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I show that stochastic contracts generate powerful incentives when agents suffer from probability distortion. When implementing these contracts, the principal can target probability distortions in order to inflate the agent's perceived benefits of exerting high levels of effort. This novel source of motivation is absent in contracts traditionally regarded as optimal. A theoretical framework and an experiment demonstrate that stochastic contracts implemented with small probabilities, which expose the agent to a high degree of risk, generate higher performance than cost‐equivalent contracts with lower or no risk exposure. I find that probability distortions that result from likelihood insensitivity—cognitive limitations that prevent the accurate evaluation of probabilities—account for this finding. The results highlight the limits of contracts traditionally regarded as optimal. [ABSTRACT FROM AUTHOR]

In order to estimate volatility-dependent probability weighting functions, we obtain risk neutral and physical densities from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) stochastic volatility and jumps model. Across volatility levels, we find pronounced inverse S-shapes, i.e. small probabilities are overweighted, and probability weighting almost monotonically increases in volatility, indicating higher skewness preferences and crash aversion in volatile market environments. Moreover, by estimating probabilistic risk attitudes, equivalent to the share of risk aversion related to probability weighting, we shed further light on the pricing kernel puzzle. While pricing kernels estimated from the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) model display the typical U-shape as documented in the literature, pricing kernels—net of probability weighting—are strictly monotonically decreasing and thus in line with economic theory. Equivalently, we find risk aversion to be positive across wealth levels. Our results are robust to alternative maturities, wealth percentiles, alternative functional forms, a nonparametric empirical setting and variations of the Pan (J Financ Econ 63(1):3–50, 2002. https://doi.org/10.1016/S0304-405X(01)00088-5) coefficient estimates. [ABSTRACT FROM AUTHOR]

Under probability weighting, entrepreneurs with skewness preference tend to seek rightskewed and avoid left-skewed risks. We show that Chinese firms managed by CEOs with professional epidemic experience, i.e., who previously experienced the outbreak of SARS during their tenure as high level executives, have a lower stock price crash risk measured by the negative skewness of stock prices in subsequent periods. In particular, those firms intentionally avoid stock price crashes by adopting more conservative strategies in decisionmaking. Overall, we provide the first evidence on the unintended effect of entrepreneurs' subjective judgments of the probabilities of disease outbreaks on financial market stability. These have long-term implications for the financial system. [ABSTRACT FROM AUTHOR]

The empirical results on the influence of inexperience and experience in decision making are inconclusive. This paper offers a resolution to the puzzle of how empirical studies that advance contradictory risk-related claims can all command empirical support. The paper employs a paradigmatic model of decision making that examines two variables: (1) the decision maker's personality, of which inexperience and experience is one component; and (2) the particulars of the decision problem. These two variables permit us to resolve the puzzle of inconclusive empirical results by identifying the separating conditions under which each risk-related claim holds. [ABSTRACT FROM AUTHOR]

Recent computational psychiatric research has dissected decision-making under risk into different underlying cognitive computational constructs and identified disease-specific changes in these constructs. Studies are underway to investigate what kind of behavioral or psychological interventions can restore these cognitive, computational constructs. In our previous study, we showed that reminiscing about positive autobiographical memories reduced risk aversion and affected probability weighting in the opposite direction from that observed in psychiatric disorders. However, in that study, we compared positive versus neutral memory retrieval by using a within-subjects crossover posttest design. Therefore, the change of decision-making from baseline is unclear. Furthermore, we used a hypothetical decision-making task and did not include monetary incentives. We attempt to address these limitations and investigated how reminiscing about positive autobiographical memories influences decision-making under risk using a between-subjects pretest posttest comparison design with performance-contingent monetary incentives. In thirty-eight healthy, young adults, we found that reminiscing about positive memories reinforced the commonly observed inverted S-shaped nonlinear probability weighting (f = 0.345, medium to large in effect size). In contrast, reminiscing about positive memories did not affect risk aversion in general. Given that the change in probability weighting after reminiscing about positive memories is in the opposite direction from that observed in psychiatric disorders, our results indicate that positive autobiographical memory retrieval might be a useful behavioral intervention strategy for amending the altered decision-making under risk in psychiatric diseases. [ABSTRACT FROM AUTHOR]

Patients rely on knowing potential risks before accepting medical treatments, but risk perception can be distorted by cognitive biases and irrelevant information. We examined the interactive effects of subjective processes, objective knowledge, and demographic characteristics on how individuals estimate risks when provided with relevant and irrelevant probabilistic information. Participants read medical scenarios describing potential adverse effects associated with declining and accepting preventative treatment, as well as the objective likelihood of experiencing adverse effects associated with one of these two courses of action. We found that the perceived negativity of outcomes influenced perceptions of risk regardless of whether relevant probabilities were available and that the use of affect heuristics to estimate risk increased with age. Introducing objective estimates ameliorated age-related increases in affective distortions. Sensitivity to relevant probabilities increased with greater perceived outcome severity and was greater for men than for women. We conclude that relevant objective information may reduce the propensity to conflate outcome severity with likelihood and that medical judgments of risk vary depending on exposure to relevant and irrelevant probabilities. Implications for how medical professionals should communicate risk information to patients are considered. [ABSTRACT FROM AUTHOR]

This paper proposes that the shape and parameter fits ofexisting probability weighting functions can be explained withsensitivity to uncertainty (as measured by information entropy)and the utility carried by reductions in uncertainty. Building onapplications of information theoretic principles to models ofperceptual and inferential processes, we suggest thatprobabilities are evaluated relative to a plausible expectation(the uniform distribution) and that the perceived distancebetween a probability and uniformity is influenced by the shape(relative entropy) of the distribution that the probability isembedded in. These intuitions are formalized in a novelprobability weighting function, VWD(p), which is simpler andhas less parameters than existing probability weightingfunctions. The proposed probability weighting functioncaptures characteristic features of existing probabilityweighting functions, introduces novel predictions, andprovides a parsimonious account of findings in probability andfrequency estimation related tasks.

Probability weighting refers to the behavioral bias in which irrational investors have a propensity to overweigh small probability tail events. In this study, we empirically investigate the asset pricing implications of probability weighting in commodity markets. We find that commodities with a high probability‐weighting value significantly underperform their low‐value pairs by 11% per annum. Neither conventional commodity risk factors nor existing characteristics explain this predictability. The predictability is more pronounced when arbitrage constraints are more binding. Commodities with a high probability‐weighting value also attract excess demand from non‐commercial traders. Collectively, these findings support a prospect theory‐based explanation for the cross‐section of commodity returns. [ABSTRACT FROM AUTHOR]

Non-linear probability weighting is an integral part of descriptive theories of choice under risk such as prospect theory. But why do these objective errors in information processing exist? Should we try to help individuals overcome their mistake of overweighting small and underweighting large probabilities? In this paper, we argue that probability weighting can be seen as a compensation for preexisting biases in evaluating payoffs. In particular, inverse S-shaped probability weighting is a flipside of S-shaped payoff valuation. Probability distortions may thus have survived as a second-best solution to a fitness maximization problem, and it can be counter-productive to correct them while keeping the value function unchanged. [ABSTRACT FROM AUTHOR]

Does Subjective Evaluation of Probability Impact Asset Prices? The Nobel Prize–winning capital asset pricing model (CAPM) predicts that expected excess return of any asset is positively proportional to its exposure to the overall market: the beta, leading to an upward-sloping security market line. However, this prediction is contradicted by empirical studies that the return–beta slope is often flat or even downward-sloping, a puzzle called the "beta anomaly." The CAPM is premised upon the notion that market participants are all rational, including that they are able to objectively evaluate probabilities. However, evidence abounds that individuals are often unable to do so, examples being purchase of lottery tickets and insurance products, in which the extremely small probabilities of winning or losing big are exaggerated. This phenomenon of distorting probabilities at both tails is called "probability weighting" (PW), which is a key component of modern behavioral finance. The paper "Beta and Coskewness Pricing: Perspective from Probability Weighting" approaches the beta anomaly through PW. It offers an explanation of the beta anomaly via a new theoretical CAPM involving PW and an extensive empirical study. The security market line is often flat or downward-sloping. We hypothesize that probability weighting plays a role and one ought to differentiate between periods in which agents overweight extreme events and those in which they underweight them. Overweighting inflates the probability of extremely bad events and demands greater compensation for beta risk, whereas underweighting does the opposite. Unconditional on probability weighting, these two effects offset each other, resulting in a flat or slightly negative return–beta relationship. Similarly, overweighting the tails enhances the negative relationship between return and coskewness, whereas underweighting reduces it. We derive a three-moment conditional capital asset pricing model for a market with rank-dependent utility agents to make these predictions, and we support our theory through an extensive empirical study. Funding: This work was supported by National Natural Science Foundation of China [Grants 71971083, 71931004, 72171138]; Program for Innovative Research Team of Shanghai University of Finance and Economics [Grant 2020110930]; Open Research Fund of Key Laboratory of Advanced Theory and Application in Statistics and Data Science-Ministry of Education, East China Normal University; a start-up grant and the Nie Center for Intelligent Asset Management at Columbia University. Supplemental Material: The online appendix is available at https://doi.org/10.1287/opre.2022.2421. [ABSTRACT FROM AUTHOR]

We provide a comprehensive analysis of the impact of probability weighting on optimal insurance demand in a unified framework. We identify decreasing relative overweighting as a new local condition on the probability weighting function that is useful for comparative static analysis. We discuss the effects of probability weighting on coinsurance, deductible choice, insurance demand for low-probability, high-impact risks versus high-probability, low-impact risks, and insurance demand in the presence of nonperformance risk. Probability weighting can make better or worse predictions than expected utility depending on the insurance demand problem at hand. [ABSTRACT FROM AUTHOR]

We report experimental data from standard market entry games and winner-take-all games. At odds with traditional decision-making models with risk aversion, the winner-take-all condition results in substantially more entry than the expected-payoff-equivalent market entry game. We explore three candidate explanations for excess entry: blind spot, illusion of control, and joy of winning, none of which receive empirical support. We provide a novel theoretical explanation for excess entry based on cumulative prospect theory and test it empirically. Our results suggest that excess entry into highly competitive environments is not caused by a genuine preference for competing, but is instead driven by probability weighting. Market entrants overweight the small probabilities associated with the high payoff outcomes in winner-take-all markets, while they underweight probable failures. This paper was accepted by Yan Chen, behavioral economics and decision analysis. Funding: This work was supported by the Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung [Grants 100018_182185 and 26022621] and the Dr. h.c. Emil Zaugg-Fonds [Grant B11162135]. Supplemental Material: The data files and e-companion are available at https://doi.org/10.1287/mnsc.2022.4397. [ABSTRACT FROM AUTHOR]

Across two experiments, we use ordinal ranking to examinethe processing and representations involved in the estimationof large-scale, real-world proportions. Specifically, in twoexperiments people estimated two kinds of important real-world proportions: the demographic makeup of theircommunities, and spending by the U.S. Federal government.Our goal was to assess the metric scaling properties thatcharacterize perceptions of these quantities. In particular,previous work in numerical proportions has positedlogarithmic or linear representations (Opfer & Siegler, 2007),or linear representations with task-dependent rescaling (Barth& Paladino, 2011; Cohen & Blanc-Goldhammer, 2011). Thecurrent context differs markedly from this prior work in thatthe values we are examining are not explicitly presented toparticipants, nor directly experienced, but must be estimatedon the basis of masses of complex experiences. Ordinalranking of the quantities, combined with a Thurstonianmodeling approach, allows a unique means for estimating theinternal scale properties of numerical structures. We find thatpeople largely rely on mixed representations that emphasizelog-odds transformations of these vaguely known, butsocially important values. While the budget data explored inExperiment 1 were unable to distinguish log and log-oddstransformed internal models, the demographic proportionsexplored in Experiment 2 favored log-odds models.

Early prediction of high depressive symptoms is crucial for selective intervention and the minimization of functional impairment. Recent cross-sectional studies indicated decision-making deficits in depression, which may be an important contributor to the disorder. Our goal was to test whether description- and experience-based decision making, two major neuroeconomic paradigms of decision-making under uncertainty, predict future depressive symptoms in young adults. One hundred young adults performed two decision-making tasks, one description-based, in which subjects chose between two gambling options given explicitly stated rewards and their probabilities, and the other experience-based, in which subjects were shown rewards but had to learn the probability of those rewards (or cue-outcome contingencies) via trial-and-error experience. We evaluated subjects' depressive symptoms with BDI-II at baseline (T1) and half a year later (T2). Comparing subjects with low versus high levels of depressive symptoms at T2 showed that the latter performed worse on the experience- but not description-based task at T1. Computational modeling of the decision-making process suggested that subjects with high levels of depressive symptoms had a more concave utility function, indicating enhanced risk aversion. Furthermore, a more concave utility function at T1 increased the odds of high depressive symptoms at T2, even after controlling depressive symptoms at T1, perceived stress at T2, and several covariates (OR = 0.251, 95% CI [0.085, 0.741]). This is the first study to demonstrate a prospective link between experience-based decision-making and depressive symptoms. Our results suggest that enhanced risk aversion in experience-based decision-making may be an important contributor to the development of depressive symptoms. [ABSTRACT FROM AUTHOR]

Nonlinear probability weighting allows cumulative prospect theory (CPT) to account for key phenomena in decision making under risk (e.g., certainty effect, fourfold pattern of risk attitudes). It describes the impact of risky outcomes on preferences in terms of a rank-dependent nonlinear transformation of their objective probabilities. The attentional Drift Diffusion Model (aDDM) formalizes the finding that attentional biases toward an option can shape preferences within a sequential sampling process. Here we link these two influential frameworks. We used the aDDM to simulate choices between two options while systematically varying the strength of attentional biases to either option. The resulting choices were modeled with CPT. Changes in preference due to attentional biases in the aDDM were reflected in highly systematic signatures in the parameters of CPT's weighting function (curvature, elevation). In a re-analysis of a large set of previously published data, we demonstrate that attentional biases are also empirically linked to patterns in probability weighting as suggested by the simulations. Our analyses also revealed a previously overlooked link between patterns in probability weighting and response times. These findings highlight that distortions in probability weighting can arise from simple option-specific attentional biases in information search, and suggest an alternative to common interpretations of weighting-function parameters in terms of probability sensitivity and optimism. They also point to novel, attention-based explanations for empirical phenomena associated with characteristic shapes of CPT's probability-weighting function (e.g., certainty effect, description-experience gap). The results advance the integration of two prominent computational frameworks for decision making. [ABSTRACT FROM AUTHOR]

The literature suggests that probability weighting and choice set dependence influence risky choices. However, their relative importance remains an open question. We present a joint test that uses binary choices between lotteries provoking Common Consequence and Common Ratio Allais Paradoxes and manipulates their joint payoff distribution. We show non-parametrically that probability weighting and choice set dependence both play a role at describing aggregate choices. To parsimoniously account for heterogeneity, we also estimate a structural model using a finite mixture approach. The model uncovers substantial heterogeneity and classifies subjects into three types: 38% Prospect Theory types whose choices are predominantly driven by probability weighting, 34% Salience Theory types whose choices are predominantly driven by choice set dependence, and 28% Expected Utility Theory types. The model predicts type-specific differences in the frequency of preference reversals out-of-sample, i.e., in choices with a different context than the ones used for estimating the model. Moreover, the out-of-sample predictions indicate that the choice context shapes the influence of choice set dependence. [ABSTRACT FROM AUTHOR]

Psychiatric disorders such as depressive and anxiety disorders are associated with altered decision-making under risk. Recent advances in neuroeconomics and computational psychiatry have further discomposed risk-based decision-making into distinct cognitive computational constructs and showed that there may be disorder-specific alterations in these constructs. As a result, it has been suggested these cognitive computational constructs may serve as useful behavioral biomarkers for these disorders. However, to date, little is known about what psychological or behavioral interventions can help to reverse and manage the altered cognitive computational constructs underlying risk-based decision-making. In the present study, we set out to investigate whether recalling positive autobiographical memories may affect risk-based decision-making in healthy volunteers using a description-based task. Specifically, based on theories of behavioral economics, we dissected risk preference into two cognitive computational constructs, utility sensitivity and probability weighting. We found that compared to recalling neutral memories, retrieving positive autobiographical memories increased utility sensitivity (Cohen's d = 0.447), indicating reduced risk aversion. Meanwhile, we also tested the influence of memory retrieval on probability weighting, the effect, however, was unreliable and requires further in-depth investigation. Of clinical relevance, the change in risk aversion after recalling positive memories was in the opposite direction compared to those reported in psychiatric disorders. These results argue for the potential therapeutic effect of positive autobiographical memory retrieval for the amendment of altered risk-based decision-making in psychiatric disorders. [ABSTRACT FROM AUTHOR]

Promoting prevention is an important goal of public policy. Fifty years ago, Ehrlich and Becker (J Polit Econ 80:623–648, 1972) proposed a simple model of prevention (or self-protection as they called it). Surprisingly enough, subsequent research, mainly within the expected utility paradigm, showed that it is hard to derive clear predictions within this simple model that can help to guide policy. This is what I refer to as the prevention puzzle: why is it so hard for economic theory to guide prevention decisions? In this article I try to shed light on this question. I review the existing literature and add some tentative new results under nonexpected utility. While the impact of risk aversion on prevention is complex, three factors seem to contribute unambiguously to underprevention: prudence, likelihood insensitivity, and loss aversion. I conclude by giving some ideas how empirical research may contribute to the understanding of prevention decisions and help to solve the prevention puzzle. [ABSTRACT FROM AUTHOR]

Risky choices often involve a tradeoff between expected payoff and payoff variability. Subjects in a simple experiment, however, exhibit more aversion to "downside risk" (with a small probability of a low payoff) and more attraction to "upside risk" (with a small probability of a high payoff). Women tend to be more averse than men for downside risk, but not for upside risk. These patterns are evaluated in terms of the utility curvature and probability weighting components of risk preferences. Gender differences in downside risk are relevant for the design of appropriately gender-tailored policies and algorithms for saving, financing, and entrepreneurship. [ABSTRACT FROM AUTHOR]

Probability weighting is a major concept for accommodating systematic departures from expected utility theory. We examine the relation between probability weighting and cognitive ability with two experiments: one recruiting subjects with a large variation in cognitive ability and the other using the within-subject manipulation of time constraints in lottery choices and cognitive tests. We find a significant association between likelihood insensitivity—the cognitive component of probability weighting—and cognitive limitation such that subjects with a lower cognitive score or more interrupted cognition due to time pressure respond less discriminately to intermediate probabilities and more over-sensitively to extreme probabilities. Our findings shed light on the sources of anomalous choices against expected utility theory. This paper was accepted by Yan Chen, behavioral economics and decision analysis. [ABSTRACT FROM AUTHOR]

This paper reports two experiments in which attitudes toward temporal risk resolution is elicited from choices between two-outcome lotteries that pay out at some future fixed date and can be resolved either now or later. We show that matching probabilities provides a simple method to measure attitudes toward temporal resolution—via the utility scale—under the recursive expected utility of Kreps and Porteus. We also analyze our data using a general recursive model that can reveal attitudes toward temporal risk resolution through the utility scale and/or the probability weighting scale. In terms of goodness of fit, as well as of prediction accuracy, our results point to a better performance of the probability weighting approach. More specifically, we show that individuals become less sensitive and more pessimistic with respect to winning probabilities when lotteries are resolved later rather than now. This paper was accepted by George Wu, decision analysis. [ABSTRACT FROM AUTHOR]

The modern world holds countless risks for humanity, both large-scale and intimately personal—from cyberwarfare, pandemics, and climate change to sexually transmitted diseases and drug use and abuse. Many risks have prompted institutional, regulatory, and technological countermeasures, the success of which depends to some extent on how individuals learn about the risks in question. We distinguish between two powerful but imperfect teachers of risk. First, people may learn by consulting symbolic and descriptive material, such as warnings, statistics, and images. More often than not, however, a risk's fluidity defies precise description. Second, people may learn about risks through personal experience. Responses to risk can differ systematically depending on whether people learn through one mode, both, or neither. One reason for these differences—and by no means the only reason—is the discrepancy in the cognitive impact that rare events (typically the risk event) and common events (typically the nonoccurrence of the risk event) have on the decision maker. We propose a description–experience framework that highlights not only the impact of each mode of learning but also the effects of their interplay on individuals' and collectives' responses to risk. We outline numerous research questions and themes suggested by this framework. [ABSTRACT FROM AUTHOR]

Prevention efforts, such as quitting smoking, flu vaccination, and exercising, are of crucial importance in health policy, but people tend to undertake too few of them. The main reason is that most prevention efforts only reduce but do not completely eliminate the risk of poor health. This makes it harder for people to assess the benefits of prevention, because they tend to misperceive and transform probabilities. In "When Risk Perception Gets in the Way: Probability Weighting and Underprevention," Baillon et al. introduce psychological insights (probability weighting) in a model of optimal decision making and show that most people undertake too little prevention when the risk of poor health is between 10% and 80%. The paper discusses several policy measures to make people spend more on prevention. Personal decisions about health hazards are the main cause of impaired health and premature death. People smoke and eat too much, and they exercise too little. The lack of preventive efforts is surprising given their proven effectiveness. In the early 1960s, Arrow suggested that moral hazard might be a reason for underprevention, but this explanation was later challenged. In this paper, we show that underprevention might be caused by misperceived probabilities. We derive when and how probability weighting gets in the way of prevention by blurring its benefits. We use a general model of prevention, encompassing several special cases from the literature. We also show how perceived ambiguity makes the problem of underprevention even worse by amplifying the effect of probability weighting. [ABSTRACT FROM AUTHOR]

Both depressive and anxiety disorders have been associated with excessive risk avoidant behaviors, which are considered an important contributor to the maintenance and recurrence of these disorders. However, given the high comorbidity between the two disorders, their independent association with risk preference remains unclear. Furthermore, due to the involvement of multiple cognitive computational factors in the decision-making tasks employed so far, the precise underlying mechanisms of risk preference are unknown. In the present study, we set out to investigate the common versus unique cognitive computational mechanisms of risk preference in depression and anxiety using a reward-based decision-making task and computational modeling based on economic theories. Specifically, in model-based analysis, we decomposed risk preference into utility sensitivity (a power function) and probability weighting (the one-parameter Prelec weighting function). Multiple linear regression incorporating depression (BDI-II) and anxiety (STAI state anxiety) simultaneously indicated that only depression was associated with one such risk preference parameter, probability weighting. As the symptoms of depression increased, subjects' tendency to overweight small probabilities and underweight large probabilities decreased. Neither depression nor anxiety was associated with utility sensitivity. These associations remained even after controlling covariates or excluding anxiety-relevant items from the depression scale. To our knowledge, this is the first study to assess risk preference due to a concave utility function and nonlinear probability weighting separately for depression and anxiety using computational modeling. Our results provide a mechanistic account of risk avoidance and may improve our understanding of decision-making deficits in depression and anxiety. [ABSTRACT FROM AUTHOR]

We analyze the impact of short-run (90 days) and long-run (30 years) earthquake risk on real estate transaction prices in five Japanese cities (Tokyo, Osaka, Nagoya, Fukuoka, and Sapporo), using quarterly data over the period 2006–2015. We exploit a rich panel dataset (331,343 observations) with property characteristics, ward attractiveness information, macroeconomic variables, and long-run seismic hazard data, supplemented with short-run earthquake probabilities generated from a seismic excitation model using historical earthquake occurrences. We design a hedonic property price model that allows for subjective probability weighting, employ a multivariate error components structure, and develop associated maximum likelihood estimation and variance computation procedures. Our approach enables us to identify the total compensation for earthquake risk embedded in property prices, to decompose this into pieces stemming from short-run and long-run risk, and to distinguish between objective and subjectively weighted ("distorted") earthquake probabilities. We find that objective long-run earthquake probabilities have a statistically significant negative impact on property prices, whereas short-run earthquake probabilities become statistically significant only when we allow them to be distorted. The total compensation for earthquake risk amounts to an average –2.0% of log property prices, slightly more than the annual income of a middle-income Japanese household. for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement. [ABSTRACT FROM AUTHOR]

Current decision‐making models assume that an individual's attitude towards risk is unique. Hence, a decision maker's processing of probabilities and the resulting degree of probability weighting should not vary within the domain of risk. This paper provides evidence that challenges this assumption. We conduct two experiments involving different gambles, that is, risky games where objective probabilities are known, no further information‐based advantages exist, and outcomes are independent of knowledge. Even though all probabilities are explicitly provided, we find that individuals exhibit more pronounced inverse‐S‐shaped probability weighting if they perceive their level of expertise regarding a gamble to be lower. This result suggests that individuals are subject to ignorance illusion in decisions under risk, constituting expertise‐dependent risk attitudes. We document that ignorance illusion stems from the wrongly assigned importance of perceived expertise in the decision‐making process and that it occurs in both the gain and the loss domain. [ABSTRACT FROM AUTHOR]

How do people distribute defenses over a directed network attack graph, where they must defend a critical node? This question is of interest to computer scientists, information technology and security professionals. Decision-makers are often subject to behavioral biases that cause them to make sub-optimal defense decisions, which can prove especially costly if the critical node is an essential infrastructure. We posit that non-linear probability weighting is one bias that may lead to sub-optimal decision-making in this environment, and provide an experimental test. We find support for this conjecture, and also identify other empirically important forms of biases such as naive diversification and preferences over the spatial timing of the revelation of an overall successful defense. The latter preference is related to the concept of anticipatory feelings induced by the timing of the resolution of uncertainty. [ABSTRACT FROM AUTHOR]

I study the effect of task difficulty on workers' effort. I find that task difficulty has an inverse-U effect on effort and that this effect is quantitatively large, especially when compared to the effect of conditional monetary rewards. Difficulty acts as a mediator of monetary rewards: conditional rewards are most effective at the intermediate or high levels of difficulty. The inverse-U pattern of effort response to difficulty is inconsistent with many popular models in the literature, including the Expected Utility models with the additively separable cost of effort. I propose an alternative mechanism for the observed behavior based on non-linear probability weighting. I structurally estimate the proposed model and find that it successfully captures the behavioral patterns observed in the data. I discuss the implications of my findings for the design of optimal incentive schemes for workers and for the models of effort provision. [ABSTRACT FROM AUTHOR]

Probability weighting is a marked feature of decision-making under risk. For poor people in rural areas of developing countries, how probabilities are evaluated matters for livelihoods decisions, especially the probabilities associated with losses. Previous studies of risky choice among poor people in developing countries seldom consider losses and do not offer a refined tracking of the probability-weighting function (PWF). We investigate probability weighting among smallholder farmers in Uganda, separately for losses and for gains, using a method (common consequence ladders) that allows refined tracking of the PWF for a population with low levels of literacy. For losses, we find marked probability weighting near zero, which is in line with evidence found in Western labs. For gains, the absence of probability weighting is remarkable, particularly its absence near 100%. We also find marked differences in probability weighting for traditional farmers which are in line with the observed livelihoods strategies in the study area. [ABSTRACT FROM AUTHOR]

Both depressive and anxiety disorders have been associated with excessive risk avoidant behaviors, which are considered an important contributor to the maintenance and recurrence of these disorders. However, given the high comorbidity between the two disorders, their independent association with risk preference remains unclear. Furthermore, due to the involvement of multiple cognitive computational factors in the decision-making tasks employed so far, the precise underlying mechanisms of risk preference are unknown. In the present study, we set out to investigate the common versus unique cognitive computational mechanisms of risk preference in depression and anxiety using a reward-based decision-making task and computational modeling based on economic theories. Specifically, in model-based analysis, we decomposed risk preference into utility sensitivity (a power function) and probability weighting (the one-parameter Prelec weighting function). Multiple linear regression incorporating depression (BDI-II) and anxiety (STAI state anxiety) simultaneously indicated that only depression was associated with one such risk preference parameter, probability weighting. As the symptoms of depression increased, subjects’ tendency to overweight small probabilities and underweight large probabilities decreased. Neither depression nor anxiety was associated with utility sensitivity. These associations remained even after controlling covariates or excluding anxiety-relevant items from the depression scale. To our knowledge, this is the first study to assess risk preference due to a concave utility function and nonlinear probability weighting separately for depression and anxiety using computational modeling. Our results provide a mechanistic account of risk avoidance and may improve our understanding of decision-making deficits in depression and anxiety.

The analysis of alternative decisions and the choice of the optimal – in a given sense – decision is an integral part of people’s purposeful activity in all areas of their social life. Many formal approaches have been proposed to solve these problems. One such approach is expected utility theory, which correctly models individuals’ subjective preferences and attitudes to risk. For a very long time this theory was the leading approach for decision making under conditions of risk. However, numerous practical studies have shown its weakness: the theory did not explicitly use subjective perceptions of decision outcome probabilities in optimal decision-making processes. This research has led to the creation and development of approaches to explicitly consider the probabilities of outcomes in decision making. This paper provides a critical analysis of the descriptive properties of expected utility theory and presents various forms of probability weighting functions. [ABSTRACT FROM AUTHOR]

We study portfolio selection in a complete continuous‐time market where the preference is dictated by the rank‐dependent utility. As such a model is inherently time inconsistent due to the underlying probability weighting, we study the investment behavior of a sophisticated consistent planners who seek (subgame perfect) intra‐personal equilibrium strategies. We provide sufficient conditions under which an equilibrium strategy is a replicating portfolio of a final wealth. We derive this final wealth profile explicitly, which turns out to be in the same form as in the classical Merton model with the market price of risk process properly scaled by a deterministic function in time. We present this scaling function explicitly through the solution to a highly nonlinear and singular ordinary differential equation, whose existence of solutions is established. Finally, we give a necessary and sufficient condition for the scaling function to be smaller than one corresponding to an effective reduction in risk premium due to probability weighting. [ABSTRACT FROM AUTHOR]

This study proposes an approach for modeling travel behavior under uncertainty coupling Cumulative Prospect Theory (CPT) with Multi-attribute Decision Making (MADM) theory. CPT is utilized to depict travelers' evaluations of each attribute, and MADM describes the process of making tradeoffs among multiple conflicting criteria. Divergent perception principles for different attributes are considered in the proposed framework. The proposed approach is utilized for an empirical analysis concerning mode shift behavior for commuting in Shanghai of China, based on data collected by stated preference surveys. Results show that the proposed approach outperforms conventional methods in terms of model performances and behavioral revelations. Empirical results demonstrate that sensitivity to gains and losses in cost and travel time are divergent in mode shift behavior. More importantly, it is found that travelers underestimate the occurrence chances of low-probability travel time and overestimate the occurrence changes of high-probability travel time in mode shift behavior, which is contrary to the findings from economics. Travelers show substantial loss aversion features as well. The heterogeneity in the value functions of CPT is investigated to shed light on differences in the evaluation process among individuals. Results reveal quite different empirical CPT parameters and behavioral mechanisms in mode shift behavior as compared to monetary experiments in economics. It highlights the importance of empirical estimations in various travel choice contexts to essentially understand travel behavior mechanisms, rather than arbitrary usage of findings from economics. [ABSTRACT FROM AUTHOR]

While much literature has focused on preferences regarding risk, preferences over skewness also have significant economic implications. An important and understudied aspect of skewness preferences is how they affect risk taking. In this paper, we design a novel laboratory experiment that elicits certainty equivalents over lotteries where the variance and skewness of the outcomes are orthogonal to each other. This design enables us to cleanly measure both skewness seeking/avoiding and risk taking behavior, and their interaction, without needing to make parametric assumptions. Our experiment includes both left- and right-skewed lotteries. The results reveal that the majority of subjects are skewness avoiding risk takers who correspondingly also take more risk when facing less skewed lotteries. Our second contribution is to link these choices to individual rank-dependent utility preference parameters estimated using a separate lottery choice protocol. Using a latent-class model, we are able to identify two classes of subjects: skewness avoiders with the classic inverse s-shaped probability weighting function and skewness neutral subjects that do not have an inverse s-shaped probability weighting function. Our results thus demonstrate the link between probability distortion and skewness seeking/avoidance choices. They also highlight the importance of accounting for individual heterogeneity. [ABSTRACT FROM AUTHOR]

Odors are strong elicitors of affect, and they play an important role in guiding human behavior, such as avoiding fire or spoiled food. However, little is known about how risky decision making changes when stimuli are olfactory. We investigated this question in an experimental study of risky decision making with unpleasant odors and monetary losses in a fully incentivized task with real outcomes. Odor and monetary decisions were matched so that monetary losses corresponded to the amount of money participants were willing to pay to avoid smelling an odor. Hierarchical Bayesian analyses using prospect theory show that participants were less sensitive to probabilities when gambling with odors than when gambling with money. These results highlight the importance of taking the sensory modality into account when studying risky decision making. [ABSTRACT FROM AUTHOR]

A recent strand of the literature on decision-making under uncertainty has pointed to an intriguing behavioral gap between decisions made from description and decisions made from experience. This study reinvestigates this description-experience gap to understand the impact that sampling experience has on decisions under risk. Our study adopts a complete sampling paradigm to address the lack of control over experienced probabilities by requiring complete sampling without replacement. We also address the roles of utilities and ambiguity, which are central in most current decision models in economics. Thus, our experiment identifies the deviations from expected utility due to over- (or under-) weighting of probabilities. Our results confirm the existence of the behavioral gap, but they provide no evidence for the underweighting of small probabilities within the complete sampling treatment. We find that sampling experience attenuates rather than reverses the inverse S-shaped probability weighting under risk. [ABSTRACT FROM AUTHOR]

We assume that the ex post utility of a regret-sensitive agent facing a menu of lotteries depends upon the payoff of the chosen lottery in the realized state together with the forgone best payoff available in the menu in that state. If two lotteries in the menu have the same distribution of payoffs, the one whose payoff is less statistically concordant with the best alternative yields a larger risk of regret, which should be rejected by regret-risk-averse individuals. This means that regret-risk aversion is equivalent to the supermodularity of the bivariate utility function. We define regret-risk aversion in the small and in the large. We also show that regret-risk aversion tends to induce a bias in favor of the risky act in any one-risky-one-safe menu, in particular when the payoff of the risky choice is highly positively skewed. This is compatible with the "possibility effect" that is well documented in prospect theory. Symmetrically, we define the aversion to rejoicing-risk that can prevail when the ex post utility is alternatively sensitive to the forgone worst payoff. We show that rejoicing-risk-seeking is compatible with the "certainty effect". We finally show that regret-risk-averse and rejoicing-risk-seeking people behave as if they had rank-dependent utility preferences with an inverse-S shaped probability weighting function that reproduces estimates existing in the literature. [ABSTRACT FROM AUTHOR]

We propose a test of the theory of skewness preferences. The probability weighting feature that is the basis of their theory relies on investors overweighting the probability of extreme, positive returns. The resulting investor preferences for positive skewness in return distributions will lead to excess demand, contemporaneous price premiums, and negative expected returns. We use the well-documented 52-week high bias as a method to truncate investors' weighted probability of expected right-tail events. We find evidence supporting the theoretical framework of Barberis and Huang as the negative return premiums associated with positive skewness is driven almost entirely by stocks that are farther away from the their 52-week high. No negative premiums related to skewness are detected when stock prices are close to the 52-week high. [ABSTRACT FROM AUTHOR]

In this paper we estimate the pricing kernel from the Hong Kong index option market and obtain the empirical probability weighting functions based on the rank-dependent expected utility. The empirical pricing kernel is estimated semi-parametrically as the ratio of the risk-neutral and objective densities. We employ a two-step estimation procedure to estimate the objective and risk-neutral densities under a consistent parametric framework of the non-affine generalised autoregressive conditional heteroskedasticity (G.A.R.C.H.) diffusion model. In the first step, we develop a continuous particle filters-based maximum likelihood estimation method to estimate the objective parameters of the G.A.R.C.H. diffusion model using the Hang Seng Index (H.S.I.) returns. In the second step of our estimation, we depart from the usual pure calibration approach and use the H.S.I. option prices to estimate the risk-neutral parameters of the G.A.R.C.H. diffusion model by constraining certain parameters to be consistent with the time-series behaviour of H.S.I. returns. Based on the estimated objective and risk-neutral parameters, the objective and risk-neutral densities are obtained by inverting the corresponding characteristic functions. Empirical results indicate that the empirical pricing kernel estimated from the Hong Kong index option market is non-monotonic and the estimated probability weighting functions are S-shaped, which implies that investors underweight small probability events and overweight large ones. [ABSTRACT FROM AUTHOR]