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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]

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]

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]

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]

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]

This paper provides experimental evidence of the role of higher order risk attitudes—especially prudence—in prevention behavior. Prudence, under an expected utility framework, increases (decreases) self-protection effort compared to the risk neutral level when the risk of losing part of an income exists in a future (the same) period. Motivated by these predictions that give the exact test on prudence, an experiment was designed where subjects go through higher order risk attitude elicitation and make a self-protection decision. In contrast to the expected utility theory, the observed efforts are less than the risk neutral level, regardless of the timing of loss. This violation of expected utility predictions can be explained by probability weighting. [ABSTRACT FROM AUTHOR]

The paper reviews the development of von Neumann and Morgenstern (vNM) utility theory. Kahneman and Tversky’s (KT’s) prospect theory is introduced. The vNM utility function is compared and contrasted with KT’s value function. We prove the uniqueness of two popular utility functions. First, we show that all power utility functions possess constant RRA. And, we show that all exponential utility functions have constant ARA. The paper concludes by discussing applications, strengths and weaknesses of various utility functions. [ABSTRACT FROM AUTHOR]

We present an integrated valuation model for diseases that are life-threatening. The model extends the standard one-period value-per-statistical-life model to three health prospects: healthy, ill, and dead. We derive willingness-to-pay values for prevention efforts that reduce a disease's incidence rate as well as for treatments that lower the corresponding health deterioration and mortality rates. We find that the demand value of prevention always exceeds that of treatment. People often overweight small risks and underweight large ones. We use the rank dependent utility framework to explore how the demand for prevention and treatment alters when people evaluate probabilities in a non-linear manner. For incidence and mortality rates associated with common types of cancers, the inverse-S shaped probability weighting found in experimental studies leads to a significant increase in the demand values of both treatment and prevention. [ABSTRACT FROM AUTHOR]

Multiple price lists have emerged as a simple and popular method for eliciting risk preferences. Despite their popularity, a key downside of multiple price lists has not been widely recognized - namely that the approach is unlikely to generate sufficient information to accurately identify different dimensions of risk preferences. The most popular theories of decision making under risk posit that preferences for risk are driven by a combination of two factors: the curvature of the utility function and the extent to which probabilities are weighted non-linearly. In this paper, we show that the widely used multiple price list introduced by Holt and Laury ( The American Economic Review 92(5) 1644-1655 2002) is likely more accurate at eliciting the shape of the probability weighting function, and we construct a different multiple price list that is likely more accurate at eliciting the shape of the utility function. We show that by combining information from different multiple price lists, greater predictive performance can be achieved. [ABSTRACT FROM AUTHOR]

This paper examines how risk preferences and loss aversion affect individual choices regarding environmental risks, specifically forest wildfires in Poland. We also examine how the same individuals make choices in the context of financial risks. Estimating risk, loss aversion and weighting probability parameters allows us to directly test whether Prospect Theory or Expected Utility Theory is the better underlying behavioural model in both domains. We find that in a sample consisting of a general population of Poles, the majority of respondents demonstrate behaviour consistent with Prospect Theory in both environmental and financial domains. This finding has significant implications for future non-market valuation studies. Additionally, in this study, we find evidence for similar risk preferences across those two domains. [ABSTRACT FROM AUTHOR]

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, ; Baucells and Heukamp, Management Science 52:1409-1423, ). 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. [ABSTRACT FROM AUTHOR]

In this article, we determine the optimal design of lottery-linked savings (LLS) programmes. LLS vehicles, such as lottery bonds, are financial instruments that preserve depositors’ principal but provide randomized variable returns to these depositors through periodic lottery drawings,in lieuof the regular coupon payments traditionally received by bondholders. This type of asset is very popular in Europe. We note that the framing of LLS instruments is linked to their popularity, and we attempt to elucidate that link and thereby determine the optimal structure of payments for LLS programmes. Our goal is to frame LLS programmes in a manner that both maximizes their investors’ satisfaction and preserves their ability to serve as inexpensive sources of capital for their issuers. We demonstrate that the optimal pay-off structure is characterized by a high level of skewness, as investors are willing to accept a decrease in the small and medium prizes of the lottery in exchange for an increase in the grand prize. Thus, to attract a maximum number of depositors, the issuers of LLS programmes should prioritize the jackpot size relative to the other lottery pay-offs and insist on high skewness for the lottery pay-offs relating to the LLS assets. [ABSTRACT FROM PUBLISHER]

Probability weighting functions relate objective probabilities and their subjective weights, and play a central role in modeling choices under risk within cumulative prospect theory. While several different parametric forms have been proposed, their qualitative similarities make it challenging to discriminate among them empirically. In this paper, we use both simulation and choice experiments to investigate the extent to which different parametric forms of the probability weighting function can be discriminated using adaptive design optimization, a computer-based methodology that identifies and exploits model differences for the purpose of model discrimination. The simulation experiments show that the correct (data-generating) form can be conclusively discriminated from its competitors. The results of an empirical experiment reveal heterogeneity between participants in terms of the functional form, with two models (Prelec-2, Linear-in-Log-Odds) emerging as the most common best-fitting models. The findings shed light on assumptions underlying these models. [ABSTRACT FROM AUTHOR]

This paper investigates whether preferences over environmental risks are best modeled using probability-weighted utility functions or can be reasonably approximated by expected utility (EU) or subjective EU models as is typically assumed. I elicit risk attitudes in the financial and environmental domains using multiple-price list experiment. I examine how subjects' behavioral, attitudinal, and demographic characteristics affect their probability weighting functions first for financial risks, then for oil-spill risks. I find that most subjects tend to overweight extreme positive outcomes relative to expected utility in both the environmental and financial domains. Subjects are more likely to overemphasize low probability, extreme environmental outcomes than low probability, extreme financial outcomes, leading subjects to offer more support for mitigating environmental gambles than financial gambles with the same odds and equivalent outcomes. I conclude that EU models are likely to underestimate subjects' willingness to pay for environmental cleanup programs or policies with uncertain outcomes. [ABSTRACT FROM AUTHOR]

A large body of experimental research has demonstrated that, on average, people violate the axioms of expected utility theory as well as of discounted utility theory. In particular, aggregate behavior is best characterized by probability distortions and hyperbolic discounting. But is it the same people who are prone to these behaviors? Based on an experiment with salient monetary incentives we demonstrate that there is a strong and significant relationship between greater departures from linear probability weighting and the degree of decreasing discount rates at the level of individual behavior. We argue that this relationship can be rationalized by the uncertainty inherent in any future event, linking discounting behavior directly to risk preferences. Consequently, decreasing discount rates may be generated by people's proneness to probability distortions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The main goal of the experimental study described in this paper is to investigate the sensitivity of probability weighting to the payoff structure of the gambling situation—namely the level of consequences at stake and the spacing between them—in the loss domain. For that purpose, three kinds of gambles are introduced: two kinds of homogeneous gambles (involving either small or large losses), and heterogeneous gambles involving both large and small losses. The findings suggest that at least for moderate/high probability of loss do both ‘level’ and ‘spacing’ effects reach significance, with the impact of ‘spacing’ being both opposite to and stronger than the impact of ‘level’. As compared to small-loss gambles, large-loss gambles appear to enhance probabilistic optimism, while heterogeneous gambles tend to increase pessimism. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]