Risk preferences and changes in background risk

We present two theorems that yield necessary and sufficient conditions for first- and second-degree stochastic dominance deteriorations of background risk to increase risk aversion with respect to foreground risk. We require that any change in a foreground risk that is undesirable remains so after a background risk changes in a way that is either unfair, undesirable in the sense of reducing expected utility, or undesirable in the sense of increasing expected marginal utility. Our results thus characterize utility functions that are, respectively, vulnerable, proper, or standard with respect to changes in background risk.

Prospect theory for continuous distributions

We extend the original form of prospect theory by Kahneman and Tversky from finite lotteries to arbitrary probability distributions, using an approximation method based on weak-⋆ convergence. The resulting formula is computationally easier than the corresponding formula for cumulative prospect theory and makes it possible to use prospect theory in future applications in economics and finance. Moreover, we suggest a method how to incorporate a crucial step of the “editing phase” into prospect theory and to remove in this way the discontinuity of the original model.

Third-generation prospect theory

We present a new theory of decision under uncertainty: third-generation prospect theory (PT³). This retains the predictive power of previous versions of prospect theory, but extends that theory by allowing reference points to be uncertain while decision weights are specified in a rank-dependent way. We show that PT³ preferences respect a state-conditional form of stochastic dominance. The theory predicts the observed tendency for willingness-to-accept valuations of lotteries to be greater than willingness-to-pay valuations. When PT³ is made operational by using simple functional forms with parameter values derived from existing experimental evidence, it predicts observed patterns of the preference reversal phenomenon.

A tractable method to measure utility and loss aversion under prospect theory

This paper provides an efficient method to measure utility under prospect theory. Our method minimizes both the number of elicitations required to measure utility and the cognitive burden for subjects, being based on the elicitation of certainty equivalents for two-outcome prospects. We applied our method in an experiment and were able to replicate the main findings on prospect theory, suggesting that our method measures what it is intended to. Our data confirmed empirically that risk seeking and concave utility can coincide under prospect theory. Utility did not depend on the probability used in the elicitation, which offers support for the validity of prospect theory.

Preferences and decision errors in the winner’s curse

The problem of asymmetric information causes a winner’s curse in many environments. Given many unsuccessful attempts to eliminate it, we hypothesize that some people ‘prefer’ the lotteries underlying the winner’s curse. Study 1 shows that after removing the hypothesized cause of error, asymmetric information, half the subjects still prefer winner’s curse lotteries, implying past efforts to de-bias the winner’s curse may have been more successful than previously recognized since subjects prefer these lotteries. Study 2 shows risk-seeking preferences only partially explain lottery preferences, while non-monetary sources of utility may explain the rest. Study 2 suggests lottery preferences are not independent of context, and offers methods to reduce the winner’s curse.

Risk aversion in the small and in the large: Calibration results for betweenness functionals

A reasonable level of risk aversion with respect to small gambles leads to a high, and absurd, level of risk aversion with respect to large gambles. This was demonstrated by Rabin (Econometrica 68:1281–1292, 2000) for expected utility theory. Later, Safra and Segal (Econometrica, 2008) extended this result by showing that similar arguments apply to many non-expected utility theories, provided they are Gateaux differentiable. In this paper we drop the differentiability assumption and by restricting attention to betweenness theories we show that much weaker conditions are sufficient for the derivation of similar calibration results.

Correcting expected utility for comparisons between alternative outcomes: A unified parameterization of regret and disappointment

A unified parameterization of an expected utility model corrected for regret and disappointment effects is presented, constrained to conform to a well-known choice pattern, the common consequence effect, a special case of the Allais paradox. For choices subject to regret and disappointment effects to be consistent with this choice pattern, the function that corrects the utility of the obtained outcome has to have a positive second derivative for its regret component and a negative second derivative for its disappointment component. These hypothesized functional forms make predictions about the relative effect that small vs. large differences between obtained and alternative outcomes should have on people’s experiences of regret or disappointment.

Dual process theories: A key for understanding the diversification bias?

The diversification bias in repeated lotteries is the finding that a majority of participants fail to select the option offering the highest probability. This phenomenon is systematic and immune to classical manipulations (e.g. monetary rewards). We apply dual process theories and argue that the diversification bias is a consequence of System 1 (automatic, intuitive, associative) triggering a matching response, which fails to be corrected by System 2 (intentional, analytic, rational). Empirically, supporting the corrective functions of System 2 through appropriate contextual cues (describing the task as a statistical test rather than as a lottery) led to a decrease of diversification.

Valuing publicly sponsored research projects: Risks,scenario adjustments,and inattention

Survey-based choice scenarios used to value non-market public goods typically preclude any risk that the benefits described may not be delivered. Our survey specifies explicit risks of (a) outright program failure and (b) program redundancy due to possible private sector substitutes. Additionally, most analyses assume that survey subjects fully accept these scenarios and that all provided information receives their complete attention. Our discounted expected utility model of choice accommodates both these objective risks and the possibility of subjective scenario adjustment or selective inattention by respondents. We then counterfactually simulate willingness-to-pay in the absence of these distortions.

Myopic risk-seeking: The impact of narrow decision bracketing on lottery play

In two experiments conducted with low-income participants, we find that individuals are more likely to buy state lottery tickets when they make several purchase decisions one-at-a-time, i.e. myopically, than when they make one decision about how many tickets to purchase. These results extend earlier findings showing that “broad bracketing” of decisions encourages behavior consistent with expected value maximization. Additionally, the results suggest that the combination of myopic decision making and the “peanuts effect”—greater risk seeking for low stakes than high stakes gambles—can help explain the popularity of state lotteries.

One-reason decision-making: Modeling violations of expected utility theory

People violate expected utility theory and this has been traditionally modeled by augmenting its weight-and-add framework by nonlinear transformations of values and probabilities. Yet individuals often use one-reason decision-making when making court decisions or choosing cellular phones, and institutions do the same when creating rules for traffic safety or fair play in sports. We analyze a model of one-reason decision-making, the priority heuristic, and show that it simultaneously implies common consequence effects, common ratio effects, reflection effects, and the fourfold pattern of risk attitude. The preferences represented by the priority heuristic satisfy some standard axioms. This work may provide the basis for a new look at bounded rationality.

Eliciting decision weights by adapting de Finetti’s betting-odds method to prospect theory

This paper extends de Finetti’s betting-odds method for assessing subjective beliefs to ambiguous events. Thus, a tractable manner for measuring decision weights under ambiguity is obtained. De Finetti’s method is so transparent that decision makers can evaluate the relevant tradeoffs in complex situations. The resulting data can easily be analyzed, using nonparametric techniques. Our extension is implemented in an experiment on predicting next-day’s performance of the Dow Jones and Nikkei stock indexes, where we test the existence and nature of rank dependence, finding usual patterns. We also find violations of rank dependence.

Risk aversion and expected-utility theory: A calibration exercise

Rabin (Econometrica 68(5):1281–1292, 2000) argues that, under expected-utility, observed risk aversion over modest stakes implies extremely high risk aversion over large stakes. Cox and Sadiraj (Games Econom. Behav. 56(1):45–60, 2006) have replied that this is a problem of expected-utility of wealth, but that expected-utility of income does not share that problem. We combine experimental data on moderate-scale risky choices with survey data on income to estimate coefficients of relative risk aversion using expected-utility of consumption. Assuming individuals cannot save implies an average coefficient of relative risk aversion of 1.92. Assuming they can decide between consuming today and saving for the future, a realistic assumption, implies quadruple-digit coefficients. This gives empirical evidence for narrow bracketing.

Valuing risks of death from terrorism and natural disasters

This paper uses a random utility model to examine stated preferences for the valuation of public risks of fatalities from terrorist attacks and natural disasters. Traffic-related deaths serve as the common reference point in two series of pairwise risk-risk tradeoff choices. Even after taking into account differences in respondent risk beliefs, the nationally representative sample values the prevention of terrorism deaths almost twice as highly as preventing natural disaster deaths and at about the same level as preventing deaths from traffic accidents, which pose greater personal risk. Education, seatbelt usage, political preferences, and terrorism risk beliefs affect valuations in the expected manner.

Whom should we believe? Aggregation of heterogeneous beliefs

We examine the collective risk attitude of a group with heterogeneous beliefs. We prove that the wealth-dependent probability distribution used by the representative agent is biased in favor of the beliefs of the more risk tolerant consumers. Moreover, increasing disagreement on the state probability raises the state probability of the representative agent. It implies that when most disagreements are concentrated in the tails of the distribution, the perceived collective risk is magnified. This can help to solve the equity premium puzzle. We show that the trade volume and the equity premium are positively correlated.

An experimental investigation of violations of transitivity in choice under uncertainty

Several models of decision-making imply systematic violations of transitivity of preference. Our experiments explored whether people show patterns of intransitivity predicted by regret theory and majority rule. To distinguish “true” violations from those produced by “error,” a model was fit in which each choice can have a different error rate and each person can have a different pattern of true preferences that need not be transitive. Error rate for a choice is estimated from preference reversals between repeated presentations of that same choice. Our results showed that very few people repeated intransitive patterns. We can retain the hypothesis that transitivity best describes the data of the vast majority of participants.

Conditional payments and self-protection

Self-protection can be financed either by upfront payments or by conditional payments (or contingent fees) in which individuals pay a provider only when a favorable outcome is realized. We find that, from the vantage point of a risk-averse individual, conditional payments welfare dominate upfront payments in the state-independent framework, but upfront payments welfare dominate conditional payments in the state-dependent framework. Moreover, more risk aversion always implies more self-protection under conditional payments, for both state-independent and state-dependent frameworks. In contrast, it has been previously argued that more risk aversion does not necessarily imply more self-protection under upfront payments.

Individual and group decision making under risk: An experimental study of Bayesian updating and violations of first-order stochastic dominance

This paper reports the results of experiments designed to test whether individuals and groups abide by monotonicity with respect to first-order stochastic dominance and Bayesian updating when making decisions under risk. The results indicate a significant number of violations of both principles. The violation rate when groups make decisions is substantially lower, and decreasing with group size, suggesting that social interaction improves the decision-making process. Greater transparency of the decision task reduces the violation rate, suggesting that these violations are due to judgment errors rather than the preference structure. In one treatment, however, less complex decisions result in a higher error rates.