In a large-scale field study of marathon runners, we test whether goals act as reference points in shaping the valuation of outcomes. Theories of reference-dependent preferences, such as Prospect Theory, imply that outcomes that are just below or just above a reference point are evaluated differently. Consistent with the Prospect Theory value function, we find that satisfaction as a function of relative performance (the difference between a runner’s finishing time goal and her actual finishing time) exhibits loss aversion and diminishing sensitivity in both predictions of and actual experienced satisfaction. However, in contrast to Prospect Theory, we observe that loss aversion is partially driven by a discontinuity or jump at the reference point. In addition, we find that a runner’s time goal as well as their previous marathon times simultaneously impact runner satisfaction, providing support for the impact of multiple reference points on satisfaction.
Theories of reference-dependent preferences propose that individuals evaluate outcomes as gains or losses relative to a neutral reference point. We test for reference dependence in a large dataset of marathon finishing times (n= 9,789,093). Models of reference-dependent preferences such as prospect theory predict bunching of finishing times at reference points. We provide visual and statistical evidence that round numbers (e.g., a four-hour marathon) serve as reference points in this environment and as a result produce significant bunching of performance at these round numbers. Bunching is driven by planning and adjustments in effort provision near the finish line and cannot be explained by explicit rewards (e.g., qualifying for the Boston Marathon), peer effects, or institutional features (e.g., pace setters).
We investigate how choices for uncertain gain and loss prospects are affected by the decision maker's perceived level of knowledge about the underlying domain of uncertainty. Specically, we test whether Heath and Tversky's (J Risk Uncertain 4:5–28, 1991) competence hypothesis extends from gains to losses. We predict that the commonly-observed preference for high knowledge over low knowledge prospects for gains reverses for losses. We employ an empirical setup in which participants make hypothetical choices between gain or loss prospects in which the outcome depends on whether a high knowledge or a low knowledge event occurs. We infer decision weighting functions for high and low knowledge events from choices using a representative agent preference model. For decisions involving gains, we replicate the results of Kilka and Weber (Manage Sci 47:1712–1726, 2001), finding that decision makers are more attracted to choices that they feel more knowledgeable about. However, for decisions involving losses, we find limited support for our extension of the competence effect.
Why do well-known ideas, practices, and people maintain their cultural prominence in the presence of equally-good or better alternatives? This article suggests that a social psychological process whereby people seek to establish common ground with their conversation partners causes familiar elements of culture to increase in prominence, independent of actual performance or quality. Two studies tested this common ground hypothesis in the context of professional baseball, showing that familiarity predicted the cultural prominence of baseball players better than performance, even in this domain with clear performance metrics. Regardless of their performance, familiar players who represented common ground were more often discussed in a dyadic experiment (Study 1) and in natural discussions on the internet (Study 2). Moreover, these conversations led to further prominence: conversational mentions mediated the link between media-driven familiarity and cultural prominence (All-Star votes) (Study 2). Implications for research on the psychological foundations of culture are discussed.
Three experiments test whether specific, challenging goals increase risk taking. We propose that goals serve as reference points, creating a region of perceived losses for outcomes below a goal (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). According to the Prospect Theory value function, decision makers become more risk seeking in the domain of losses. In all three experiments we compared a “do your best” condition with a “specific, challenging goal” condition. The goal condition consistently increased risky behavior in both negotiation and decision making tasks. The discussion considers how goals influence expectations, strategy choice, and unethical behavior.
We investigate a basic premise of prospect theory, that the valuation of gains and losses is separable. In prospect theory, gain-loss separability implies that a mixed gamble is valued by summing the valuations of the gain and loss portions of that gamble. Two experimental studies demonstrate a systematic violation of the double matching axiom, an axiom that is necessary for gain-loss separability. We document a reversal between preferences for mixed gambles and the associated gain and loss gambles—mixed gamble A is preferred to mixed gamble B, but the gain and loss portions of B are preferred to the gain and loss portions of A. The observed choice patterns are consistent with a process in which individuals are less sensitive to probability differences when choosing among mixed gambles than when choosing among either gain or loss gambles.
Three studies show that negotiators consistently underestimate the size of the bargaining zone in distributive negotiations (the small-pie bias) and, by implication, overestimate the share of the surplus they claim (the large-slice bias). The authors explain the results by asymmetric disconfirmation: Negotiators with initial estimates of their counterpart's reservation price that are “inside” the bargaining zone tend to behave consistently with these estimates, which become self-fulfilling, whereas negotiators with initial “outside” estimates revise their perceptions in the face of strong disconfirming evidence. Asymmetric disconfirmation can produce a population-level bias, even when initial perceptions are accurate on average. The authors suggest that asymmetric disconfirmation has implications for confirmation bias and self-fulfilling-prophecy research in social perception.
Expected utility theory, prospect theory, and most other models of risky choice are based on the fundamental premise that individuals choose among risky prospects by balancing the value of the possible consequences. These models, therefore, require that the value of a risky prospect lie between the value of that prospect’s highest and lowest outcome. Although this requirement seems essential for any theory of risky decision making, we document a violation of this condition in which individuals value a risky prospect less than its worst possible realization. This demonstration, which we term the uncertainty effect, draws from more than 1000 experimental participants, and includes hypothetical and real pricing and choice tasks, as well as field experiments in real markets with financial incentives. Our results suggest that there are choice situations in which decision makers discount lotteries for uncertainty in a manner that cannot be accommodated by standard models of risky choice.
Many decision makers operate in dynamic environments in which markets, competitors, and technology change regularly. The ability to detect and respond to these regime shifts is critical for economic success. We conduct three experiments to test how effective individuals are at detecting such regime shifts. Specifically, we investigate when individuals are most likely to underreact to change and when they are most likely to overreact to it. We develop a system-neglect hypothesis: Individuals react primarily to the signals they observe and secondarily to the environmental system that produced the signal. The experiments, two involving probability estimation and one involving prediction, reveal a behavioral pattern consistent with our system-neglect hypothesis: Underreaction is most common in unstable environments with precise signals, and overreaction is most common in stable environments with noisy signals. We test this pattern formally in a statistical comparison of the Bayesian model with a parametric specification of the system-neglect model.
The two versions of prospect theory, original prospect theory (OPT; Kahneman and Tversky, 1979) and cumulative prospect theory (CPT;Tversky and Kahneman, 1992), use different composition rules to combine the value function and the probability weighting function and hence value gambles with two or more non-zero outcomes differently. Previous tests of OPT and CPT have yielded mixed results, with some investigations supporting OPT and some supporting CPT. We extend the probability tradeoff consistency axiom used in Abdellaoui (2002) for CPT to OPT, and develop a critical test of the two prospect theories based on their respective probability tradeoff consistency conditions. An empirical investigation of the critical test shows that choices are consistent with OPT, but not CPT, for gambles that do not involve a certainty effect, and consistent with both CPT and OPT for gambles that do involve a certainty effect, provided that an editing operation is invoked for OPT.
Narasimhan, Chakravarthi, Chuan He, Eric Anderson, Lyle Brenner, Preyas Desai, Dmitri Kuksov, Paul Messinger, Sridhar Moorthy, Joseph Nunes, Yuval Rottenstreich, Rick Staelin, George Wu, and Z. John Zhang (2005). "Incorporating Behavioral Anomalies in Strategic Models", Marketing Letters, 16, 361-373.
Behavioral decision researchers have documented number of anomalies that seem to run counter to established theories of consumer behavior from microeconomics that are often at the core of analytical models in marketing. A natural question therefore is how equilibrium behavior and strategies would change if models were to incorporate these anomalies in a consistent way. In this paper we identify several important and generalizable anomalies that modelers may want to incorporate in their models. We briefly discuss each phenomenon, identify a key unresolved issue and outline a research agenda to be pursued.
Wu, George, Chip Heath and Marc Knez (2003). "A timidity error in evaluations: Evaluators judge others to be too risk averse", Organizational Behavior and Human Decision Processes 90, 50-62.
Managers often lament that their employees are risk averse and do not take sufficient risks. While in some instances employees might in fact be too risk averse, we explore situations in which managers may incorrectly judge their employees to be overly risk averse or timid. In two studies, we find evidence of a timidity error in evaluations-evaluators judge target decision makers to be risk averse, even when the targets are actually employing a more thoughtful approach (as measured by better calibration) than their evaluators.
Wathieu, Luc, Lyle Brenner, Ziv Carmon, Amitava Chattopadhyay, Aimee Drolet, John Gourville, A.V. Muthukrishnan, Nathan Novemsky, Rebecca Ratner, Klaus Wertenbroch, and George Wu (2002). "Consumer Control and Empowerment: A Primer", Marketing Letters 13, 297-305.
This paper introduces consumer empowerment as a promising research area. Going beyond lay wisdom that more control is always better, we outline several hypotheses concerning (a) the factors that influence the perception of empowerment, and (b) the consequences of greater control and the subjective experience of empowerment on consumer satisfaction and confidence.
Empirical studies have shown that decision makers do not usually treat probabilities linearly. Instead, people tend to overweight small probabilities and underweight large probabilities. One way to model such distortions in decision making under risk is through a probability weighting function. We present a nonparametric estimation procedure for assessing the probability weighting function and value function at the level of the individual subject. The evidence in the domain of gains supports a two-parameter weighting function, where each parameter is given a psychological interpretation: one parameter measures how the decision maker discriminates probabilities, and the other parameter measures how attractive the decision maker views gambling. These findings are consistent with a growing body of empirical and theoretical work attempting to establish a psychological rationale for the probability weighting function.
Heath, Chip, Richard P. Larrick, and George Wu (1999). "Goals as Reference Points", Cognitive Psychology 38, 79-109.
We argue that goals serve as reference points and alter outcomes in a manner consistent with the value function of Prospect Theory (Kahneman & Tversky, 1979; Tversky & Kahneman, 1992). We present new evidence that goals inherit the properties of the value function-not only a reference point, but also loss aversion and diminishing sensitivity. We also use the value function to explain previous empirical results in the goal literature on affect, effort, persistence, and performance.
In most real-world decisions, consequences are tied explicitly to the outcome of events. Previous studies of decision making under uncertainty have indicated that the psychological weight attached to an event, called a decision weight, usually differs from the probability of that event. We investigate two sources of nonlinearity of decision weights: subadditivity of probability judgments, and the overweighting of small probabilities and underweighting of medium and large probabilities. These two sources of nonlinearity are combined into a two-stage model of choice under uncertainty. In the first stage, events are taken into subjective probability judgments, and the second stage takes probability judgments into decision weights. We then characterize the curvature of the decision weights by extending a condition employed by Wu & Gonzalez (1996) in the domain of risk to the domain of uncertainty and show that the nonlinearity of decision weights can be decomposed into subadditivity of probability judgments and the curvature of the probability weighting function. Empirical tests support the proposed two-stage model and indicate that decision weights are concave then convex. More specifically, our results lend support for a new property of subjective probability judgments, interior additivity (subadditive at the boundaries, but additive away from the boundaries), and show that the probability weighting function is inverse S-shaped as in Wu & Gonzalez (1996).
Wu, George and Richard Gonzalez (1998). "Common Consequence Effects in Decision Making under Risk", Journal of Risk and Uncertainty 16, 115-139.
We generalize the Allais common consequence effect by describing three common consequence effect conditions and characterizing their implications for the probability weighting function in rank-dependent expected utility. The three conditions – horizontal, vertical, and diagonal shifts within the probability triangle – are necessary and sufficient for different curvature properties of the probability weighting function. The first two conditions, shifts in probability mass from the lowest to middle outcomes and middle to highest outcomes respectively, are alternative conditions for concavity and convexity of the weighting function. The third condition, decreasing Pratt-Arrow absolute concavity, is consistent with recently proposed weighting functions. The three conditions collectively characterize where indifference curves fan out and where they fan in. The common consequence conditions indicate that for nonlinear weighting functions in the context of rank-dependent expected utility, there must exist a region where indifference curves fan out in one direction and fan in the other direction.
Wu, George (1994). "An Empirical Test of Ordinal Independence," Journal of Risk and Uncertainty 9, 39-60.
When individuals choose among risky alternatives, the psychological weight attached to an outcome may not correspond to the probability of that outcome. In rank-dependent utility theories, including prospect theory, probability weighting functions permit probabilities to be weighted nonlinearly. Previous empirical studies of the weighting function have suggested an inverse S-shaped function, first concave and then convex. However, these studies suffer from a methodological shortcoming: estimation procedures have required assumptions about the functional form of the value and/or weighting functions. We propose two preference conditions that are necessary and sufficient for concavity and convexity of the weighting function. Empirical tests of these conditions are independent of the form of the value function. We test these conditions using preference "ladders": a series of questions that differ only by a common consequence. The concavity-convexity ladders validate previous findings of an S-shaped weighting function, concave up to p < .40, and convex beyond that probability. The tests also show significant nonlinearity away from the boundaries, 0 and 1. Finally, we fit the ladder data with weighting functions proposed by Tversky & Kahneman (1992) and Prelec (1995).
In this article, we test Green and Jullien's (1988) Ordinal Independence (OI) Axiom, an axiom necessary for any rank-dependent expected utility (RDEU) model, including Cumulative Prospect Theory (Tversky and Kahneman, 1992). We observe systematic violations of OI (some within-subject violation rates of over 50%). These patterns of choice cannot be explained by any RDEU theory alone. We suggest that subjects are employing an editing operation prior to evaluation: if an outcome-probability pair is common to both gambles, it is cancelled when the commonality is transparent; otherwise, it is not cancelled. We interpret the results with respect to both original and cumulative prospect theory and the known empirical properties of the weighting function.
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Unpublished Papers and Manuscripts
Li, Ye, Cade Massey, and George Wu (2014). "Learning to Detect Change"
Across a wide range of personal and professional domains, people need to accurately detect whether their environment has changed. Previous research has documented a systematic pattern of over- and under-reaction to signals of change due to system neglect, or the tendency to overweight signals and underweight the system producing the signals. We investigate whether and when experience improves the ability to detect change and reduces system neglect. We find that although the system-neglect pattern is not completely attenuated by experience, average performance did improve with experience. However, the degree of learning varied substantially across the range of decision environments we investigated: Participants showed substantial improvement in environments that provide less fickle feedback (i.e., less likely to produce false alarms) and that have lower entropy (i.e., have more information value). These characteristics of the decision environment explain a significant portion of the variance in learning between conditions and have implications for understanding learning in other dynamic tasks.
Wu, George, Chip Heath, and Richard Larrick (2004). "A prospect theory model of goal behavior"
Goals have a powerful effect on performance: higher goals typically produce better performance. Previous research has proposed three key mechanisms to explain these results: effort, persistence, and attention. We present a formal model that relates these mechanisms to a single underlying process. Our model assumes that goals divide performance into two regions, gains and losses, and that the resulting gains and losses are coded according to a prospect theory value function (Kahneman & Tversky, 1979). This simple model explains the stylized findings in the goal setting literature, while also offering several new testable predictions.
Gonzalez, Richard and George Wu (2003). "Composition Rules in Original and Cumulative Prospect Theory"
Original and cumulative prospect theory differ in the composition rule used to combine the probability weighting function and the value function. We test these composition rules by estimating prospect theory's weighting and value function using two-outcome cash equivalents, a domain where original and cumulative prospect theory coincide. We apply these estimates to three-outcome cash equivalents, a domain where the composition rules of the two theories differ. We find systematic under-prediction for cumulative prospect theory and systematic over-prediction for original prospect theory. We use these findings to motivate new areas for theoretical and empirical investigation.
Shu, Suzanne and George Wu (2003). "Belief Bracketing: Can Partitioning Information Change Consumer Judgments?"
Firms often choose whether to present information in narrow or broad brackets. For example, a firm may provide financial performance in daily, weekly, or monthly formats. What influence does this bracketing have on consumer judgments? We propose that when individuals form beliefs about an underlying process based on bracketed information, the information is first evaluated based on its representativeness to the hypothesis under consideration, and then integrated into the overall judgment using a process that shows strong primacy and recency effects. Since bracketing affects both the representativeness-based coding step and the integration step, the final judgment will be affected by the size of the brackets. This is tested and confirmed in a series of five studies, using a variety of measures and contexts (investment categorization, restaurant rating, and probabilistic judgment). Although these studies vary in the use of memory, the frequency of judgment, and the type of judgment, the results of all five studies provide support for the existence of belief bracketing effects. The overall finding is that judgments are more extreme for information delivered in broad brackets, as our model predicts. We also find bracketing effects for behavioral intentions and for accuracy.
Wu, George and Richard Gonzalez (1999). "Dominance Violations and Event Splitting in Decision under Uncertainty"
A standard requirement of rationality is that preferences obey stochastic dominance. In this paper, we investigate a new variety of dominance violation from the domain of uncertainty. We find that subjects systematically value a packed prospect, $x if one of two mutually exclusive events E1 or E2 obtains, less than an unpacked and dominated prospect, $x if E1 obtains, and $x-e if E2 obtains. We account for these violations in terms of subadditivity of probability judgments (Tversky and Koehler, 1995): unpacking an event into constituent components increases the total probability assigned to that event. We discuss the implications of these dominance violations for compositions rules in prospect theory.
Wu, George (1999). "Temporal Risk and Probability Weights: A Descriptive Model of Delayed Resolution of Uncertainty"
Many meaningful decision problems are choices among gambles with delayed resolution of uncertainty (DRU). Notably, students of decision making have concentrated their attention largely on gambles with instantaneously resolved uncertainty. A descriptive theory is proposed for evaluating gambles with DRU such that period gambles (i.e., gambles resolved at the same time) are evaluated by cumulative prospect theory (Tversky and Kahneman, 1992). In this context, the probability weighting function can depend on the timing of uncertainty resolution and thus captures both attitudes toward risk and preferences for early or delayed resolution of uncertainty. Stochastic stationarity conditions are used to relate the period weighting functions. It is argued that a second-order stochastic stationarity condition adapted from axiomatizations of hyperbolic discounting will produce an analogous property of hyperbolic probability discounting. The model makes some sharp predictions for decision behavior in delayed resolution settings, most notably preferences for delayed resolution for small probabilities of gains and most losses. In addition, this model may provide some insight into the origins of the non-linearities of the prospect theory probability weighting function.