Loss Averse Behavior

A behavioral condition of loss aversion is proposed and tested. Forty-nine students participated in experiments on binary choices among lotteries involving small scale real gains and losses. At the aggregate level, a significant proportion of the choices are in the direction predicted by loss aversion. Individuals can be classified as loss averse (28 participants), gain seeking (12), and unclassified (9). A comparison with risk behavior for binary choices on lotteries involving only gains shows that risk attitudes vary across these domains of lotteries. A gender effect is also observed: proportionally more women are loss averse. In contrast to the predictions of comonotonic independence, the size of common outcomes has systematic influence on choice behavior. JEL Classification: D81, C91     

What is Loss Aversion?

A behavioral definition of loss aversion is proposed and its implications for original and cumulative prospect theory are analyzed. Original prospect theory is in agreement with the new loss aversion condition, and there utility is capturing all effects of loss aversion. In cumulative prospect theory loss aversion is captured by both the weighting functions and the utility function. Further, some restrictions apply for the weighting functions involved in the latter model.We are indebted to Michèle Cohen and Peter Wakker for helpful comments. The suggestions of an anonymous referee have improved the presentation of the paper.     

Estimating individual and group preference functionals using experimental data

In this paper, the empirical performance of several preference functionals is assessed using individual and group experimental data. We investigate if there is a risky choice theory that fits group decisions better than alternative theories, and if there are significant differences between individual and group choices. Experimental findings reported in this paper provide answers to both of those questions showing that expected utility gains a “winning” position over higher-level functionals (we considered disappoint aversion and two variants of rank-dependent utility) when risky choices are undertaken by individuals as well as by small groups. However, in the group experiment, alternatives (and, most notably, disappoint aversion) improve their relative performance, a fact that hints at the existence of differences between individual and group choices. We interpreted this result as evidence that feelings-like disappointment aversion become stronger in group decision.     

Loss Aversion and Bargaining

We consider bargaining situations where two players evaluate outcomes with reference-dependent utility functions, analyzing the effect of differing levels of loss aversion on bargaining outcomes. We find that as with risk aversion, increasing loss aversion for a player leads to worse outcomes for that player in bargaining situations. An extension of Nash's axioms is used to define a solution for bargaining problems with exogenous reference points. Using this solution concept we endogenize the reference points into the model and find a unique solution giving reference points and outcomes that satisfy two reasonable properties, which we predict would be observed in a steady state. The resulting solution also emerges in two other approaches, a strategic (non-cooperative) approach using Rubinstein's (1982) alternating offers model and a dynamic approach in which we find that even under weak assumptions, outcomes and reference points converge to the steady state solution from any non-equilibrium state.     

Risk behavior for gain,loss, and mixed prospects

This study extends experimental tests of (cumulative) prospect theory (PT) over prospects with more than three outcomes and tests second-order stochastic dominance principles (Levy and Levy, Management Science 48:1334–1349, 2002; Baucells and Heukamp, Management Science 52:1409–1423, 2006). It considers choice behavior of people facing prospects of three different types: gain prospects (losing is not possible), loss prospects (gaining is not possible), and mixed prospects (both gaining and losing are possible). The data supports the distinction of risk behavior into these three categories of prospects, Further, probability weighting and diminishing sensitivity of utility as predicted by PT are observed. Loss aversion is, however, less pronounced, except for choices where one prospect is degenerate. The data suggests that the probability of losing may be relevant for loss aversion.     

On probabilities and loss aversion

This paper reviews the most common approaches that have been adopted to analyze and describe loss aversion under prospect theory. Subsequently, it is argued that loss aversion is a property of observable choice behavior and two new definitions of loss averse behavior are advocated. Under prospect theory, the new properties hold if the commonly used utility based measures of loss aversion are corrected by a probability based measure of loss aversion and their product exceeds 1. It is shown that prominent parametric families of weighting functions, while successful in accommodating empirical findings on probabilistic risk attitudes, may not fit well with the theoretical implications of the new loss averse behavior conditions.     

Effects of Outcome and Probabilistic Ambiguity on Managerial Choices

Information ambiguity is prevalent in organizations and likely influences management decisions. This study examines, given imprecise probabilities and outcomes, how managers make choices when they are provided with single-figure benchmarks. Seventy-nine MBA students completed two experiments. We found that, in a decision framed as a decision under certainty involving an ambiguous outcome, the majority of the subjects were ambiguity prone in the loss condition and switched to ambiguity aversion in the gain condition. However, in the presence of probabilistic ambiguity in a decision under risk, this expected switching pattern was shown only when the difference in riskiness between the two choice options (in the loss condition) was perceived to be relatively small. In a companion study, we used a written protocol approach to identify factors that affect decision makers' investment choices when faced with ambiguous outcomes. Protocols frequently mentioned that the ambiguous outcome option was risky, even in the case which was framed as a decision under certainty in the problem statement. In a decision under risk with ambiguous outcomes, the combination of probabilistic risk and outcome ambiguity was seen as even more risky.     

The “bomb” risk elicitation task

This paper presents the Bomb Risk Elicitation Task (BRET), an intuitive procedure aimed at measuring risk attitudes. Subjects decide how many boxes to collect out of 100, one of which contains a bomb. Earnings increase linearly with the number of boxes accumulated but are zero if the bomb is also collected. The BRET requires minimal numeracy skills, avoids truncation of the data, allows the precise estimation of both risk aversion and risk seeking, and is not affected by the degree of loss aversion or by violations of the Reduction Axiom. We validate the BRET, test its robustness in a large-scale experiment, and compare it to three popular risk elicitation tasks. Choices react significantly only to increased stakes, and are sensible to wealth effects. Our experiment rationalizes the gender gap that often characterizes choices under uncertainty by means of a higher loss rather than risk aversion.     

Accommodating stake effects under prospect theory

This paper investigates how letting people predict others’ choices under risk affects subsequent own choices. We find an improvement of strong rationality (risk neutrality) for losses in own choices, but no such improvement for gains. There is no improvement of weak rationality (avoiding preference reversals). Overall, risk aversion in own choices increases. Conversely, for the effects of own choices on predicting for others, the risk aversion predicted in others’ choices is reduced if preceded by own choices, for both gains and losses. Remarkably, we find a new probability matching paradox at the group level. Relative to preceding studies on the effects of predicting others’ choices, we added real incentives, pure framing effects, and simplicity of stimuli. Our stimuli were maximally targeted towards our research questions.     

Aggregation theorems and multidimensional stochastic choice models

In many choice situations, the options are multidimensional. Numerous probabilistic models have been developed for such choices between multidimensional options and for the parallel choices determined by one or more components of such options. In this paper, it is assumed that a functional relation exists between the choice probabilities over the multidimensional options and the choice probabilities over the associated component unidimensional options. It is shown that if that function satisfies a marginalization property then it is essentially an arithmetic mean, and if the function satisfies a likelihood independence property then it is a weighted geometric mean. The results are related to those on the combination of expert opinion, and various probabilistic models in the choice literature are shown to have the geometric mean form.     

Testing between alternative models of choice under uncertainty: Some initial results

Experiments have identified a number of well-known violations of expected utility theory, giving rise to alternative models of choice under uncertainty, all of which are able to explain these violations. In this article, predictions of several prominent rival formulations are examined. No single alternative consistently organizes choices. Among the more important inconsistencies, we identify conditions generating systematic fanning in of indifference curves in the unit probability triangle, and find risk-loving over a number of gambles with all positive payoffs, in cases where prospect theory predicts risk aversion.     

Survival through the Allais paradox

This paper investigates the allegation that behavior such as the Allais Paradox reduces the probability of survival. Examples are demonstrated where maximizing probability of survival in two choice situations imply a set of choices that add up to the Allais Paradox.     

Subjective Probability Weighting and the Discovered Preference Hypothesis

Numerous studies have convincingly shown that prospect theory can better describe risky choice behavior than the classical expected utility model because it makes the plausible assumption that risk aversion is driven not only by the degree of sensitivity toward outcomes, but also by the degree of sensitivity toward probabilities. This article presents the results of an experiment aimed at testing whether agents become more sensitive toward probabilities over time when they repeatedly face similar decisions, receive feedback on the consequences of their decisions, and are given ample incentives to reflect on their decisions, as predicted by Plott’s Discovered Preference Hypothesis (DPH). The results of a laboratory experiment with N = 62 participants support this hypothesis. The elicited subjective probability weighting function converges significantly toward linearity when respondents are asked to make repeated choices and are given direct feedback after each choice. Such convergence to linearity is absent in an experimental treatment where respondents are asked to make repeated choices but do not experience the resolution of risk directly after each choice, as predicted by the DPH. I thank Peter P. Wakker for useful comments and suggestions.     

Choice Bracketing

When making many choices, a person can broadly bracket them by assessing the consequences of all of them taken together, or narrowly bracket them by making each choice in isolation. We integrate research conducted in a wide range of decision contexts which shows that choice bracketing is an important determinant of behavior. Because broad bracketing allows people to take into account all the consequences of their actions, it generally leads to choices that yield higher utility. The evidence that we review, however, shows that people often fail to bracket broadly when it would be feasible for them to do so. In addition to documenting the diverse effects of bracketing, we also discuss factors that determine whether people bracket narrowly or broadly. We conclude with a discussion of normative aspects of bracketing and argue that there are some situations in which narrower bracketing results in superior decision making.     

Ambiguity framed

In his exposition of subjective expected utility theory, Savage (1954) proposed that the Allais paradox could be reduced if it were recast into a format which made the appeal of the independence axiom of expected utility theory more transparent. Recent studies consistently find support for this prediction. We consider a salience-based choice model which explains this frame-dependence of the Allais paradox. We then derive the novel prediction that the presentation format responsible for reductions in Allais-style violations of expected utility theory will also reduce Ellsberg-style violations of subjective expected utility theory. This format makes the appeal of Savage’s “sure thing principle” more transparent. We design an experiment to test this prediction and find strong support for such frame-dependence of ambiguity aversion in Ellsberg-style choices. In particular, we observe markedly less ambiguity-averse behavior in Savage’s matrix format than in a more standard “prospect” format. This finding poses a new challenge for the leading models of ambiguity aversion.     

School Choice in London and Paris – A Comparison of Middle‐class Strategies

Education is one major public service in which quasi‐markets and other choice‐based mechanisms are now established methods of delivery. The types of school people choose, and the extent to which their choices are realized, have a fundamental impact on the outcomes of any mechanism of school choice. In this article, we provide a comparative analysis of the school choice strategies of middle‐class families in London and Paris. We draw on approximately 200 in‐depth interviews carried out across the two cities. This enables us to investigate the extent to which middle‐class school choice strategies transcend the institutional context provided by both the local (state and private) schools market and national education policy in England and France. We discuss these findings in the context of current school choice policy and consider their implications for future policy design.     

Comparative Risk Sensitivity with Reference-Dependent Preferences

Experimental evidence suggests that individuals are risk averse over gains and risk seeking over losses (i.e., they have S-shaped utility functions in an expected utility setting) and that they are loss averse. Furthermore, the evidence leads to a single definition of S-shaped utility, but it has led to several alternative specifications of loss aversion. This paper characterizes the relations more S-shaped than and more loss averse than for a utility function, and in so doing arrives at a new definition of loss aversion based on average instead of marginal utility.     

Social comparison and risk taking behavior

This paper studies the effects of social comparison on risk taking behavior. In our theoretical framework, decision makers evaluate the consequences of their choices relative to both their own and their peers’ conditions. We test experimentally whether the position in the social ranking affects risk attitudes. Subjects interact in a simulated workplace environment where they perform a work task, receive possibly different wages, and then undertake a risky decision that may produce an extra gain. We find that social comparison matters for risk attitudes. Subjects are more risk averse in the presence of small social gain than social loss. In addition, risk aversion is decreasing in the size of the social gain.     

An axiomatization of cumulative prospect theory

This paper presents a method for axiomatizing a variety of models for decision making under uncertainty, including Expected Utility and Cumulative Prospect Theory. This method identifies, for each model, the situations that permit consistent inferences about the ordering of value differences. Examples of rankdependent and sign-dependent preference patterns are used to motivate the models and the “tradeoff consistency” axioms that characterize them. The major properties of the value function in Cumulative Prospect Theory—diminishing sensitivity and loss aversion—are contrasted with the principle of diminishing marginal utility that is commonly assumed in Expected Utility.     

Monetary incentives in the loss domain and behavior toward risk: An experimental comparison of three reward schemes including real losses

In the loss domain, both practical and ethical considerations rule out the systematic use of an incentive-compatible procedure involving real losses. The experimental study presented here aims at investigating whether some easier-to-implement procedure could be adequately used. For that purpose, the subjects’ degree of risk aversion is compared across three payment conditions: a real-losses condition based on a random-lottery (incentive-compatible) system, which serves as a benchmark, and two challengers, namely a “losses-from-an-initial-endowment” procedure and a hypothetical-losses condition. As a by-product, our experimental design also allows us to investigate the impact of monetary incentives in the gain domain. The main result is twofold: no significant difference arises between the three payment conditions in the loss domain, while real and hypothetical choices significantly differ in the gain domain. Our results suggest that the use of monetary incentives may be more crucial in the gain domain than in the loss domain.