instead?
Indifference curves are normally taken to indicate corresponding trade-offs of goods A for B or B for A over the same interval: “the rate of commodity substitution at a point on an indifference curve is the same for movements in either direction” (James Henderson and Richard Quandt, 1971, p. 12). However, recent empirical findings of asymmetric evaluations of gains and losses imply that the presumed reversibility may not accurately reflect preferences, and that people commonly make choices that differ depending on the direction of proposed trades.
The evidence from a wide variety of tests is consistent with the suggestions of Daniel Kahneman and Amos Tversky (1979), and Richard Thaler (1980), that losses from a reference position are systematically valued far more than commensurate gains. The minimum compensation people demand to give up a good has been found to be several times larger than the maximum amount they are willing to pay for a commensurate entitlement. For example, when questioned about the possible destruction of a duck habitat, hunters responded that they would be willing to pay an average of $247 to prevent its loss but would demand $1044 to accept it (Judd Hammack and Gardner Brown, 1974). Respondents in another study demanded payments to accept various levels of visibility degradation that were from 5 to over 16 times higher than their valuations based on payment measures (Robert Rowe, Ralph d'Arge, and David Brookshire, 1980). Similar large differences in valuations of a wide variety of goods and entitlements have been reported in numerous survey studies.
ABSTRACT. Mental accounting is the set of cognitive operations used by individuals and households to organize, evaluate, and keep track of financial activities. Making use of research on this topic over the past decade, this paper summarizes the current state of our knowledge about how people engage in mental accounting activities. Three components of mental accounting receive the most attention. This first captures how outcomes are perceived and experienced, and how decisions are made and subsequently evaluated. The accounting system provides the inputs to be both ex ante and ex post cost-benefit analyses. A second component of mental accounting involves the assignment of activities to specific accounts. Both the sources and uses of funds are labeled in real as well as in mental accounting systems. Expenditures are grouped into categories (housing, food, etc.) and spending is sometimes constrained by implicit or explicit budgets. The third component of mental accounting concerns the frequency with which accounts are evaluated and ‘choice bracketing’. Accounts can be balanced daily, weekly, yearly, and so on, and can be defined narrowly or broadly. Each of the components of mental accounting violates the economic principle of fungibility. As a result, mental accounting influences choice, that is, it matters.
A former colleague of mine, a professor of finance, prides himself on being a thoroughly rational man. Long ago he adopted a clever strategy to deal with life's misfortunes. At the beginning of each year he establishes a target donation to the local United Way charity.
ABSTRACT. This paper considers the role of reasons and arguments in the making of decisions. It is proposed that, when faced with the need to choose, decision makers often seek and construct reasons in order to resolve the conflict and justify their choice, to themselves and to others. Experiments that explore and manipulate the role of reasons are reviewed, and other decision studies are interpreted from this perspective. The role of reasons in decision making is considered as it relates to uncertainty, conflict, context effects, and normative decision rules.
The result is that peculiar feeling of inward unrest known as indecision. Fortunately it is too familiar to need description, for to describe it would be impossible. As long as it lasts, with the various objects before the attention, we are said to deliberate; and when finally the original suggestion either prevails and makes the movement take place, or gets definitively quenched by its antagonists, we are said to decide… in favor of one or the other course. The reinforcing and inhibiting ideas meanwhile are termed the reasons or motives by which the decision is brought about.
ABSTRACT. Decisions under uncertainty depend not only on the degree of uncertainty but also on its source, as illustrated by Ellsberg's observation of ambiguity aversion. In this article we propose the comparative ignorance hypothesis, according to which ambiguity aversion is produced by a comparison with less ambiguous events or with more knowledgeable individuals. This hypothesis is supported in a series of studies showing that ambiguity aversion, present in a comparative context in which a person evaluates both clear and vague prospects, seems to disappear in a noncomparative context in which a person evaluates only one of these prospects in isolation.
INTRODUCTION
One of the fundamental problems of modern decision theory is the analysis of decisions under ignorance or ambiguity, where the probabilities of potential outcomes are neither specified in advance nor readily assessed on the basis of the available evidence. This issue was addressed by Knight [1921], who distinguished between measurable uncertainty or risk, which can be represented by precise probabilities, and unmeasurable uncertainty, which cannot. Furthermore, he suggested that entrepreneurs are compensated for bearing unmeasurable uncertainty as opposed to risk. Contemporaneously, Keynes [1921] distinguished between probability, representing the balance of evidence in favor of a particular proposition and the weight of evidence, representing the quantity of evidence supporting that balance. He then asked, “If two probabilities are equal in degree, ought we, in choosing our course of action, to prefer that one which is based on a greater body of knowledge?” [p. 313].
Economists pervasively explain widespread risk aversion by the realistic assumption that people generally have diminishing marginal utility of wealth. Indeed, diminishing marginal utility of wealth probably explains much of our aversion to large-scale financial risk: We dislike vast uncertainty in lifetime wealth because the marginal value of a dollar when we are poor is higher than when we are rich.
Within the expected-utility framework, the concavity of the utility-of-wealth function is not only sufficient to explain risk aversion - it is also necessary: Diminishing marginal utility of wealth is the sole explanation for risk aversion. Unfortunately, it is an utterly implausible explanation for appreciable risk aversion, except when the stakes are very large. Any utility-of-wealth function that does not predict absurdly severe risk aversion over very large stakes predicts negligible risk aversion over modest stakes.
Arrow (1971, p. 100) shows that an expected-utility maximizer with a differentiable utility function will always want to take a sufficiently small stake in any positive-expected-value bet. That is, expected-utility maximizers are arbitrarily close to risk neutral when stakes are arbitrarily small. Although most economists understand this formal limit result, fewer appreciate that the approximate risk-neutrality prediction holds not just for very small stakes but for quite sizable and economically important stakes as well. Diminishing marginal utility of wealth is not a plausible explanation of people's aversion to risk on the scale of $10, $100, $1,000, or even more.
ABSTRACT. We contrast the rational theory of choice in the form of expected utility theory with descriptive psychological analysis in the form of prospect theory, using problems involving the choice between political candidates and public referendum issues. The results showed that the assumptions underlying the classical theory of risky choice are systematically violated in the manner predicted by prospect theory. In particular, our respondents exhibited risk aversion in the domain of gains, risk seeking in the domain of losses, and a greater sensitivity to losses than to gains. This is consistent with the advantage of the incumbent under normal conditions and the potential advantage of the challenger in bad times. The results further show how a shift in the reference point could lead to reversals of preferences in the evaluation of political and economic options, contrary to the assumption of invariance. Finally, we contrast the normative and descriptive analyses of uncertainty in choice and address the rationality of voting.
The assumption of individual rationality plays a central role in the social sciences, especially in economics and political science. Indeed, it is commonly assumed that most if not all economic and political agents obey the maxims of consistency and coherence leading to the maximization of utility. This notion has been captured by several models that constitute the rational theory of choice, including the expected utility model for decision making under risk, the riskless theory of choice among commodity bundles, and the Bayesian theory for the updating of belief.
ABSTRACT. We discuss the cognitive and the psychophysical determinants of choice in risky and riskless contexts. The psychophysics of value induce risk aversion in the domain of gains and risk seeking in the domain of losses. The psychophysics of chance induce overweighting of sure things and of improbable events, relative to events of moderate probability. Decision problems can be described or framed in multiple ways that give rise to different preferences, contrary to the invariance criterion of rational choice. The process of mental accounting, in which people organize the outcomes of transactions, explains some anomalies of consumer behavior. In particular, the acceptability of an option can depend on whether a negative outcome is evaluated as a cost or as an uncompensated loss. The relation between decision values and experience values is discussed.
Making decisions is like speaking prose - people do it all the time, knowingly or unknowingly. It is hardly surprising, then, that the topic of decision making is shared by many disciplines, from mathematics and statistics, through economics and political science, to sociology and psychology. The study of decisions addresses both normative and descriptive questions. The normative analysis is concerned with the nature of rationality and the logic of decision making. The descriptive analysis, in contrast, is concerned with people's beliefs and preferences as they are, not as they should be. The tension between normative and descriptive considerations characterizes much of the study of judgment and choice.
ABSTRACT. Decision theory distinguishes between risky prospects, where the probabilities associated with the possible outcomes are assumed to be known, and uncertain prospects, where these probabilities are not assumed to be known. Studies of choice between risky prospects have suggested a nonlinear transformation of the probability scale that overweights low probabilities and underweights moderate and high probabilities. The present article extends this notion from risk to uncertainty by invoking the principle of bounded subadditivity: An event has greater impact when it turns impossibility into possibility, or possibility into certainty, than when it merely makes a possibility more or less likely. A series of studies provides support for this principle in decision under both risk and uncertainty and shows that people are less sensitive to uncertainty than to risk. Finally, the article discusses the relationship between probability judgments and decision weights and distinguishes relative sensitivity from ambiguity aversion.
Decisions are generally made without definite knowledge of their consequences. The decisions to invest in the stock market, to undergo a medical operation, or to go to court are generally made without knowing in advance whether the market will go up, the operation will be successful, or the court will decide in one's favor. Decision under uncertainty, therefore, calls for an evaluation of two attributes: the desirability of possible outcomes and their likelihood of occurrence. Indeed, much of the study of decision making is concerned with the assessment of these values and the manner in which they are - or should be - combined.
ABSTRACT. Preference can be inferred from direct choice between options or from a matching procedure in which the decision maker adjusts one option to match another. Studies of preferences between two-dimensional options (e.g., public policies, job applicants, benefit plans) show that the more prominent dimension looms larger in choice than in matching. Thus, choice is more lexicographic than matching. This finding is viewed as an instance of a general principle of compatibility: The weighting of inputs is enhanced by their compatibility with the output. To account for such effects, we develop a hierarchy of models in which the trade-off between attributes is contingent on the nature of the response. The simplest theory of this type, called the contingent weighting model, is applied to the analysis of various compatibility effects, including the choice-matching discrepancy and the preference-reversal phenomenon. These results raise both conceptual and practical questions concerning the nature, the meaning and the assessment of preference.
The relation of preference between acts or options is the key element of decision theory that provides the basis for the measurement of utility or value. In axiomatic treatments of decision theory, the concept of preference appears as an abstract relation that is given an empirical interpretation through specific methods of elicitation, such as choice and matching. In choice the decision maker selects an option from an offered set of two or more alternatives. In matching the decision maker is required to set the value of some variable in order to achieve an equivalence between options (e.g., what chance to win $750 is as attractive as 1 chance in 10 to win $2,500?).