A parametric analysis of prospect theory’s functionals for the general population

This article presents the results of an experiment that completely measures the utility function and probability weighting function for different positive and negative monetary outcomes, using a representative sample of N = 1,935 from the general public. The results confirm earlier findings in the lab, suggesting that utility is less pronounced than what is found in classical measurements where expected utility is assumed. Utility for losses is found to be convex, consistent with diminishing sensitivity, and the obtained loss-aversion coefficient of 1.6 is moderate but in agreement with contemporary evidence. The estimated probability weighting functions have an inverse-S shape and they imply pessimism in both domains. These results show that probability weighting is also an important phenomenon in the general population. Women and lower educated individuals are found to be more risk averse, in agreement with common findings. In contrast to previous studies that ascribed gender differences in risk attitudes solely to differences in the degree utility curvature, however, our results show that this finding is primarily driven by loss aversion and, for women, also by a more pessimistic psychological response toward the probability of obtaining the best possible outcome.     

Emotional balance and probability weighting

We find suggestive evidence that emotional balance has an impact on probability weighting incremental to demographic controls. Specifically, low negative affectivity (implying high emotional balance) tends to be a characteristic of those whose probability weighting functions exhibit lower curvature and more neutral elevation. In other words, emotional balance seems to push people in the direction of normative expected utility theory.     

Rationality on the rise: Why relative risk aversion increases with stake size

How does risk tolerance vary with stake size? This important question cannot be adequately answered if framing effects, nonlinear probability weighting, and heterogeneity of preference types are neglected. We show that the observed increase in relative risk aversion over gains cannot be captured by the curvature of the value function. Rather, it is predominantly driven by a change in probability weighting of a majority group of individuals who weight probabilities of high gains more conservatively. Contrary to gains, no coherent change in relative risk aversion is observed for losses. These results not only challenge expected utility theory, but also prospect theory.     

Is Probability Weighting Sensitive to the Magnitude of Consequences? An Experimental Investigation on Losses

Experimental investigations of the probability weighting function over losses are scarce and all involve small payoffs. The paper aims to give new insight into the probability weighting function for losses, by eliciting it through a simple two-stage semi-parametric procedure over more realistic losses, and by investigating its sensitivity to the magnitude of the payoffs. Current data confirm previous evidence of convex utility functions and inverse-S-shaped weighting functions. Still, at least for small probabilities, probability weighting appears to be affected by the size of consequences: the larger the losses, the more aversive the gambles and the more pessimistic the subjects are.     

Common Consequence Conditions in Decision Making under Risk

We generalize the Allais common consequence effect by describing three common consequence effect conditions and characterizing their implications for the probability weighting function in rank-dependent expected utility. The three conditions—horizontal, vertical, and diagonal shifts within the probability triangle—are necessary and sufficient for different curvature properties of the probability weighting function. The first two conditions, shifts in probability mass from the lowest to middle outcomes and middle to highest outcomes respectively, are alternative conditions for concavity and convexity of the weighting function. The third condition, decreasing Pratt-Arrow absolute concavity, is consistent with recently proposed weighting functions. The three conditions collectively characterize where indifference curves fan out and where they fan in. The common consequence conditions indicate that for nonlinear weighting functions in the context of rank-dependent expected utility, there must exist a region where indifference curves fan out in one direction and fan in the other direction.     

Probability weighting and the ‘level’ and ‘spacing’ of outcomes: An experimental study over losses

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.

Preferences for information on probabilities versus prizes: The role of risk-taking attitudes

Many real-world decisions entail choices between information on either probabilities or payoffs (i.e., prizes). Simplified versions of such decisions are examined to gain insight into preferences for different types of information as a function of risk-attitudes. General and simple decision rules are derived for cases where the utility function is concave (or convex) over the relevant payoff interval.The article further describes several experiments to test business students' intuitions concerning these optimal decision rules. In general, risk-taking attitudes did not correlate significantly with subjects' preferences for information, in violation of theorems regarding mean-preserving spreads of risk. Other tests, e.g., narrowing certain probability ranges, also resulted in preferences contrary to expected utility (EU) theory.     

It is Whether You Win or Lose: The Importance of the Overall Probabilities of Winning or Losing in Risky Choice

Imagine that you own a five-outcome gamble with the following payoffs and probabilities: ($100, .20; $50, .20; Imagine that you own a five-outcome gamble with the following payoffs and probabilities: ($100, .20; $50, .20; $0, .20; –$25, .20; –$50, .20). What happens when the opportunity to improve such a gamble is provided by a manipulation that adds value to one outcome versus another outcome, particularly when the opportunity to add value to one outcome versus another outcome changes the overall probability of a gain or the overall probability of a loss? Such a choice provides a simple test of the expected utility model (EU), original prospect theory (OPT), and cumulative prospect theory (CPT). A study of risky choices involving 375 respondents indicates that respondents were most sensitive to changes in outcome values that either increased the overall probability of a strict gain or decreased the overall probability of a strict loss. These results indicate more support for OPT rather than CPT and EU under various assumptions about the shape of the utility and value and weighting functions. Most importantly, the main difference between the various expectation models of risky choice occurs for outcomes near the reference value. A second study of risky choice involving 151 respondents again demonstrated the sensitivity of subjects to reducing the probability of a strict loss even at the cost of reduced expected value. Consequently, we argue that theories of how people choose among gambles that involve three or more consequences with both gains and losses need to include measures of the overall probabilities of a gain and of a loss.JEL Classification  D81     

What can multiple price lists really tell us about risk preferences?

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.     

Pessimism and optimism towards new discoveries

Theory and Decision - In this paper, we provide an axiomatic foundation of pessimism and optimism towards ambiguity that emerges due to growing awareness. In our setup, this corresponds to a...     

Expected utility with ambiguous probabilities and ‘irrational’ parameters

Savage's expected utility theory has been criticized for various reasons. Two of these are: (1) Subjective probabilities may be more or less ambiguous; this may affect the preference order. Savage's theory rules out any such effect. (2) Savage's theory rules out any influence of certain parameters of a probability distribution on the preference order. Such parameters are fractiles or pairs of fractiles, e.g., which have gained widespread attention as risk measures.This paper generalizes expected utility theory to include effects of ambiguity and those parameters on the preference order. Basic to this generalization is the classic paper by Herstein/Milnor.     

Rethinking Risk Attitude: Aspiration as Pure Risk

There exists no completely satisfactory theory of risk attitude in current normative decision theories. Existing notions confound attitudes to pure risk with unrelated psychological factors such as strength of preference for certain outcomes, and probability weighting. In addition traditional measures of risk attitude frequently cannot be applied to non-numerical consequences, and are not psychologically intuitive. I develop Pure Risk theory which resolves these problems – it is consistent with existing normative theories, and both internalises and generalises the intuitive notion of risk being related to the probability of not achieving one’s aspirations. Existing models which ignore pure risk attitudes may be misspecified, and effects hitherto modelled as loss aversion or utility curvature may be due instead to Pure Risk attitudes.     

Subjective utility with upper and lower probabilities on finite states

This article is concerned with thresholds of discrimination of preference judgments under uncertainty. We establish an axiomatic characterization for a threshold representation, where thresholds are represented by inexact measurement of subjective probabilities, i.e., upper and lower probabilities. Since upper and lower probabilities need not be additive, the representational form adopts the Choquet integration.     

Covid-19 in Central America: Firm resilience and policy responses on employment

This paper examines how government support interacts with firm-level resilience capabilities in the reduction of layoffs among formal firms in Central America. Our analysis suggests that government support measures play a role in reducing the probability of layoffs among firms with only dynamic resilience capabilities (i.e., those that are developed after the pandemic onset). The effect of government support is not statistically different from the effect of static resilience capabilities alone (i.e., those that were present before the pandemic); thus, in firms with such capabilities, the effect of government support will be marginal. These results hold across sectors - exhibiting a marginally higher treatment effect in service sectors. Our results do not imply that Covid-19 supportive measures are to be disregarded, but instead raise the question of how government support policies could improve the allocation of support among firms in times of crises. Moreover, it underlines the necessity of policies that enhance resilience more broadly – a task that hints at structural issues and requires continuous government support in lieu of ad-hoc measures.     

Resolving Rabin’s paradox

We present a theoretical model of Rabin’s famous calibration paradox that resolves confusions in the literature and that makes it possible to identify the causes of the paradox. Using suitable experimental stimuli, we show that the paradox truly violates expected utility and that it is caused by reference dependence. Rabin already showed that utility curvature alone cannot explain his paradox. We, more strongly, do not find any contribution of utility curvature to the explanation of the paradox. We find no contribution of probability weighting either. We conclude that Rabin’s paradox underscores the importance of reference dependence.

     

Information,risk perceptions,and smoking choices of youth

Conventional wisdom maintains that youths take risks because they underestimate probabilities of harm. Presumably if they knew the true probabilities, they would behave differently. We used the National Longitudinal Survey of Youth 1997 to assess whether differences between subjective and objective probabilities that an adverse outcome to self will occur are systematically related to a harmful behavior, initiating smoking. We find that youths are generally pessimistic about probabilities of their own deaths and being violent crime victims. After smoking initiation, youths increase subjective probabilities of death by more than the objective increase in mortality risk, implying recognition of potential harms. Virtually all 12–14 year-olds know that smoking causes heart disease. The minority who believe that smoking causes AIDS are less likely to become smokers; i.e., risk misperceptions deter rather than cause smoking initiation. Messages designed to deter smoking initiation should stress other disadvantages of smoking than just probabilities of harm.     

Are people overoptimistic about the effects of heavy drinking?

We test whether heavy or binge drinkers are overly optimistic about probabilities of adverse consequences from these activities or are relatively accurate about these probabilities. Using data from a survey in eight cities, we evaluate the relationship between subjective beliefs and drinking. We assess accuracy of beliefs about several outcomes of heavy/binge drinking: reduced longevity, liver disease onset, link between alcohol consumption and Driving While Intoxicated (DWI), probability of an accident after drinking, accuracy of beliefs about encountering intoxicated drivers on the road, and legal consequences of DWI—ranging from being stopped to receiving fines and jail terms. Overall, there is no empirical support for the optimism bias hypothesis. We do find that persons consuming a lot of alcohol tend to be more overconfident about their driving abilities and ability to handle alcohol. However, such overconfidence does not translate into over-optimism about consequences of high levels of alcohol consumption.     

Discriminating among probability weighting functions using adaptive design optimization

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.     

叔本华和尼采哲学比较研究

叔本华和尼采同为19世纪著名的意志主义者,他们的哲学思想存在着明显的时代烙印。他们同是对生活持悲观的态度,但他们在摆脱痛苦的途径上却不同,叔本华采取的是否定生命,而尼采则是对生命的肯定,这样就出现了生存意志和强力意志、悲观主义和乐观主义的差异。     

Gender, Financial Risk, and Probability Weights

Women are commonly stereotyped as more risk averse than men in financial decision making. In this paper we examine whether this stereotype reflects gender differences in actual risk-taking behavior by means of a laboratory experiment with monetary incentives. Gender differences in risk taking may be due to differences in valuations of outcomes or in probability weights. The results of our experiment indicate that value functions do not differ significantly between men and women. Men and women differ in their probability weighting schemes, however. In general, women tend to be less sensitive to probability changes. They also tend to underestimate large probabilities of gains more strongly than do men. This effect is particularly pronounced when the decisions are framed in investment terms. As a result, women appear to be more risk averse than men in specific circumstances.