Subjective Expected Utility Model Research Articles

A Revealed Preference Test for Choquet and Max-Min Expected Utility with Ambiguity Aversion

We develop a revealed preference test for the Choquet expected utility model with ambiguity aversion, which does not rely on specific functional form assumptions on the utility index. It is computationally efficient if the number of states is not too large, even for a large number of observations. This is a nice feature compared to other existing revealed preference tests for decision models with ambiguity. We illustrate the usefulness of our results by implementing our test on two experimental datasets from the literature, and we compare the empirical fit of this model to the subjective expected utility model. (JEL C91, D81, D91, G41)

Aiming high: Learning investments in German upper secondary education. Differences between immigrant and non-immigrant youth

This article addresses important aspects of the largely unexplored interplay between high educational aspirations and low academic achievement in migratory contexts. Using data from the German National Educational Panel Study (NEPS), I examine the determinants of learning investments of students who changed from vocational to academic tracking at the transition to upper secondary education. I also explore additional social challenges to upward track mobility that might affect immigrant students in a particular way. As educational disparities are often interpreted as a cumulative consequence of class- and migration-specific educational choices, I develop a learning investment model that explains differences in learning investments between immigrant and non-immigrant youth. I introduce the essential mechanisms of psychological motivation theory into a subjective expected utility (SEU) model, which allows for a specific examination of the relationship between educational aspirations, motivation, and learning investments. Results show that newcomers to academic tracking are more likely to invest in learning. Yet, learning investments in upward mobility processes may be influenced by the different learning environments of stratified education and by family dynamics. Here, I find differences between immigrant and non-immigrant youth. Thus, introducing motivational factors into an SEU model helps to understand when youth invest in learning.

Testing negative value of information and ambiguity aversion

The standard Subjective Expected Utility model of decision-making implies that information can never have a negative value ex-ante. Many ambiguity theories have since questioned this property. We provide an experimental test of the connection between the value of information and ambiguity attitude. Our results show that the value of information can indeed be negative when new information renders hedging against ambiguity impossible. Moreover, the value of information is correlated with ambiguity aversion. This confirms the predictions from ambiguity theories and may have implications for decision-making in uncertain and dynamic environments. Neither complexity avoidance nor information with ambiguous reliability can reproduce the results.

Randomizing without randomness

We provide a methodology for eliciting utility midpoints from preferences, assuming that payoffs are consumption plans and that preferences satisfy a minimal form of additive separability. The methodology does not require any subjective or objective uncertainty. Thus, this construction of utility midpoints allows us to define mixtures of acts in a purely subjective fashion, without making any assumptions as to the decision maker’s reaction to the uncertainty that may be present. This approach makes it possible to provide a simple and fully subjective characterization of the second-order subjective expected utility model, allowing a clear distinction of such model from subjective expected utility.

Why Did F. P. Ramsey Never Repeat the Claims He Had Made on the First Page of His Jan., 1922 Cambridge Magazine Three Page Note Concerning Keynes’s Logical Theory of Probability?: It Is Easy for a Reader To See That Ramsey’s Review Is Dead Wrong if That Reader Has Actually Read the 'A Treatise on Probability'

The first page of the 18 year old, F. P. Ramsey’s very short three page review, in the Cambridge Magazine issue of Jan., 1922, of Keynes’s A Treatise on Probability is comprised of claims about Keynes’s logical theory of probability that, to use L. J. Savage’s characterization of academics who tried to apply his Subjective Expected Utility model to Large Worlds (macro, intertemporal, long run decision making), as opposed to Small Worlds (micro ,short run decision making), was “utterly preposterous” and complete ”nonsense”. Ramsey’s very small review was obviously never refereed J. M. Keynes and/or Bertrand Russell could have made short work of the 18 year old Ramsey’s note in a few minutes, thereby permanently ending his academic career at Cambridge before it ever had a chance to get started. However, they decided not to do so, as they recognized that Ramsey had special intellectual gifts, although they were clearly undeveloped at the time. Keynes decided to take Ramsey under his wing and train him. The very, very severe problems with the first page consist of two claims made by Ramsey. The first claim made by F. P. Ramsey is that: “We have, then, numerous probability relations; these it is commonly supposed are all numerical, that is, correlated with the real numbers from 0 to 1 in such a way that the ordinary rules of the probability calculus hold, e.g., that the product of the numbers correlated with two probabilities is equal to the number correlated with the product (in Mr. Keynes' sense) of the two probabilities. Mr. Keynes denies this; he supposes not only that not all probabilities are numerical, but also that it is possible to have two probabilities which are unequal and such that neither is greater than the other. This view is based on the difficulty in so many cases of saying with any confidence which of two probabilities is the greater, or of assigning any numerical measures to them. But it would appear that the force of this objection to the ordinary view is exaggerated to Mr. Keynes for two reasons.” The second claim made by F.P. Ramsey is that: “First, he thinks that between any two non-self-contradictory propositions there holds a probability relation (Axiom I), for example between 'My carpet is blue' and 'Napoleon was a great general'; it is easily seen that it leads to contradictions to assign the probability 1/2 to such cases, and Mr. Keynes would conclude that the probability is not numerical. But it would seem that in such cases there is no probability; that, for a logical relation, other than a truth function, to hold between two propositions, there must be some connection between them. If this be so, there is no such probability as the probability that 'my carpet is blue' given only that 'Napoleon was a great general', and there is therefore no question of assigning a numerical value.” Ramsey’s first claim is the result of his gross ignorance of Keynes’s imprecise, interval valued ,non additive approach to probability, as was illustrated by Keynes in the discussions of the beauty contest problem on pp.25-28, as well as by six other illustrations contained in Chapter III of the A Treatise on Probability. The mathematical analysis was presented in Part II of the book, a part that Ramsey never got around to ever reading in his lifetime. The second claim made by Ramsey has nothing to do with Keynes’s use of propositions, which must be stated in the form of an argument- one proposition must contain relevant evidence while the second proposition must be a conclusion with respect to the proposition containing the relevant evidence. Only then is a relation of logical probability present. Nowhere at any place in his A Treatise on Probability or any other work written in Keynes’s lifetime did Keynes state: “…that between any two non-self-contradictory propositions there holds a probability relation (Axiom I)…” There is no such Axiom I in Keynes’s A Treatise on Probability. Therefore, Ramsey’s”… 'My carpet is blue' and 'Napoleon was a great general…” example is an oxymoron because his two propositions do not form an argument. The current belief among academics, that has been a belief for 100 years, that Ramsey not only destroyed and demolished Keynes’s logical theory of probability, but that Keynes himself felt compelled by the overwhelming logical power of Ramsey’s critique to accept Ramsey’s critique and adopted a subjective theory of probability himself, calls into question the claims made by academics writing on Keynes that they are publishing scientific works that contribute to the growth of knowledge. All I see is utter and complete nonsense.

Structural Estimation of Decision Making under Natural Hazard Risk

The use of structural models for decision-making under risk and uncertainty in applied economics is scarce compared to reduced form approaches. This is unfortunate, as structural models have clear connections to theory and permit direct tests of hypotheses and exploration of potential causal mechanisms. In this paper, we derive and estimate a structural model of decision making in the presence of natural hazard risk. Utilizing a unique data set that includes information on risk preferences, subjective likelihood of hurricane strike, and expectations of damage, we estimate several variants of a subjective expected utility model for coastal households’ decisions to purchase flood insurance. We benchmark our model’s out of sample accuracy by comparing it against both reduced-form and machine learning estimates. Overall, we find our structural models perform about as well as a reduced-form probit model in predicting out of sample behavior, but offer increased external validity and insight into theory and mechanisms.

Adversarial Risk Analysis to Allocate Optimal Defense Resources for Protecting Cyber-Physical Systems from Cyber Attacks.

Defenders have to enforce defense strategies by taking decisions on allocation of resources to protect the integrity and survivability of cyber-physical systems (CPSs) from intentional and malicious cyber attacks. In this work, we propose an adversarial risk analysis approach to provide a novel one-sided prescriptive support strategy for the defender to optimize the defensive resource allocation, based on a subjective expected utility model, in which the decisions of the adversaries are uncertain. This increases confidence in cyber security through robustness of CPS protection actions against uncertain malicious threats compared with prescriptions provided by a classical defend-attack game-theoretical approach. We present the approach and the results of its application to a nuclear CPS, specifically the digital instrumentation and control system of the advanced lead-cooled fast reactor European demonstrator.

Models of risky choice: A state-trace and signed difference analysis

Models of risky choice fall into two broad classes; fixed utility models that satisfy the condition of simple scalability and everything else. While it is known that choice behavior can be observed that is inconsistent with all models, this has largely been based on the construction of special cases. We use state-trace analysis and signed difference analysis to test a set of models on a set of ecologically representative risky choices. An advantage of this approach is that there is no requirement to posit a particular form for the error function that links the difference in the utilities of two gambles, A and B, with the probability of choosing A over B. We presented groups of participants with 30 variable gambles (A), each paired with one of four fixed gambles (B). We use state-trace analysis to test the prediction of all fixed utility models that the probability of choosing each A has the same order for all B. The results show that this prediction is not confirmed and a more complex model is required. We then use signed difference analysis to test two more complex models — the random subjective expected utility model based on Decision Field Theory and a fixed utility mixture model. We derive a key prediction from the random subjective expected utility model and show that it is confirmed by the data. In contrast, the data are shown to be inconsistent with the fixed utility mixture model.

Ambiguity sensitive preferences in Ellsberg frameworks

We study the market implications of ambiguity sensitive preferences using the \(\alpha \)-maxmin expected utility (\(\alpha \)-MEU) model. In the standard Ellsberg framework, we prove that \(\alpha \)-MEU preferences are equivalent to either maxmin, maxmax or subjective expected utility (SEU). We show how ambiguity aversion impacts equilibrium asset prices, and revisit the laboratory experimental findings in Bossaerts et al. (Rev Financ Stud 23:1325–1359, 2010). Only when there are three or more ambiguous states, \(\alpha \)-MEU, maxmin, maxmax and SEU models induce different portfolio choices. We suggest criteria to discriminate among these models in laboratory experiments and show that ambiguity seeking agents may prevent the existence of market equilibrium. Our results indicate that ambiguity matters for portfolio choice and does not wash out in equilibrium.

Motors of influenza vaccination uptake and vaccination advocacy in healthcare workers: Development and validation of two short scales

Healthcare workers (HCWs) are an important priority group for vaccination against influenza, yet, flu vaccine uptake remains low among them. Psychosocial studies of HCWs’ decisions to get vaccinated have commonly drawn on subjective expected utility models to assess predictors of vaccination, assuming HCWs’ choices result from a rational information-weighing process. By contrast, we recast those decisions asa commitment to vaccination and we aimed to understand why HCWs may want to (rather than believe they need to) get vaccinated against the flu. This article outlines the development and validation of a 9-item measure of cognitive empowerment towards flu vaccination (MoVac-flu scale) and an 11-item measure of cognitive empowerment towards vaccination advocacy. Both scales were administered to 784 frontline NHS HCWs with direct patient contact between June 2014 and July 2015. The scales exhibited excellent reliability and a clear unidimensional factor structure. An examination of the nomological network of the cognitive empowerment construct in relation to HCWs’ vaccination against the flu revealed that this construct was distinct from traditional measures of risk perception and the strongest predictor of HCWs’ decisions to vaccinate. Similarly, cognitive empowerment in relation to vaccination advocacy was a strong predictor of HCWs’ engagement with vaccination advocacy. These findings suggest that the cognitive empowerment construct has important implications for advancing our understanding of HCWs’ decisions to vaccinate as well as their advocacy behavior.

Uncertain discount and hyperbolic preferences

This paper studies the interaction between savagean uncertainty and time preferences. We introduce a variation of the discounted subjective expected utility model, where time preferences are state dependent. Before uncertainty is resolved, the individual is unsure about the discount factor that will be used, even when evaluating certain payoffs. The model can account for the present bias and diminishing impatience, even if the future is discounted geometrically. The present bias disappears when the immediate payoff becomes uncertain. Although preferences are not stationary, choices may be time consistent.

Should I Stay Ot Should I Go? - A Laboratory Analysis of Investment Opportunities Under Ambiguity

This paper investigates the impact of uncertainty on an irreversible investment decisions in the laboratory. Subjects own the option to seize a claim on the future sum of realizations from an (ambiguous) random walk. I contrast model predictions of the Subjective Expected Utility model (SEU, Savage, 1954) with model predictions made by Multiple-prior Expected Utility models (MEU, Gilboa & Schmeidler, 1989; Epstein & Schneider, 2003b). I present an experimental design that allows to identify behaviorally meaningful deviations from SEU. Observed behavior is at odds with the SEU prediction. On average, subjects in a treatment group, facing an ambiguous random walk, exhibit an ambiguity premium that presents a mark-up on average reservation profits in a control group. Hence, subjects shun to expose themselves to an ambiguous payoff process and invest later than participants facing a risky payoff process.

Extending the argument engagement model

This investigation considers the factors that predict the intent to engage in interpersonal arguments. By adapting the argument engagement model (Hample, Paglieri, and Na 2012), a subjective expected utility model was tested to determine the effects of (1) evaluative assessments, in addition to probabilistic assessments, and (2) probabilistic assessment-trait interactions on argument engagement. Participants (N = 273) read three argument vignettes and answered questions about their intent to argue in each situation. Results were mixed regarding the significance of expected values and situation-trait interactions in predicting intentions to argue. Participants overwhelmingly reported an optimism bias, whereby they tended to perceive positive outcomes of argument as likely and negative outcomes of argument as unlikely. Possible reasons for these findings and their implications are discussed.

Should I Stay or Should I Go? A Laboratory Analysis of Investment Opportunities Under Ambiguity

This paper investigates the impact of uncertainty on an irreversible investment decisions in the laboratory. Subjects own the option to seize a claim on the future sum of realizations from an (ambiguous) random walk. I contrast model predicitions of the Subjective Expected Utility model (SEU, Savage, 1954) with model predictions made by Multiple-prior Expected Utility models (MEU, Gilboa & Schmeidler, 1989; Epstein & Schneider, 2003b). I present an experimental design that allows to identify behaviorally meaningful deviations from SEU. Observed behavior is at odds with the SEU prediction. On average, subjects in a treatment group, facing an ambiguous random walk, exhibit an ambiguity premium that presents a mark-up on average reservation profits in a control group. Hence, subjects shun to expose themselves to an ambiguous payoff process and invest later than participants facing a risky payoff process.

Savage in the Market

We develop a behavioral axiomatic characterization of subjective expected utility (SEU) under risk aversion. Given is an individual agent's behavior in the market: assume a finite collection of asset purchases with corresponding prices. We show that such behavior satisfies a “revealed preference axiom” if and only if there exists a SEU model (a subjective probability over states and a concave utility function over money) that accounts for the given asset purchases.

Second order beliefs models of choice under imprecise risk: Nonadditive second order beliefs versus nonlinear second order utility

This paper discusses models of choice under imprecise objective probabilistic information featuring beliefs about beliefs, i.e., second order beliefs. A new model, called second order dual expected utility, featuring nonadditive second order beliefs, is introduced, axiomatized, and systematically contrasted with the leading alternative model of this kind, i.e., the second order subjective expected utility model (Klibanoff et al. 2005, Nau 2006, Seo 2009) for which, for the sake of comparison, we provide a new axiomatization, dispensing with the complex constructs used in extant axiomatizations. Ambiguity attitude and attitude toward information in general are discussed and characterized.

Ambiguity Aversion in the Ellsberg Framework

We study optimal portfolio choice and equilibrium asset prices induced by alpha-maxmin expected utility (alpha-MEU) models. In the standard Ellsberg framework we prove that alpha-MEU preferences are equivalent to either maxmin, maxmax or subjective expected utility (SEU). We show how ambiguity aversion impacts equilibrium asset prices, and revisit the laboratory experimental findings in Bossaerts, Ghirardato, Guarnaschelli, and Zame (2010). Only when there are three or more ambiguous states the alpha-MEU, maxmin, maxmax and SEU models induce different portfolio choices. We suggest criteria to discriminate among these models in laboratory experiments. Finally, we find that ambiguity seeking alpha-MEU agents may prevent the existence of market equilibrium. Our results indicate that ambiguity matters for portfolio choice and does not wash out in equilibrium.

Classical subjective expected utility

We consider decision makers who know that payoff-relevant observations are generated by a process that belongs to a given class M, as postulated in Wald [Wald A (1950) Statistical Decision Functions (Wiley, New York)]. We incorporate this Waldean piece of objective information within an otherwise subjective setting à la Savage [Savage LJ (1954) The Foundations of Statistics (Wiley, New York)] and show that this leads to a two-stage subjective expected utility model that accounts for both state and model uncertainty.

Subjective Expected Utility With Incomplete Preferences

This paper extends the subjective expected utility model of decision making under uncertainty to include incomplete beliefs and tastes. The main results are two axiomatizations of the multiprior expected multiutility representations of preference relations under uncertainty. The paper also introduces new axiomatizations of Knightian uncertainty and the expected multiutility model with complete beliefs.

Comparing risk preferences over financial and environmental lotteries

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.