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Much of the literature on theories of decision making under risk has emphasized differences between theories. One enduring theme has been the attempt to develop a distinction between “normative” and “descriptive” theories of choice. Bernoulli (1738) introduced log utility because expected value theory was alleged to have descriptively incorrect predictions for behavior in St. Petersburg games. Much later, Kahneman and Tversky (1979) introduced prospect theory because of the alleged descriptive failure of expected utility (EU) theory (von Neumann & Morgenstern, 1947).

Choice under risk has a large stochastic (unpredictable) component. This chapter examines five stochastic models for binary discrete choice under risk and how they combine with “structural” theories of choice under risk. Stochastic models are substantive theoretical hypotheses that are frequently testable in and of themselves, and also identifying restrictions for hypothesis tests, estimation and prediction. Econometric comparisons suggest that for the purpose of prediction (as opposed to explanation), choices of stochastic models may be far more consequential than choices of structures such as expected utility or rank-dependent utility.

We review the experimental evidence on risk aversion in controlled laboratory settings. We review the strengths and weaknesses of alternative elicitation procedures, the strengths and weaknesses of alternative estimation procedures, and finally the effect of controlling for risk attitudes on inferences in experiments.

Charitable lotteries represent one of today's most popular fund-raising schemes. This study begins by developing theory examining the optimal design of a charitable lottery. We show that any prize distribution is only optimal for a group of n symmetric agents with given risk preference. However, there exist multiple prize distributions that generate contributions approaching the optimal level over a range of individual risk posture. We test our theory using a battery of experimental treatments. Our results suggest that lotteries dominate the voluntary contribution mechanism (VCM) in terms of total dollars raised. Moreover, the performance of lotteries weakly depends on individual risk preference.

We take Cumulative Prospect Theory (CPT) seriously by rigorously estimating structural models using the full set of CPT parameters. Much of the literature only estimates a subset of CPT parameters, or more simply assumes CPT parameter values from prior studies. Our data are from laboratory experiments with undergraduate students and MBA students facing substantial real incentives and losses. We also estimate structural models from Expected Utility Theory (EUT), Dual Theory (DT), Rank-Dependent Utility (RDU), and Disappointment Aversion (DA) for comparison. Our major finding is that a majority of individuals in our sample locally asset integrate. That is, they see a loss frame for what it is, a frame, and behave as if they evaluate the net payment rather than the gross loss when one is presented to them. This finding is devastating to the direct application of CPT to these data for those subjects. Support for CPT is greater when losses are covered out of an earned endowment rather than house money, but RDU is still the best single characterization of individual and pooled choices. Defenders of the CPT model claim, correctly, that the CPT model exists “because the data says it should.” In other words, the CPT model was borne from a wide range of stylized facts culled from parts of the cognitive psychology literature. If one is to take the CPT model seriously and rigorously then it needs to do a much better job of explaining the data than we see here.

Behavioral economics poses a challenge for the welfare evaluation of choices, particularly those that involve risk. It demands that we recognize that the descriptive account of behavior toward those choices might not be the ones we were all taught, and still teach, and that subjective risk perceptions might not accord with expert assessments of probabilities. In addition to these challenges, we are faced with the need to jettison naive notions of revealed preferences, according to which every choice by a subject expresses her objective function, as behavioral evidence forces us to confront pervasive inconsistencies and noise in a typical individual’s choice data. A principled account of errant choice must be built into models used for identification and estimation. These challenges demand close attention to the methodological claims often used to justify policy interventions. They also require, we argue, closer attention by economists to relevant contributions from cognitive science. We propose that a quantitative application of the “intentional stance” of Dennett provides a coherent, attractive and general approach to behavioral welfare economics.

Risk preferences play a critical role in almost every facet of economic activity. Experimental economists have sought to infer the risk preferences of subjects from choice behavior over lotteries. To help mitigate the influence of observable, and unobservable, heterogeneity in their samples, risk preferences have been estimated at the level of the individual subject. Recent work has detailed the lack of statistical power in descriptively classifying individual subjects as conforming to Expected Utility Theory (EUT) or Rank Dependent Utility (RDU). I discuss the normative consequences of this lack of power and provide some suggestions to improve the accuracy of normative inferences about individual-level choice behavior.

Purpose: The purpose of this paper is to investigate whether inequality aversion is influenced by the risk level. Recently empirical evidence points to deviations from selfish behavior of Homo economicus. Thus, people are not motivated solely by their own monetary payoffs, but are also concerned about issues of equality and fairness. This paper distinguishes between inequality aversion and risk aversion and discusses whether the level of risk affects these motivations.

Design: In an experimental framework the attitude toward inequality is separated from the attitude toward risk. A risky environment is generated by a set of lotteries. The subjects had to determine the method for payment, equally (CG) or nonequally (IG), for three lotteries with different levels of risk. The inequality preferences are measured by the level of the selected probability for CG.

Findings: The main finding of this paper is that preferences for inequality are influenced by level of risk. We found that aversion to inequality was stronger when the level of risk was higher. In the low and medium risk lotteries participants preferred the individual gamble – the nonegalitarian method. Only in the high-risk lottery the participants preferred the common gamble that assured them equal payments.

Originality/value: The paper distinguishes between inequality aversion and risk aversion and subjects are allowed to trade one off against the other. Thus, it contributes to the understanding of the interrelationship between income inequality and risk.

This paper reports a new experimental test of the notion that behavior switches from risk averse to risk seeking when gains are “reflected” into the loss domain. We conduct a sequence of experiments that allows us to directly compare choices under reflected gains and losses where real and hypothetical payoffs range from several dollars to over $100. Lotteries with positive payoffs are transformed into lotteries over losses by multiplying all payoffs by –1, that is, by reflecting payoffs around zero. When we use hypothetical payments, more than half of the subjects who are risk averse for gains turn out to be risk seeking for losses. This reflection effect is diminished considerably with cash payoffs, where the modal choice pattern is to exhibit risk aversion for both gains and losses. However, we do observe a significant difference in risk attitudes between losses (where most subjects are approximately risk neutral) and gains (where most subjects are risk averse). Reflection rates are further reduced when payoffs are scaled up by a factor of 15 (for both real and hypothetical payoffs).

This chapter conducts a systematic comparison of behavioral economics’s challenges to the standard accounts of economic behaviors within three dimensions: under risk, over time, and regarding other people. A new perspective on two underlying methodological issues, i.e., inter-disciplinarity and the positive/normative distinction, is proposed by following the entanglement thesis of Hilary Putnam, Vivian Walsh, and Amartya Sen. This thesis holds that facts, values, and conventions have inter-dependent meanings in science which can be understood by scrutinizing formal and ordinary language uses. The goal is to provide a broad and self-contained picture of how behavioral economics is changing the mainstream of economics.