We conduct a laboratory experiment to investigate the impact of deliberation time on behavior under risk and uncertainty. Towards this end we ask our participant to make quick, intuitive evaluations of a number of lotteries and report resulting certainty equivalents. Yet, we invite them to modify these initial decisions, whenever they find, after (additional) deliberation, that they do not precisely represent their preference. Both certainty equivalents are incentivized (a double-response method). The choice of evaluated lotteries allows us to semi-parametrically estimate the value function and the probability weighting function within the paradigm of the cumulative prospect theory. The main finding is that deliberation raises the probability weighting function (reduces pessimism), especially in the case of lotteries involving unknown probabilities.

The literature on emotion and risk-taking is large and heterogeneous. Whereas some studies have found that positive emotions increase risk-taking and negative emotions increase risk aversion, others have found just the opposite. In this study, we investigated this question in the context of a risky decision-making task with embedded high-resolution sampling of participants’ subjective emotional valence. Across two large-scale experiments (N = 329 and 524), we consistently found evidence for a negative association between self-reported emotional valence and risk-taking behaviors. That is, more negative subjective affect was associated with increased risk-seeking, and more positive subjective affect was associated with increased risk aversion. This effect was evident both when we compared participants with different levels of mean emotional valence as well as when we considered within-participant emotional fluctuations over the course of the task. Prospect-theoretic computational modeling analyses suggested that both between- and within-participant effects were driven by an effect of emotional valence on the curvature of the subjective utility function (i.e., increased risk tolerance in more negative emotional states), as well as by an effect of within-person emotion fluctuations on loss aversion. We interpret findings in terms of a tendency for participants in negative emotional states to choose high-risk, high-reward options in an attempt to improve their emotional state.

The heart of prospect theory is the value function, proposing that the carriers of value are positive or negative changes from a reference point. Daniel Kahneman observed that if prospect theory had a flag, the value function would be drawn on it. The function is nonlinear, reflecting diminishing sensitivity to magnitude. When describing how human lives are valued, the function exposes profound incoherence. An individual life is highly valued and thus vigorously protected if it is the only life at risk. But that life loses its value when it is one of many endangered by a larger tragedy. Beyond this insensitivity, the function may actually decline when many lives at risk become mere numbers. The more who die, the less we care. Implications of this deadly ‘arithmetic of compassion’ for understanding and managing the risk from nuclear weapons are briefly discussed.

In March 2024, Daniel Kahneman – the man who did perhaps more than anyone else to shape the field of behavioural public policy – died. He is among a small handful of scholars who have had a huge effect on my own career, and in this essay – the first in a series of essays in a special section of the Journal that honour him – I reflect on how his work inspired much of my own.

Precision irrigation is a potential viable strategy for water use reductions on golf courses by making variable or site-specific irrigation applications. A group of US golf course superintendents were surveyed to examine whether and how superintendents’ risk preferences (attitudes) affect the adoption decisions of precision irrigation technologies on their golf courses. Under the prospect theory (PT) framework, a lottery experiment was used to elicit the measures of three risk attitudes, that is, risk curvature, probability distortion, and loss aversion. Using these three measures and other questions in the survey, we found that risk curvature has a significant positive effect on the precision irrigation technologies adoption on golf courses, while probability distortion affects the adoption negatively. Compared to the golf course in low precipitation areas, superintendents’ risk attitudes are more likely to affect the precision irrigation technologies adoption in the golf course in high precipitation areas. Additionally, risk curvature dominates the adoption decisions for newer technologies, while probability distortion dominates the older technologies adoption decisions. Our research enriches the literature on the decision-making behaviors of managers by considering how probability distortion, a factor typically ignored by other studies, affects technology adoption decisions and adds to the literature on examining the technology adoption behaviors under PT by focusing on golf course superintendents, a group that has not been studied.

Adopting eco-friendly technologies, such as converting lawns to alternative low-input grass species, can reduce household expenditures and mitigate negative environmental impacts at the same time. However, the rate of adoption of these technologies has not been as high as expected. This study develops a behavioral framework to identify barriers to new technology adoption by incorporating both prospect theory and present bias. We apply the framework in a choice experiment to investigate the relative importance of several factors that shape decisions associated with adoption of low-input turfgrass. We find that loss aversion plays a significant role. Though consumers exhibit present bias, long-term benefits still matter to them. Insights from the behavior model suggest that marketing and government programs that promote cost–benefit-efficient technologies should focus on eliminating or reducing potential losses caused by product failure.

Although many models for risky choices between gambles assume that information is somehow integrated, the recently proposed priority heuristic (PH) claims that choices are based on one piece of information only. That is, although the current reason for a choice according to the PH can vary, all other reasons are claimed to be ignored. However, the choices predicted by the PH and other pieces of information are often confounded, thus rendering critical tests of whether decisions are actually based on one reason only, impossible. The current study aims to remedy this problem by manipulating the number of reasons additionally in line with the choice implied by the PH. The results show that participants’ choices and decision times depend heavily on the number of reasons in line with the PH — thus contradicting the notion of non-compensatory, one-reason decision making.

In “Risky choice framing: Task versions and a comparison of prospect theory and fuzzy-trace theory”, Kühberger and Tanner (2010) examined the impacts of removing stated zero/non-zero complements of risky options on the gain/loss framing effect. They also tested two rival theoretical explanations for this effect: prospect theory and fuzzy-trace theory. The present study aimed to examine the reliability and robustness of the evidence provided by Kühberger and Tanner by precise replication in Study 1. The original findings were reported for conditions in which the probability of the risky option was fixed, and the expected value of the two alternatives was approximately equivalent. The present study also aimed to examine the generality of their findings under additional conditions in which large, medium and small probabilities of the risky option were assigned, and the expected value of the certain or risky options differed. The main findings of Kühberger and Tanner (2010) were successfully replicated and confirmed under the original and additional conditions. The implications of these findings are discussed.

We propose a constructed-choice model for general decision making. The model departs from utility theory and prospect theory in its treatment of multiple goals and it suggests several different ways in which context can affect choice.

It is particularly instructive to apply this model to protective decisions, which are often puzzling. Among other anomalies, people insure against non-catastrophic events, underinsure against catastrophic risks, and allow extraneous factors to influence insurance purchases and other protective decisions. Neither expected-utility theory nor prospect theory can explain these anomalies satisfactorily. To apply this model to the above anomalies, we consider many different insurance-related goals, organized in a taxonomy, and we consider the effects of context on goals, resources, plans and decision rules.

The paper concludes by suggesting some prescriptions for improving individual decision making with respect to protective measures.

This paper investigates choices about “distributional fairness” (sometimes called “distributive justice”), i.e., selection of the proper way for resources to be distributed in group. The study finds evidence that several of the same biases of risky decision making also apply to choices about distributional fairness, in particular focusing on the key biases that lead to prospect theory. This finding is achieved by introducing a novel thought experiment regarding the fairness of resource distributions, then manipulating the percentage of individuals who gain or lose in these distributions, and changing the sizes of gains and losses. Shared biases may mean similar heuristics are being employed. The mechanism behind this result leaves room for future exploration, as do the implications of the finding for related applications in inequality research.

A new theory of decision-making under risk, the Opportunity-Threat Theory is proposed. Analysis of risk into opportunity and threat components allows description of behavior as a combination of opportunity seeking and threat aversion. Expected utility is a special case of this model. The final evaluation is an integration of the impacts of opportunity and threat with this expectation. The model can account for basic results as well as several “new paradoxes” that refuted cumulative prospect theory in favor of configural weight models. The discussion notes similarities and differences of this model to the configural weight TAX model, which can also account for the new paradoxes.

The use of gamification to motivate engagement has greatly increased the number of ways in which people compete. Many of these competitions allow individuals to see how they rank as a competition progresses. Our work aims to provide a better understanding of how individuals feel about different rank outcomes in competitions. We do this by applying the principles of expected utility theory to elicit utility curves for over 3,000 people across three studies using hypothetical competition scenarios. We find consistent support for the following generalizations: 1) individuals are risk-seeking when in second place, 2) they are risk-averse when in second-to-last place, and 3) the utility decrease going from first to second place is greater than their decrease going from second-to-last to last place. Our results suggest individuals are both last-place averse and first-place seeking, with an even stronger inclination towards the latter.

The Allais Paradox, or common consequence effect, has been a standard challenge to normative theories of risky choice since its proposal over 60 years ago. However, neither its causes nor the conditions necessary to create the effect are well understood. Two experiments test the effects of losses and event splitting on the Allais Paradox. Experiment 1 found that the Allais Paradox occurs for both gain and mixed gambles and is reflected for loss gambles produced by reflection across the origin. Experiment 2 found that the Allais Paradox is eliminated by splitting the outcomes even when the probabilities used do not increase the salience of the common consequence. The results of Experiment 1 are consistent with Cumulative Prospect Theory, the current leading theory of risky choice. However, the results of Experiment 2 are problematic for Cumulative Prospect Theory and suggest that alternate explanations for the Allais Paradox must be sought.

Sunk costs have been known to elicit violations of expected utility theory, in particular, the independence or cancellation axiom. Separately, violations of the stochastic dominance principle have been demonstrated in various settings despite the fact that descriptive models of choice favored in economics deem such violations irrational. However, it is currently unknown whether sunk costs also yield stochastic dominance violations. In two studies using a tri-colored roulette wheel choice task with non-equiprobable events yet equal payoffs, we observed that those who had sunk costs selected a stochastically dominated option significantly more than did those who had no costs. Moreover, a second study revealed that people chose a stochastically dominated option significantly more when the expected value was low compared to high. A model comparison of psychological explanations demonstrated that theories that incorporate a reference shift of the status quo could predict these sunk cost-based violations of stochastic dominance whereas other models could not.

Previous studies of loss aversion in decisions under risk have led to mixed results. Losses appear to loom larger than gains in some settings, but not in others. The current paper clarifies these results by highlighting six experimental manipulations that tend to increase the likelihood of the behavior predicted by loss aversion. These manipulations include: (1) framing of the safe alternative as the status quo; (2) ensuring that the choice pattern predicted by loss aversion maximizes the probability of positive (rather than zero or negative) outcomes; (3) the use of high nominal (numerical) payoffs; (4) the use of high stakes; (5) the inclusion of highly attractive risky prospects that creates a contrast effect; and (6) the use of long experiments in which no feedback is provided and in which the computation of the expected values is difficult. In addition, the results suggest the possibility of learning in the absence of feedback: The tendency to select simple strategies, like “maximize the worst outcome” which implies “loss aversion”, increases when this behavior is not costly. Theoretical and practical implications are discussed.

According to prospect theory, people overweight low probability events and underweight high probability events. Several recent papers (notably, Hertwig, Barron, Weber & Erev, 2004) have argued that although this pattern holds for “description-based” decisions, in which people are explicitly provided with probability distributions over potential outcomes, it is actually reversed in “experience-based” decisions, in which people must learn these distributions through sampling. We reanalyze the data of Hertwig et al. (2004) and present a replication to determine the extent to which their phenomenon can be attributed to sampling error (a statistical rather than psychological phenomenon) versus underestimation of rare events (i.e., judgmental bias) versus actual underweighting of judged probabilities. We find that the apparent reversal of prospect theory in decisions from experience can be attributed almost entirely to sampling error, and are consistent with prospect theory and the two-stage model of decision under uncertainty (Fox & Tversky, 1998).