Rank-dependent Utility Theory Research Articles

A Feasible Estimation of a “Corrected” EQ-5D Social Tariff

ObjectivesTo demonstrate the feasibility of estimating a social tariff free of utility curvature and probability weighting biases and to test transferability between riskless and risky contexts. MethodsValuations for a selection of EQ-5D-3L health states were collected from a large and representative sample (N = 1676) of the Spanish general population through computer-assisted personal interviewing. Two elicitation methods were used: the traditional time trade-off (TTO) and a novel risky-TTO procedure. Both methods are equivalent for better than death states, which allowed us to test transferability of utilities across riskless and risky contexts. Corrective procedures applied are based on rank-dependent utility theory, identifying parameter estimates at the individual level. All corrections are health-state specific, which is a unique feature of our corrective approach. ResultsTwo corrected value sets for the EQ-5D-3L system are estimated, highlighting the feasibility of developing national tariffs under nonexpected utility theories, such as rank-dependent utility. Furthermore, transferability was not supported for at least half of the health states valued by our sample. ConclusionsIt is feasible to estimate a social tariff by using interviewing techniques, sample sizes, and sample representativeness equivalent to prior studies designed to generate national value sets for the EQ-5D. Utilities obtained in distinct contexts may not be interchangeable. Our findings caution against routinely taking transferability of utility for granted.

Assessing key behavioural theories of drought risk adaptation: Evidence from rural Kenya.

The Horn of Africa Drylands are increasingly experiencing severe droughts, which impose a threat on traditional livelihood strategies. Understanding adaptation behavior in rural communities is key to helping reduce the impact of these droughts. We investigate adaptation behavior by assessing four established economic and social psychological theories on decision making under risk: expected utility theory (EUT), rank dependent utility theory (RDU), protection motivation theory (PMT), and theory of planned behavior (PMT). To measure adaptation behavior and the theory constructs, we conducted a household survey in Kenya (N=502). Regression analysis shows that the economic theories (EUT and RDU) have the best fit for our data. Risk and time preferences are found to play an important role in adaptation decisions. An analysis of differences in decision making for distinct types of adaptation measures shows that risk averse (agro-)pastoralists are more likely to implement adaptation measures that are adjustments to their current livelihood practices, and less willing to invest in adaptation measures that require a shift to other livelihood activities. Moreover, we find significant effects for elements of the social psychological theories (PMT and TPB). A person's belief in their own ability to implement an adaptation measure (perceived self-efficacy) and adaptation by family and friends are important factors in explaining adaptation decisions. Finally, we find that the type of adaptation measures that people implement is influenced by, among others, gender, education level, access to financial resources, and access to government support or aid. Our analysis gives insights into the drivers of individual adaptation decisions, which can enhance policies promoting adaptation of dryland communities.

On the psychology of the relation between optimism and risk taking

In this paper, we provide an explanation for why risk taking is related to optimism. Using a laboratory experiment, we show that the degree of optimism predicts whether people tend to focus on the positive or negative outcomes of risky decisions. While optimists tend to focus on the good outcomes, pessimists focus on the bad outcomes of risk. The tendency to focus on good or bad outcomes of risk in turn affects both the self-reported willingness to take risk and actual risk taking behavior. This suggests that dispositional optimism may affect risk taking mainly by shifting attention to specific outcomes rather than causing misperception of probabilities. In a second study we find evidence that dispositional optimism is related to elicited parameters of rank dependent utility theory suggesting that focusing may be among the psychological determinants of decision weights. Finally, we corroborate our findings with process data related to focusing showing that optimists tend to remember more and attend more to good outcomes and this in turn affects their risk taking.

Optimal sourcing decisions considering quantity constraints under rank-dependent utility theory

To improve profits, retailers can order products from two suppliers: one cheap supplier with a long lead time and one quick-response supplier with a high cost. Business practices and empirical investigations have shown that retailers’ actual ordering decisions often deviate from expected utility due to behavioural factors. This paper investigates a sourcing problem for a retailer from two manufacturers with different lead times and costs under quantity constraints considering rank-dependent utility theory (RDEU). RDEU involves behavioural factors, including loss aversion, reference profit and weighting of probabilities. For this problem, we build a two-stage ordering model and derive the optimal ordering decisions before and during the selling season by using convex optimisation methods. We characterise the optimal ordering decisions of the retailer under RDEU considering different quantity constraints. We compare the results with those under the expected utility theory (EUT). We analyse the effects of behavioural factors on the retailer’s ordering decisions. It is found that when the selling price is larger, a retailer will always order more from the manufacturers before the selling season under EUT but may order less under RDEU when facing demand uncertainty and quantity constraints during the selling season. Additionally, when the selling price is high, the loss-averse retailer should order more than the risk-neutral retailer to avoid inventory shortage. A higher degree of loss averseness will induce the retailer to delay placing orders to gain more demand information and reduce the possibility of stock out or overstock.

Predicting Behavior in Games: Loss Aversion vs. Rank Dependent Utility vs. Range Utility Theory

Predicting Behavior in Games: Loss Aversion vs. Rank Dependent Utility vs. Range Utility Theory

All at once! A comprehensive and tractable semi-parametric method to elicit prospect theory components

Eliciting all the components of prospect theory – curvature of the utility function, weighting function and loss aversion – remains an open empirical challenge. We develop a semi-parametric method that keeps the tractability of parametric methods while providing more precise estimates. Applying the new method to the datasets of Tversky and Kahneman (1992) and Bruhin et al. (2010), we reject the convexity of the utility function in the loss domain and show that the probability weighting function does not exhibit duality and equality across domains, in line with cumulative prospect theory and in contrast with original prospect and rank dependent utility theories. Furthermore, our method highlights that the overweighting of tail probabilities is more pronounced in the gain domain than in the loss domain. Overall, our results show that the utility function varies little across domains, thus suggesting that probability distortions are key to capture differences in risk attitudes in the gain and loss domains.

Fractional stochastic dominance in rank-dependent utility and cumulative prospect theory

Two notions of fractional stochastic dominance (SD) were recently proposed by Müller et al. (2017) and Huang et al. (2020) based on mean-reducing spreads and the coefficient of absolute risk aversion, respectively. We formulate a general class of fractional SD generated by a convex transform, which includes those built from absolute or relative risk aversion as special cases, and this serves as a convenient technical tool for construction of new notions of fractional SD. We obtain equivalent conditions for a preference modeled by rank-dependent utility or cumulative prospect theory to be consistent with each notion of fractional SD. Furthermore, we provide an empirical estimator for the parameters in fractional SD relationships, and we illustrate this with a financial data analysis.

Moral-hazard-free insurance: mean-variance premium principle and rank-dependent utility theory

This paper investigates a Pareto-optimal insurance problem, where the insured maximizes her rank-dependent utility preference and the insurer is risk-neutral and employs the mean-variance premium principle. To eliminate potential moral hazard issues, we only consider the so-called moral-hazard-free insurance contracts that obey the incentive compatibility constraint. The insurance problem is first formulated as a non-concave maximization problem involving Choquet expectation, then turned into a concave quantile optimization problem and finally solved by the calculus of variations method. The optimal contract is expressed by a semi-linear second-order double-obstacle ordinary differential equation with nonlocal operator. An effective numerical method is proposed to compute the optimal contract assuming the probability weighting function has a density. Also, we provide an example that is analytically solved.

Quantum decision theory augments rank-dependent expected utility and Cumulative Prospect Theory

Using experimental data on choices between pairs of lotteries, we compare a new parameterized Quantum Decision Theory (QDT) with Rank Dependent Utility Theory (RDU) and Cumulative Prospect Theory (CPT). At the aggregate level, CPT-based QDT outperforms. At the individual level, the considerable heterogeneity across subjects is best described by the RDU-based QDT, at odds with the conclusion using the representative agent approach. The quantum attraction factor thus plays a key role in describing subjects’ behaviors at both levels. A large fraction of subjects exhibit temporal stability of asset integration attitudes. Another significant fraction of subjects are diagnosed to be using mixtures of mental models, which are elicited selectively depending on the nature of the presented choice alternatives. • The quantum factor plays a key role in describing human risky choices. • Significant differences between aggregate and individual level analysis. • Stability of asset integration pattern over time. • Hierarchical maximum likelihood estimation.

Concave/convex weighting and utility functions for risk: A new light on classical theorems

This paper analyzes concave and convex utility and probability distortion functions for decision under risk (law-invariant functionals). We characterize concave utility for virtually all existing models, and concave/convex probability distortion functions for rank-dependent utility and prospect theory in complete generality, through an appealing and well-known condition (convexity of preference, i.e., quasiconcavity of the functional). Unlike preceding results, we do not need to presuppose any continuity, let be differentiability.An example of a new light shed on classical results: whereas, in general, convexity/concavity with respect to probability mixing is mathematically distinct from convexity/concavity with respect to outcome mixing, in Yaari's dual theory (i.e., Wang's premium principle) these conditions are not only dual, as was well-known, but also logically equivalent, which had not been known before.

Estimation and Comparison Between Rank-Dependent Expected Utility, Cumulative Prospect Theory and Quantum Decision Theory

We propose a new parametrization of Quantum Decision Theory (QDT), based on Rank Dependent Utility Theory (RDU). Using experimental data made of choices between pairs of lotteries, we compare QDT with decision theories, RDU and Cumulative Prospect Theory (CPT). At the aggregate level, calibrating together all decisions performed by all subjects (representative agent approach), we find that CPT-based QDT outperforms, with the quantum models always improving their classical counterpart. At the individual level, adopting a hierarchical maximum likelihood estimation to avoid overfitting, we classify decision makers as either RDU, RDU-based QDT, CPT or CPT-based QDT. Our major findings are the following: the quantum attraction factor plays a key role in describing subjects’ behaviors; there is a considerable heterogeneity across subjects, at odds with the representative agent approach; RDU and RDU-based QDT describe a larger fraction of subjects than CPT and CPT-based QDT, again at odds with the conclusion using the representative agent approach; a temporal stability of asset integration attitudes is found for a good fraction of the subjects; another significant fraction of subjects may be using mixtures of mental models, which are elicited selectively depending on the nature of the presented choice alternatives.

Decisions under risk: Dispersion and skewness

When people take decisions under risk, it is not only the expected utility that is important, but also the shape of the distribution of utility: clearly the dispersion is important, but also the skewness. For given mean and dispersion, decision-makers treat positively and negatively skewed prospects differently. This paper presents a new behaviourally-inspired model for decision making under risk, incorporating both dispersion and skewness. We run a horse race of this new model against six other models of decision making under risk and show that it outperforms many in terms of goodness of fit and shows a reasonable performance in predictive ability. It can incorporate the prominent anomalies of standard theory such as the Allais paradox, the valuation gap, and preference reversals, and also the behavioural patterns observed in experiments that cannot be explained by Rank Dependent Utility Theory.

Effects of Household Shocks on Risk Preferences and Loss Aversion: Evidence from Upland Smallholders of South East Asia

Avoiding risk in financial decisions is credited to be a key contributor to persistent poverty and poverty traps. In spite of this, the methods used to measure behaviour under risk rarely reflect an adequate representation of the lives of smallholders in low income economies. We estimate risk preferences and their determinants by including two key aspects: aversion to losses and exposure to long term risk and vulnerability. We examine risk preferences of 93 smallholders in Cambodia and 91 smallholders in Lao PDR with an incentivised lottery design under the framework of Expected Utility Theory (EUT), Rank Dependent Utility Theory (RDU) and Cumulative Prospect Theory (CPT). We find that CPT best explains our data, but parameter values vary to those most commonly found in the literature. We report that the experience of household shocks have a significant effect on choice behaviour in the loss domain, even when we control for a large set of socio-economic and demographic variables.

A rank-dependent utility approach to model intra- and inter-individual heterogeneity in risky choice behaviours

ABSTRACT Using a stated preferences survey, the objective of this paper is to investigate the intra- and inter-individual heterogeneity of mode choice, when travel time is subject to variability. By‘inter-individual heterogeneity’ is meant that people are different in terms of attitude to risk and have different utility functions. By ‘intra-individual heterogeneity’ is meant that the behaviour may be different even when performed by the same individual when faced with a different mode of transport. Based on Rank-Dependent Utility Theory, the paper shows that the occurrence of delays associated with train trips is overestimated whereas they are underestimated for car trips. A latent-class logit model offers a somewhat different perspective: if, overall, car users are more likely to perceive possible delays for train trips than for car trips, train users tend to consider the objective occurrence of delays as they are presented in the survey and adopt a risk neutral choice behaviour.

All at Once! A Comprehensive and Tractable Semi-Parametric Method to Elicit Prospect Theory Components

Eliciting all the components of prospect theory –curvature of the utility function, weighting function and loss aversion– remains an open empirical challenge. We develop a semi-parametric method that keeps the tractability of parametric methods while providing more precise estimates. Using the data of Tversky and Kahneman (1992), we revisit their main parametric results. We reject the convexity of the utility function in the loss domain, find lower probability weighting, and confirm loss aversion. We also report that the probability weighting function does not exhibit duality and equality across domains, in line with cumulative prospect theory and in contrast with original prospect and rank dependent utility theories.

Estimating uncertainty aversion using the source method in stylized tasks with varying degrees of uncertainty

The source method provides a tractable way to analyze uncertainty aversion using source functions. In this analytical framework, uncertainty aversion is defined using the index of pessimism and the index of likelihood insensitivity. The focus of this paper is to use the source method to examine how uncertainty aversion differs across events that have the same underlying objective probabilities but are presented under varying degrees of uncertainty. In a controlled laboratory setting, subjects are presented with three lottery tasks that are ranked in order of increasing uncertainty. Given the choices observed in each task, a “source function” is estimated jointly with risk attitudes assuming Rank-Dependent Utility Theory under different probability weighting specifications for the source function. Results from the Prelec (Prelec (1998)) specification suggest that, as the degree of uncertainty increases, subjects display increasing pessimism; in contrast, the Tversky-Kahneman (Tversky-Kahneman (1992)) and the Power specifications detect no such difference. Thus, conclusions regarding uncertainty aversion are contingent upon which probability weighting specification is assumed for the source function, and caution should be taken when selecting specifications for the source function.

Beliefs and preferences for food-safety policies: a discrete choice model under uncertainty

Abstract Outcomes of food policies are highly uncertain. Therefore, the public’s support for these policies depends on individuals’ beliefs and the provision of scientific information. Using data collected from a discrete choice experiment survey, we explore whether new information regarding a food-safety policy influences respondents’ support, while controlling for risk and time preferences. Additionally, we examine if support depends on whether information is perceived as either good or bad news. Results from the estimation of parametric error component logit models, based on expected utility theory and rank dependent utility theory, suggest that good and bad news affects preferences and welfare measures.

Portfolio choice in personal equilibrium

This paper finds that in portfolio choice where reference point arises endogenously in personal equilibria, investors behave as if they had a concave probability weighting function. This finding establishes a link between the reference-dependent utility and the rank-dependent utility theories.

Decisions Under Risk Dispersion and Skewness

When people take decisions under risk, it is not only the expected utility that is important, but also the shape of the distribution of utility: clearly the dispersion is important, but also the skewness. For given mean and dispersion, decision-makers treat positively and negatively skewed prospects differently. This paper presents a new behaviourally-inspired model for decision making under risk, incorporating both dispersion and skewness. We run a horse-race of this new model against six other models of decision-making under risk and show that it outperforms many in terms of goodness of fit and shows a reasonable performance in predictive ability. It can incorporate the prominent anomalies of standard theory such as the Allais paradox, the valuation gap, and preference reversals, and also the behavioural patterns observed in experiments that cannot be explained by Rank Dependent Utility Theory.

A second-generation disappointment aversion theory of decision making under risk

This paper presents a new decision theory for modelling choice under risk. The new theory is a two-parameter generalization of expected utility theory. The proposed theory assumes that a decision maker: (1) behaves as if maximizing expected utility; but (2) may experience disappointment (elation) when the utility of a lottery’s outcome falls short of (exceeds) the expected utility of the lottery; and (3) may have a preference for gambling (attraction/aversion to positively/negatively skewed lotteries). The proposed theory can rationalize the fourfold pattern of risk attitudes; the common ratio effect and the reverse thereof (in certain types of decision problems); the Allais paradox in classical common consequence problems and the reverse Allais paradox—in common consequence problems with an even split of a probability mass; violations of the betweenness axiom; switching behavior in the Samuelson’s example; violations of ordinal, upper and lower cumulative independence (which falsify rank-dependent utility and cumulative prospect theory); and preference reversals between valuations and choice. In application to insurance, the theory can rationalize full insurance with an actuarially unfair premium and aversion to probabilistic insurance. In application to optimal portfolio investment, the theory can rationalize the equity premium puzzle.