Non-expected Utility Theories 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.

Behavioral Theories That Have Influenced the Way Health State Preferences Are Elicited and Interpreted: A Bibliometric Mapping Analysis of the Time Trade-Off Method With VOSviewer Visualization.

The aim of this paper is to develop an understanding of how behavioral theories have influenced the way preferences for health-related quality of life are elicited and interpreted. We focus on the Time Trade-off (TTO) method given it represents the quality-adjusted life-year (QALY) concept-that survival in less-than-full health can be deemed equivalent to a shorter survival in full health. To our knowledge this is the first review using a combination of systematic scoping review, bibliometrics and VOSviewer visualization to map the development of ideas in health economics. A priori, we selected three behavioral theories to explore within our review, referred to here as Expected Utility Theory, Non-Expected Utility Theory and Probabilistic Choice Theory. A fourth topic, Order Effects, is defined broadly to encompass behavioral theories around timing/sequence of events. For the main search, Scopus was used to identify literature that had (a) elicited TTO values and/or (b) contributed to the way TTO values were elicited and interpreted, from inception to July 2021. Papers that focused on the latter category were given the label "behavioral" and underwent additional analyses. A two stage-screening was applied to assess eligibility. Co-citation, co-authorship and co-occurrence of keywords was used to chart the development of TTO over time. A total of 1,727 records were retrieved from Scopus and were supplemented by an additional 188 papers. There were 856 applied and 280 behavioral papers included in the final corpus, with the behavioral set split equally into four sets of 70 papers to chart the development of keywords over time: (1) 1972-1999; (2) 2000-2010, (3) 2010-2015 and (4) 2015-2021. The keyword analysis suggested that whilst some ideas transition quickly from economic theory to the TTO literature, such as the impact of Order Effects, others take longer to be assimilated, for example Non-Expected Utility models or failure of constant discounting. It is therefore important that researchers within health economics work more closely with those in mainstream economics and keep abreast of the wider economics and behavioral sciences to expedite the uptake of new and relevant ideas.

On the indeterminacy of the representation of beliefs by probabilities

This paper examines the indeterminacy of the representations of beliefs by subjective probabilities in non-expected utility theories of decision making under uncertainty. These theories include the rank-dependent utility models, probabilistically sophisticated choice and probabilistic sophistication based on event exchangeability.

Calibrated uncertainty

We define a binary relation (qualitative uncertainty assessment) that describes the shared likelihood assessments of decision makers with diverse ambiguity attitudes. Ambiguity renders this binary relation incomplete. Our axioms yield a representation according to which A is more likely than B if and only if a capacity, called uncertainty measure, assigns a higher value to A than to B and a higher value to B-complement than to A-complement. Agents combine this uncertainty perception with their uncertainty attitude to form a complete ranking of bets. We provide a representation theorem for this extended model, show that its parameters are uniquely identified and characterize a new measure of comparative ambiguity aversion. For general acts, we modify Machina and Schmeidler's (1992) sophistication axiom to allow for ambiguity and analyze three nested extensions: first, we axiomatize a minimal extension which reduces to expected utility when there is no ambiguity; the second and third extensions show how non-expected utility theories can be accommodated in our framework.

Utilitarianism with and without expected utility

We give two social aggregation theorems under conditions of risk, one for constant population cases, the other an extension to variable populations. Intra and interpersonal welfare comparisons are encoded in a single ‘individual preorder’. The theorems give axioms that uniquely determine a social preorder in terms of this individual preorder. The social preorders described by these theorems have features that may be considered characteristic of Harsanyi-style utilitarianism, such as indifference to ex ante and ex post equality. However, the theorems are also consistent with the rejection of all of the expected utility axioms, completeness, continuity, and independence, at both the individual and social levels. In that sense, expected utility is inessential to Harsanyi-style utilitarianism. In fact, the variable population theorem imposes only a mild constraint on the individual preorder, while the constant population theorem imposes no constraint at all. We then derive further results under the assumption of our basic axioms. First, the individual preorder satisfies the main expected utility axiom of strong independence if and only if the social preorder has a vector-valued expected total utility representation, covering Harsanyi’s utilitarian theorem as a special case. Second, stronger utilitarian-friendly assumptions, like Pareto or strong separability, are essentially equivalent to strong independence. Third, if the individual preorder satisfies a ‘local expected utility’ condition popular in non-expected utility theory, then the social preorder has a ‘local expected total utility’ representation. Fourth, a wide range of non-expected utility theories nevertheless lead to social preorders of outcomes that have been seen as canonically egalitarian, such as rank-dependent social preorders. Although our aggregation theorems are stated under conditions of risk, they are valid in more general frameworks for representing uncertainty or ambiguity.

Optimal Audit Policies With Heterogeneous Agents

This paper considers a tax evasion game where the tax authority intends to prevent income under-reporting within a network of heterogeneous taxpayers who are engaged in social interactions and exchange information. I propose a two-step game-theoretic optimal audit strategy from the point of view of the tax authority, which consists of a credible threat-to-audit message followed by a network-based audit policy. Subsequently, the tax authority targets taxpayers in function of their individual productivity and their position inside the network, triggering a series of spillover effects which eventually maximize the mean perceived subjective probability of being audited among all taxpayers. Moreover, the optimal audit strategy is robust to expected and non-expected utility theories, and it is invariant for any taxpayer utility function. Additionally, computer simulations determined that the proposed enforcement regime is robust to an ample range of parameter specifications and settings.

Can advisors eliminate the outcome bias in judgements and outcome-based emotions?

PurposeAn outcome bias occurs when performance is evaluated based upon the outcome of the decision rather than upon the quality of the decision itself. The purpose of this paper is to test experimentally whether advisors eliminating the uncertainty in the quality of decisions as a potential driver of the outcome bias can eliminate this bias in judgements. Additionally, the paper analyses whether such advisors can attenuate the emotional experience after decisions’ outcomes by supporting the cognitive understanding of these outcomes.Design/methodology/approachThe paper employs a between-subject experimental setting where decision makers are asked to make investment decisions. The two variables manipulated were advice (receiving advice vs deciding without an advice) and state (loss vs neutral vs gain state). Participants were randomly assigned to each group. One group completed all tasks while receiving advice before making a final decision. Another group completed all tasks without any advice. After completing each investment task, participants were randomly assigned to one of three possible states that determine their payoff.FindingsThe results reveal that advisors eliminating the uncertainty in the quality of decision can eliminate the outcome bias in the judgements of decision quality, especially after bad outcomes. Nevertheless, after controlling for the perceived quality of the decisions, advised individuals show a greater emotional sensitivity to bad outcomes than non-advised decision makers. These observations suggest that advisors eliminating the uncertainty in the decision quality can improve the understanding that good decisions can lead to bad outcomes just by chance, but they are not able to prevent affective reactions after bad outcomes; on the contrary, they may even reinforce them.Research limitations/implicationsThe observation that, after bad outcomes, advised decision makers are less willing to decide the same way than non-advised decision makers is consistent with empirical findings on the risk-taking behaviour of self-directed and mutual fund investors. Self-directed investors are less likely to revise their decision and sell an investment at a loss than mutual fund investors (Chang et al., 2016). While investors might sell funds because they are unable to observe the decision process of the manager and use the outcome to judge the manager’s skills, this study shows that such learning from decision outcomes is not necessary for observing the risk-taking behaviour of the investors. Even if the decision process of the advisor is observable (as in this study), the decision makers’ willingness to decide the same way is influenced by the losses – an effect that goes beyond the assessed quality of advice as the results of this study show.Practical implicationsThe results of this study have important implications for advisors aiming to maintain a positive relationship with their clients. Convincing clients that an advice is optimal supports their understanding that a good advice can have bad outcomes. However, this understanding may not prevent affective reactions after bad outcomes. On the contrary, the affective response after bad outcomes is even stronger with the advice than without it. Hence, advisors should address not only issues related to the quality of the provided advice, but also emotional aspects, which could be related to what clients expect from following the advice.Originality/valueThis study is one of the few that account for the possibility that the outcome bias may arise because there is uncertainty regarding the optimal choice. In particular, this paper uses a much more powerful criterion to define an optimal choice than the expected value criterion used in previous studies. The criterion represents a minimal requirement for rational behaviour in expected utility theory and many non-expected utility theories.

Expectational v. Instrumental Reasoning: What Statistics Contributes to Practical Reasoning

Utility theories—both Expected Utility (EU) and non-Expected Utility (non-EU) theories—offer numericalized representations of classical principles meant for the regulation of choice under conditions of risk—a type of formal representation that reduces the representation of risk to a single number. I shall refer to these as risk-numericalizing theories of decision . I shall argue that risk--numericalizing theories (referring both to the representations and to the underlying axioms that render numericalization possible) are not satisfactory answers to the question: “How do I take the (best) means to my ends?” In other words, they are inadequate or incomplete as instrumental theories. They are inadequate because they are poor answers to the question of what it is for an option to be instrumental towards an end. To say it another way, they do not offer a sufficiently rich account of what it is for something to be a means (an instrument) toward an end.

Decision making generalized by a cumulative probability weighting function

Typical examples of intertemporal decision making involve situations in which individuals must choose between a smaller reward, but more immediate, and a larger one, delivered later. Analogously, probabilistic decision making involves choices between options whose consequences differ in relation to their probability of receiving. In Economics, the expected utility theory (EUT) and the discounted utility theory (DUT) are traditionally accepted normative models for describing, respectively, probabilistic and intertemporal decision making. A large number of experiments confirmed that the linearity assumed by the EUT does not explain some observed behaviors, as nonlinear preference, risk-seeking and loss aversion. That observation led to the development of new theoretical models, called non-expected utility theories (NEUT), which include a nonlinear transformation of the probability scale. An essential feature of the so-called preference function of these theories is that the probabilities are transformed by decision weights by means of a (cumulative) probability weighting function, w(p). We obtain in this article a generalized function for the probabilistic discount process. This function has as particular cases mathematical forms already consecrated in the literature, including discount models that consider effects of psychophysical perception. We also propose a new generalized function for the functional form of w. The limiting cases of this function encompass some parametric forms already proposed in the literature. Far beyond a mere generalization, our function allows the interpretation of probabilistic decision making theories based on the assumption that individuals behave similarly in the face of probabilities and delays and is supported by phenomenological models.

An Extension of the Becker Proposition to Non-Expected Utility Theory

In a seminal paper, Becker (1968) showed that the most efficient way to deter crime is to impose the severest possible penalty (to maintain adequate deterrence) with the lowest possible probability (to economize on costs of enforcement). We shall call this the Becker proposition (BP). The BP is derived under the assumptions of expected utility theory (EU). However, EU is heavily rejected by the evidence. A range of non-expected utility theories have been proposed to explain the evidence. The two leading alternatives to EU are rank dependent utility (RDU) and cumulative prospect theory (CP). The main contributions of this paper are: (1) We formalize the BP in a more satisfactory manner. (2) We show that the BP holds under RDU and CP. (3) We give a formal behavioral approach to crime and punishment that could have applicability to a wide range of problems in the economics of crime.

Other-Regarding Preferences, Concerns for Others' Opportunities and Violations of Stochastic Dominance: A Choice-Theoretic Analysis

Decision makers with other-regarding preferences may care not just about others' outcomes but also about their opportunities. In social situations involving risk, this often results in their choices violating stochastic dominance, a property that underlies both expected and non-expected utility theories. We propose and axiomatize a model of other-regarding preferences, which we refer to as opportunity adjusted expected utility, that accommodates opportunity concerns and possible violations of stochastic dominance. Our model considers a set-up with a decision maker (DM) and another individual and characterizes the DM's preferences over allocation-lotteries through a representation that is based on (i) a baseline expected utility assessment and (ii) an adjustment that captures her attitude toward the other individual's opportunities.

Calibration without reduction for non-expected utility

Calibration results in Rabin (2000) and Safra and Segal (2008, 2009) suggest that both expected and non-expected utility theories cannot produce non-negligible risk aversion over small stakes without producing implausible risk aversion over large stakes. This paper provides calibration results for recursive non-expected utility theories that relax the Reduction of Compound Lotteries axiom (as in Segal, 1990). These calibration results imply that a broad class of non-expected utility theories can accommodate both small and large stakes risk aversion, even for a decision-maker who faces background risk.

Developments in non-expected utility theories: an empirical study of risk aversion

This paper investigates different developments in non-expected utility theories. Our focus is to study the agent’s attitude towards risk in a context of monetary gambles. Based on simulated data of the “Deal or No Deal” TV game show, we first compare the performance of the expected utility model versus a loss-aversion model. We find that the loss-aversion model has a better performance compared to the expected utility model. We then study the attitude towards risk according to two parameters: the relative risk aversion coefficient defined over the value function and the probability weighting coefficient proposed by the Cumulative Prospect Theory. We find evidence for probability weighting being undertaken by contestants reflecting less risk aversion over large stakes. We also explore the performance of two models of rank-dependant utility: the Quiggin (1982) and the power probability weighting models. We find that the probability weighting coefficient is still significant for both models. Finally, we integrate initial wealth into the contestants’ preferences function and we show that the initial wealth level affects the estimates of risk attitudes.

A State-of-the-Art Review: Developments in Utility Theory, Prospect Theory and Regret Theory to Investigate Travellers' Behaviour in Situations Involving Travel Time Uncertainty

Despite the wide use of utility theory to model travellers' behaviour, the interest in non-expected utility theories has increased due to their potential to capture more realistic behaviour. A main question raised is whether travellers are better described as utility maximizers or should be qualified differently.This paper presents a literature review on the use of expected utility theory (EUT), prospect theory (PT) and regret theory (RT) to model travellers' behaviour. Gaps in the literature are identified and a discussion about advantages and disadvantages of each theory is presented. A case study illustrates the differences between the theories.Under certain conditions, PT and RT restrict themselves to EUT. Their added value, however, is the possibility of capturing loss aversion, risk aversion and risk-seeking (PT) and regret aversion (RT). On the practical level, the use of EUT is well established, while contributions of PT and RT are marginal. On the theoretical level, however, RT seems to be (marginally) more suitable to model travellers' behaviour, while EUT and PT are equally suitable. This suggests that the large use of EUT is highly influenced by its very tractable framework. We do not claim the superiority of any theory, but propose to compare them through a systematic review.

Perception du risque routier par les adultes rhodaniens – département du Rhône, France

In a seminal paper, Becker (1968) showed that the most efficient way to deter crime is to impose the severest possible penalty (to maintain adequate deterrence) with the lowest possible probability (to economize on costs of enforcement). We shall call this the Becker proposition (BP). The BP is derived under the assumptions of expected utility theory (EU). However, EU is heavily rejected by the evidence. A range of non-expected utility theories have been proposed to explain the evidence. The two leading alternatives to EU are rank dependent utility (RDU) and cumulative prospect theory (CP). The main contributions of this paper are: (1) we formalize the BP in a more satisfactory manner; (2) we show that the BP holds under RDU and CP; and (3) we give a formal behavioral approach to crime and punishment that could have applicability to a wide range of problems in the economics of crime.

Risk Preferences in Strategic Wildfire Decision Making: A Choice Experiment with U.S. Wildfire Managers

Federal policy has embraced risa management as an appropriate paradigm for wildfire management. Economic theory suggests that over repeated wildfire events, potential economic costs and risas of ecological damage are optimally balanced when management decisions are free from biases, risa aversion, and risa seeking. Of primary concern in this article is how managers respond to wildfire risa, including the potential effect of wildfires (on ecological values, structures, and safety) and the likelihood of different fire outcomes. We use responses to a choice experiment questionnaire of U.S. federal wildfire managers to measure attitudes toward several components of wildfire risa and to test whether observed risa attitudes are consistent with the efficient allocation of wildfire suppression resources. Our results indicate that fire managers' decisions are consistent with nonexpected utility theories of decisions under risa. Managers may overallocate firefighting resources when the likelihood or potential magnitude of damage from fires is low, and sensitivity to changes in the probability of fire outcomes depends on whether probabilities are close to one or zero and the magnitude of the potential harm.

RISK AVERSION AND EXPECTED UTILITY THEORY: AN EXPERIMENT WITH LARGE AND SMALL STAKES

We employ a novel data set to estimate a structural econometric model of the decisions under risk of players in a game show where lotteries present payoffs in excess of half a million dollars. The decisions under risk of players in the presence of large payoffs allow us to estimate the parameters of the curvature of the von Neumann–Morgenstern utility function—not only locally, as in previous studies in the literature, but also globally. Our estimates of relative risk aversion indicate that a constant relative risk aversion parameter of about 1 captures the average of the sample population. We also find that individuals are practically risk neutral at small stakes and risk averse at large stakes—a necessary condition, according to Rabin’s calibration theorem, for expected utility to provide a unified account of individuals’ attitudes toward risk. Finally, we show that for lotteries characterized by substantial stakes, nonexpected utility theories fit the data equally as well as expected utility theory.

An extension of the Becker proposition to non-expected utility theory

In a seminal paper, Becker (1968) showed that the most efficient way to deter crime is to impose the severest possible penalty (to maintain adequate deterrence) with the lowest possible probability (to economize on costs of enforcement). We shall call this the Becker proposition (BP). The BP is derived under the assumptions of expected utility theory (EU). However, EU is heavily rejected by the evidence. A range of non-expected utility theories have been proposed to explain the evidence. The two leading alternatives to EU are rank dependent utility (RDU) and cumulative prospect theory (CP). The main contributions of this paper are: (1) we formalize the BP in a more satisfactory manner; (2) we show that the BP holds under RDU and CP; and (3) we give a formal behavioral approach to crime and punishment that could have applicability to a wide range of problems in the economics of crime.

Weak* Axiom of Independence and the Non-Expected Utility Theory

The axiomatic foundation of the expected utility theory (which states that given a set of uncertain prospects individuals pick up the prospect which yields the highest expected utility) was first laid down by Von Neumann and Morgenstern (1947). This axiom has come under severe criticisms in recent years. A large number of experiments have shown that in making decisions involving uncertain prospects people frequently violate the independence axiom. In this paper we shall consider the problem of choice under uncertainty from a wider point of view and we shall examine the nature of the restriction imposed by the axiom of independence. We shall use the mean-variance utility function to prove our point. Then we shall consider a weak version of the independence axiom namely the weak* axiom of independence. This is the point of departure from the expected utility theory to the realm of the non-expected utility theory. The weak* axiom allows aversion to pure uncertainty and, in the context of the mean-variance utility theory, it is compatible with utility being an increasing function of expected returns at all levels.

Uncertainty plus prior equals rational bias: An intuitive Bayesian probability weighting function.

Empirical research has shown that when making choices based on probabilistic options, people behave as if they overestimate small probabilities, underestimate large probabilities, and treat positive and negative outcomes differently. These distortions have been modeled using a nonlinear probability weighting function, which is found in several nonexpected utility theories, including rank-dependent models and prospect theory; here, we propose a Bayesian approach to the probability weighting function and, with it, a psychological rationale. In the real world, uncertainty is ubiquitous and, accordingly, the optimal strategy is to combine probability statements with prior information using Bayes' rule. First, we show that any reasonable prior on probabilities leads to 2 of the observed effects; overweighting of low probabilities and underweighting of high probabilities. We then investigate 2 plausible kinds of priors: informative priors based on previous experience and uninformative priors of ignorance. Individually, these priors potentially lead to large problems of bias and inefficiency, respectively; however, when combined using Bayesian model comparison methods, both forms of prior can be applied adaptively, gaining the efficiency of empirical priors and the robustness of ignorance priors. We illustrate this for the simple case of generic good and bad options, using Internet blogs to estimate the relevant priors of inference. Given this combined ignorant/informative prior, the Bayesian probability weighting function is not only robust and efficient but also matches all of the major characteristics of the distortions found in empirical research.