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ABSTRACT. We develop a new version of prospect theory that employs cumulative rather than separable decision weights and extends the theory in several respects. This version, called cumulative prospect theory, applies to uncertain as well as to risky prospects with any number of outcomes, and it allows different weighting functions for gains and for losses. Two principles, diminishing sensitivity and loss aversion, are invoked to explain the characteristic curvature of the value function and the weighting functions. A review of the experimental evidence and the results of a new experiment confirm a distinctive fourfold pattern of risk attitudes: risk aversion for gains and risk seeking for losses of high probability; risk seeking for gains and risk aversion for losses of low probability.
KEYWORDS cumulative prospect theory
Expected utility theory reigned for several decades as the dominant normative and descriptive model of decision making under uncertainty, but it has come under serious question in recent years. There is now general agreement that the theory does not provide an adequate description of individual choice: a substantial body of evidence shows that decision makers systematically violate its basic tenets. Many alternative models have been proposed in response to this empirical challenge (for reviews, see Camerer, 1989; Fishburn, 1988; Machina, 1987).
ABSTRACT. I test the disposition effect, the tendency of investors to hold losing investments too long and sell winning investments too soon, by analyzing trading records for 10,000 accounts at a large discount brokerage house. These investors demonstrate a strong preference for realizing winners rather than losers. Their behavior does not appear to be motivated by a desire to rebalance portfolios, or to avoid the higher trading costs of low priced stocks. Nor is it justified by subsequent portfolio performance. For taxable investments, it is suboptimal and leads to lower after-tax returns. Tax-motivated selling is most evident in December.
The tendency to hold losers too long and sell winners too soon has been labeled the disposition effect by Shefrin and Statman (1985). For taxable investments the disposition effect predicts that people will behave quite differently than they would if they paid attention to tax consequences. To test the disposition effect, I obtained the trading records from 1987 through 1993 for 10,000 accounts at a large discount brokerage house. An analysis of these records shows that, overall, investors realize their gains more readily than their losses. The analysis also indicates that many investors engage in taxmotivated selling, especially in December. Alternative explanations have been proposed for why investors might realize their profitable investments while retaining their losing investments.
ABSTRACT. Decision makers have a strong tendency to consider problems as unique. They isolate the current choice from future opportunities and neglect the statistics of the past in evaluating current plans. Overly cautious attitudes to risk result from a failure to appreciate the effects of statistical aggregation in mitigating relative risk. Overly optimistic forecasts result from the adoption of an inside view of the problem, which anchors predictions on plans and scenarios. The conflicting biases are documented in psychological research. Possible implications for decision making in organizations are examined.
KEY WORDS decision making; risk; forecasting; managerial cognition
The thesis of this essay is that decision makers are excessively prone to treat problems as unique, neglecting both the statistics of the past and the multiple opportunities of the future. In part as a result, they are susceptible to two biases, which we label isolation errors: their forecasts of future outcomes are often anchored on plans and scenarios of success rather than on past results and are therefore overly optimistic; their evaluations of single risky prospects neglect the possibilities of pooling risks and are therefore overly timid. We argue that the balance of the two isolation errors affects the risk-taking propensities of individuals and organizations.
The cognitive analysis of risk taking that we sketch differs from the standard rational model of economics and also from managers' views of their own activities. The rational model describes business decisions as choices among gambles with financial outcomes, and assumes that managers' judgments of the odds are Bayesian, and that their choices maximize expected utility.
ABSTRACT. In contrast to logical criteria of rationality, which can be assessed entirely by reference to the system of preferences, substantive criteria of rational choice refer to an independent evaluation of the outcomes of decisions. One of these substantive criteria is the experienced hedonic utility of outcomes. Research indicates that people are myopic in their decisions, may lack skill in predicting their future tastes, and can be led to erroneous choices by fallible memory and incorrect evaluation of past experiences. Theoretical and practical implications of these challenges to the assumption of economic rationality are discussed. (JEL: A 00)
INTRODUCTION
The assumption that agents are rational is central to much theory in the social sciences. Its role is particularly obvious in economic analysis, where it supports the useful corollary that no significant opportunity will remain unexploited. In the domain of social policy, the rationality assumption supports the position that it is unnecessary to protect people against the consequences of their choices. The status of this assumption is therefore a matter of considerable interest. This article will argue for an enriched definition of rationality that considers the actual outcomes of decisions, and will present evidence that challenges the rationality assumption in new ways.
The criteria for using the terms “rational” or “irrational” in non-technical discourse are substantive: one asks whether beliefs are grossly out of kilter with available evidence, and whether decisions serve or damage the agent's interests.
ABSTRACT. We develop a belief-based account of decision under uncertainty. This model predicts decisions under uncertainty from (i) judgments of probability, which are assumed to satisfy support theory; and (ii) decisions under risk, which are assumed to satisfy prospect theory. In two experiments, subjects evaluated uncertain prospects and assessed the probability of the respective events. Study 1 involved the 1995 professional basketball playoffs; Study 2 involved the movement of economic indicators in a simulated economy. The results of both studies are consistent with the belief-based account, but violate the partition inequality implied by the classical theory of decision under uncertainty.
KEY WORDS decision making; risk; uncertainty; expected utility; prospect theory; support theory; decision weights; judgment; probability
INTRODUCTION
It seems obvious that the decisions to invest in the stock market, undergo a medical treatment, or settle out of court depend on the strength of people's beliefs that the market will go up, that the treatment will be successful, or that the court will decide in their favor. It is less obvious how to elicit and measure such beliefs. The classical theory of decision under uncertainty derives beliefs about the likelihood of uncertain events from people's choices between prospects whose consequences are contingent on these events. This approach, first advanced by Ramsey (1931), gives rise to an elegant axiomatic theory that yields simultaneous measurement of utility and subjective probability, thereby bypassing the thorny problem of how to interpret direct expressions of belief.
In a recent educational television program, an amnesic patient was asked about his childhood and high-school experiences. Verbally fluent, he was able to converse about daily events but could not remember any details about his past. Finally, the interviewer asked him how happy he was. The patient pondered this question for a few seconds before answering, “I don't know.”
As Tom Schelling observed, “We consume past events that we can bring up from memory” (1984, p. 344). Thus, the memory of the past is an essential element of present well-being. As our opening anecdote suggests, the present alone may not provide enough information to define happiness without reference to the past. Yet memories have a complex effect on our current sense of well-being. They represent a direct source of happiness or unhappiness, and they also affect the criteria by which current events are evaluated. In other words, a salient hedonic event (positive or negative) influences later evaluations of well-being in two ways: through an endowment effect and a contrast effect. The endowment effect of an event represents its direct contribution to one's happiness or satisfaction. Good news and positive experiences enrich our lives and make us happier; bad news and hard times diminish our well-being. Events also exercise an indirect contrast effect on the evaluation of subsequent events. A positive experience makes us happy, but it also renders similar experiences less exciting. A negative experience makes us unhappy, but it also helps us appreciate subsequent experiences that are less bad. The hedonic impact of an event, we suggest, reflects a balance of its endowment1 and contrast effects. This chapter explores some descriptive and prescriptive implications of this notion.
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.