Classical Expected Utility Theory Research Articles

Accurate Updating for the Risk-Sensitive

Abstract Philosophers have recently attempted to justify particular belief revision procedures by arguing that they are the optimal means towards the epistemic end of accurate credences. These attempts, however, presuppose that means should be evaluated according to classical expected utility theory; and there is a long tradition maintaining that expected utility theory is too restrictive as a theory of means–end rationality, ruling out too many natural ways of taking risk into account. In this paper, we investigate what belief-revision procedures are supported by accuracy-theoretic considerations once we depart from expected utility theory to allow agents to be risk-sensitive. We argue that if accuracy-theoretic considerations tell risk-sensitive agents anything about belief-revision, they tell them the same thing they tell risk-neutral agents: they should conditionalize.

Decision-making dynamic evolution among groups regarding express packaging waste recycling under different reference dependence and information policy.

The reveal of express packaging waste recycling behavior evolution trend is crucial to waste management. Current models are mostly based on the classic expected utility theory, without considering groups are susceptible to internal and external factors. To address this drawback, we construct an evolutionary game model of express packaging waste recycling behavior by considering information policy and reference dependence factors to explore groups' decision-making with different initial adoption rates. A system dynamics simulation model based on survey data is then built, and simulation experiments are also designed to reveal the impacts of key factors on the evolution path of recycling behavior. The results show that, without information policy, groups cyclically oscillate around the initial state. The stable trend depends on the information intensity, and the information effect is marginal diminishing. Groups with a lower initial adoption rate will evolve to an ideal stable strategy only when information intensity exceeds the threshold of ten. Reference points can change behavior strategies and are characterized by significant loss aversion. The benefits and costs affect groups' adoption or rejection behaviors. These findings can provide new ideas for related research and offer a reference for the government to formulate efficient waste management policies.

When Choosing is Painful: A Psychological Opportunity Cost Model

This paper is a contribution to regret theory, which we generalize in two ways. Since the intensity of regret depends on the information the decision-maker has about the results of the foregone strategies, we build a model of choice which accommodates any feedback structure. We also show that the reference point, which characterizes the regret utility function introduced by Quiggin (1994), does not always represent a feeling of regret. It corresponds to a broader concept, which we call psychological opportunity cost (POC), of which regret is no more than a specific expression. We find behavioral deviations from the predictions of the classical Expected Utility Theory. We obtain correlation loving, greater reluctance to take on risk and information avoidance at decision time. Our model equally offers a theoretical framework for experimental studies about inaction inertia.

Risk aversion in Entrepreneurship Panels: Measurement Problems and Alternative Explanations

In this study, we investigate the pitfalls associated with measuring risk aversion within studies of entrepreneurial behavior. First, we raise substantial concerns as to whether standard questions employed can be used to infer risk aversion among nascent entrepreneurs. In our work we show that the US, Canadian and Swedish panel study datasets do not offer evidence that entrepreneurs are more risk averse than non‐entrepreneurs. In fact, we show that the measurements used for risk aversion in these studies are not compatible with classic expected utility theory. Furthermore, our analysis reveals that probability weighting may even counteract the respondent's risk attitude. Therefore, inferring the respondent's risk attitude from choices in the panel study datasets can be misleading in the presence of probability weighting. We therefore suggest that alternative theories of decision making under risk, like prospect theory, are relevant and should be taken into account in future studies on entrepreneurship. Copyright © 2017 John Wiley & Sons, Ltd.

Quantitative Predictions in Quantum Decision Theory

Quantum Decision Theory, advanced earlier by the authors, and illustrated for lotteries with gains, is generalized to the games containing lotteries with gains as well as losses. The mathematical structure of the approach is based on the theory of quantum measurements, which makes this approach relevant both for the description of decision making of humans and the creation of artificial quantum intelligence. General rules are formulated allowing for the explicit calculation of quantum probabilities representing the fraction of decision makers preferring the considered prospects. This provides a method to quantitatively predict decision-maker choices, including the cases of games with high uncertainty for which the classical expected utility theory fails. The approach is applied to experimental results obtained on a set of lottery gambles with gains and losses. Our predictions, involving no fitting parameters, are in very good agreement with experimental data. The use of quantum decision making in game theory is described. A principal scheme of creating quantum artificial intelligence is suggested.

Behavioral mechanism design

Incentives are more likely to elicit desired outcomes when they are based on accurate models of agent behavior. A growing literature---from behavioral economics, as well as online user studies---suggests, however, that people do not quite behave like standard economic agents in a variety of environments, both online and offline. What consequences might such differences have for the optimal design of these environments? In this note, we summarize our results from Easley and Ghosh [2015] which explores this question of behavioral design---how departures from standard economic models of agent behavior affect mechanism design---via the problem of the optimal choice of contract structure in crowdsourcing markets where workers make decisions according to prospect theory preferences [Kahneman and Tversky 1979] rather than classical expected utility theory: we show that a principal might indeed choose a fundamentally different kind of mechanism---an output-contingent contest versus a 'safe', output-independent, fixed-payment scheme---and do better as a result, if he accounts for deviations from the standard economic models of decision-making that are typically used in theoretical design.

One Approximation of the Real-World Corporate Financing Decisions

This paper is the first attempt to reconcile the prospect theory and the contract theory in explaining the observed financing decisions. In a world of ambitious and aggressive economic agents, even the original equilibria under the presence of asymmetric information break down. When the aggressiveness in the market is prevailing, there exist multi-pooling-equilibria, which might help explain why the academic can not find the optimal leverage. In the meanwhile, debt issuance would be lower, which shed light on the distinct liquidity provision patterns between bull and bear market. Firm with lottery-like investment opportunity will more easily get external financing than that with safe project, as both market participants, entrepreneur and financier, perceive the project more valuable than the value would otherwise be suggested by the classical expected utility theory.

Aggregating Infinitely Many Probability Measures

The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and (ii) when an individual whose belief system is compatible with several (possibly infinitely many) probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory (a psychologically plausible account of individual decisions). We investigate this problem by first recalling some negative results from preference and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected-utility preferences. We describe how McConway’s (Journal of the American Statistical Association, vol. 76, no. 374, pp. 410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely-additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms a la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed.

Aggregating infinitely many probability measures

The problem of how to rationally aggregate probability measures occurs in particular (i) when a group of agents, each holding probabilistic beliefs, needs to rationalise a collective decision on the basis of a single ‘aggregate belief system’ and (ii) when an individual whose belief system is compatible with several (possibly infinitely many) probability measures wishes to evaluate her options on the basis of a single aggregate prior via classical expected utility theory (a psychologically plausible account of individual decisions). We investigate this problem by first recalling some negative results from preference and judgment aggregation theory which show that the aggregate of several probability measures should not be conceived as the probability measure induced by the aggregate of the corresponding expected utility preferences. We describe how McConway’s (Journal of the American Statistical Association, 76(374):410–414, 1981) theory of probabilistic opinion pooling can be generalised to cover the case of the aggregation of infinite profiles of finitely additive probability measures, too; we prove the existence of aggregation functionals satisfying responsiveness axioms a la McConway plus additional desiderata even for infinite electorates. On the basis of the theory of propositional-attitude aggregation, we argue that this is the most natural aggregation theory for probability measures. Our aggregation functionals for the case of infinite electorates are neither oligarchic nor integral-based and satisfy (at least) a weak anonymity condition. The delicate set-theoretic status of integral-based aggregation functionals for infinite electorates is discussed.

The bipolar Choquet integral representation

Cumulative Prospect Theory is the modern version of Prospect Theory and it is nowadays considered a valid alternative to the classical Expected Utility Theory. Cumulative Prospect theory implies Gain-Loss Separability, i.e., the separate evaluation of losses and gains within a mixed gamble. Recently, some authors have questioned this assumption of the theory, proposing new paradoxes where the Gain-Loss Separability is violated. We present a generalization of Cumulative Prospect Theory which does not imply Gain-Loss Separability and is able to explain the cited paradoxes. On the other hand, the new model, which we call the bipolar Cumulative Prospect Theory, genuinely generalizes the original Prospect Theory of Kahneman and Tversky, preserving the main features of the theory. We present also a characterization of the bipolar Choquet Integral with respect to a bi-capacity in a discrete setting.

Dynamic decision-making in uncertain environments II. Allais paradox in human behavior

In both animal and human behavioral repertoires, classical expected utility theory is considered a fundamental element of decision making under conditions of uncertainty. This theory has been widely applied to problems of animal behavior and evolutionary game theory, as well as to human economic behavior. The Allais paradox hinges on the expression of avoidance of bankruptcy by humans, or death by starvation in animals. This paradox reveals that human behavioral patterns are often inconsistent with predictions under the classical expected utility theory as formulated by von Neumann and Morgenstern. None of the many attempts to reformulate utility theory has been entirely successful in resolving this paradox with rigorous logic. We present a simple, but novel approach to the theory of decision making, in which utility is dependent on current wealth, and in which losses are more heavily weighted than gains. Our approach resolves the Allais paradox in a manner that is consistent with how humans formulate decisions under uncertainty. Our results indicate that animals, including humans, are in principle risk-averse. Our restructuring of dynamic utility theory presents a basic optimization scheme for sequential or dynamic decisions in both animals and humans.

Reference dependent preferences, hedonic adaptation and tax evasion: Does the tax burden matter?

We study the effects of the tax burden on tax evasion both theoretically and experimentally. We develop a theoretical framework of tax evasion decisions that is based on two behavioral assumptions: (1) taxpayers are endowed with reference dependent preferences that are subject to hedonic adaptation and (2) in making their choices, taxpayers are affected by ethical concerns. The model generates new predictions on how a change in the tax rate affects the decision to evade taxes. Contrary to the classical expected utility theory, but in line with previous applications of reference dependent preferences to taxpayers’ decisions, an increase in the tax rate increases tax evasion. Moreover, as taxpayers adapt to the new legal tax rate, the decision to evade taxes becomes independent of the tax rate. We present results from a laboratory experiment that support the main predictions of the model.

Risk Preferences Over Small Stakes: Evidence from Deductible Choice

This paper provides new field evidence on risk preferences over small stakes. Using unique population and survey data on deductible choice in Dutch universal health insurance, we find that risk preferences are a dominant factor in decision-making. In fact, our results indicate that risk preferences are both statistically and quantitatively more significant in explaining deductible choice behavior than risk type. This finding contrasts with classical expected utility theory, as it implies risk neutrality over small stakes. More recently developed reference-dependent utility models, however, can rationalize risk aversion over small stakes, on account of loss aversion and narrow framing.

Shadow Probability Theory for Asset Pricing under Ambiguity

Assuming that probabilities (capacities) of events are random, this paper introduces a novel model of decision making under ambiguity, called Shadow probability theory, a generalization of the Choquet expected utility. In this model, probabilities of observable events in a subordinated outcome-space are dominated by second-order unobservable events in a directing probability space. The level of ambiguity, and the decision maker’s attitude toward it, are measured with respect to the directing space. Risk and risk attitude, on the other hand, apply to the subordinated space, as in classical expected utility theory. The desired distinction between preferences and beliefs and between risk and ambiguity is then obtained. A measure of ambiguity is naturally carried over on these settings. The present paper proves that in most cases ambiguity cannot be diversified. Counterintuitively, adding an ambiguous lottery to a portfolio of lotteries usually increases its ambiguity. This result, which implies that full diversification is not always optimal, challenges the common notion in the financial literature that investors should hold a fully diversified portfolio. Using this model of choice, the current paper generalizes the classical asset pricing theory by incorporating ambiguous probabilities. It proposes a well defined ambiguity premium that can be measured empirically.

General Equilibrium with Uncertainty: The Work of Kenneth Arrow

This article summarizes the theory of markets under uncertainty that Arrow and Debreu created, its achievements and the critical issues that it raises. It focuses on the way Arrow introduced securities: how he defined them and what were the most useful developments of this theory. It mentions the theory of insurance that Arrow pioneered together with Malinvaud and others, and Arrow’s theory of risk bearing that follows the axiomatic treatment of Von Neumann and Morgenstern, Milnor, Hernstein, De Groot, and Villegas. The classic expected utility theory embraces normal or frequent risks at the expense of neglecting rare events, even those with important consequences such as catastrophes, causing paradoxical experimental behavior as shown by the author. Kenneth Arrow encouraged the creation of an extension of classic axiomatic theory, and in the early 1990s the author proposed axioms that treat symmetrically frequent and rare events, leading to a new definition of rationality and a new form of choice under uncertainty that conforms better to the experimental evidence. Additionally, the introduction of markets with endogenous uncertainty in the early 1990s challenged the foundation of Arrow Debreu's theory of markets. Endogenous uncertainty is generated by the workings of the economy, and breaks down the equivalence between markets with and without uncertainty that prevails in Arrow Debreu's theory. This leads to a new world of uncertainty creation through financial innovation and regulation that is at the heart of the financial markets turmoil of 2008. In 1999 Arrow contributed to the theory of endogenous uncertainty in his work with Frank Hahn.

A reference-dependent regret model for deterministic tradeoff studies

Today's typical multi-criteria decision analysis is based on classical expected utility theory that assumes a mythical “Rational Individual” immune to psychological influences such as anticipated regret. It is therefore in conflict with rational individuals who trade off some benefits and forgo the alternative with the highest total classical utility for a more balanced alternative in order to reduce their levels of anticipated regret. This paper focuses on decision making under certainty. It presents a reference-dependent regret model (RDRM) in which the level of regret that an individual experiences depends on the absolute values rather than the differences of the utilities of the chosen and forgone alternatives. The RDRM best choice may differ from the conventional linear additive utility model, the analytic hierarchy process, and the regret theory of Bell and Loomes and Sugden. Examples are presented that indicate that RDRM is the better predictive descriptor for decision-making under certainty. RDRM satisfies transitivity of the alternatives under pairwise comparisons and models rank reversal consistent with observed reasonable choices under dynamic or distinct situations. Like regret theory, the RDRM utilities of all the alternatives under consideration are interrelated. For complex tradeoff studies, regret is incorporated as an element of a cost-utility-regret analysis that characterizes each alternative in terms of its monetary cost, an aggregate performance utility, and a regret value. This provides decision makers adequate information to compare the alternatives and depending on their values they may trade off some performance and/or cost to avoid high levels of regret. The result is a well-balanced alternative often preferred by reasonable decision-makers to the optimal choice of classical multi-attribute utility analysis. The model can readily be extended to incorporate rejoicing to suit decision makers who seek it. The approach is illustrated using a hypothetical but realistic aircraft selection problem. © 2005 Wiley Periodicals, Inc. Syst Eng 8: 119–137, 2005

Optimal Insurance With Divergent Beliefs About Insurer Total Default Risk

This paper extends the classic expected utility theory analysis of optimal insurance contracting to the case where the insurer has a positive probability of total default and the buyer and insurer have divergent beliefs about this probability. The optimal marginal indemnity above the deductible is smaller (greater) than one if the buyer's assessment of default risk is more pessimistic (optimistic) than the insurer's. As an application of the model, we consider the market for reinsurance against catastrophic property loss and propose an expected utility theory explanation for the increasing and concave marginal indemnity schedule observed in this market.

To achieve or not to achieve: A self-regulation perspective on adolescents' academic decision making.

In 2 studies, the authors investigated the utility of the self-regulation model of decision making for explaining and predicting adolescents' academic decision making. Participants were mostly 9th and 1 lth graders. The 1st study consisted of all boys, and a 2nd similar study consisted of boys and girls. Measures included a newly developed assessment of decision-maki ng skill (the Decision-Making-Competency Inventory), select scales of the Learning and Study Strategies Inventory—High School Version, an assessment of the importance of academic goals, and teacher ratings of achievement behavior. Adolescents' valuing of academic goals and their decision-making competency were typically the best predictors of their achievement behavior. Older adolescent boys did not affirm achievement striving compared with younger adolescent boys and older adolescent girls. There is ample reason for research on decision making to intersect with that of academic achievement. From everyday decisions like deciding whether to study for tests to more weighty ones like high school course selection and, even more consequential, deciding whether to complete high school or go on to higher education, decisions related to academic achievement are some of the most salient in the lives of young people. Furthermore, decision making takes on increasing importance with age given that children's growing independence necessitates that they make more decisions for themselves. Thus, it is important to chart the development of decision making through the adolescent period using a theory that effectively captures the key features of this skill that relate to academic achievement and other aspects of adolescents' lives. Such a theory would provide guideposts to the kinds of skills that should be developing, as well as clues regarding ways to intervene, if these skills are found not to be developing as they should. There are three major shortcomings in existing models of decision making (Byrnes, 1998; Slovic, Lichtenstein, & Fischhoff, 1988). First, those based on classical expected utility theory fail to take into account information-processing limitations of the human mind. In effect, they are not accurate models of how humans actually make decisions. Second, most models are not powerful

Some hypotheses about risk in venture capital investing

Venture capital investing differs in important respects from investment decisions involving the securities of Fortune 500 companies, or decisions to purchase established companies, which are generally made in accord with widely recognized financial models. Investing in new ventures involves a high level of uncertainty as well as a high risk of failure. Venture capital investing is characterized by high variability in the outcomes of new ventures and in the performance of venture capital portfolios. Venture capital investing decisions are complicated by a general lack of quantifiable financial and market data for early-stage ventures, and investment decisions remain hostage to unanticipated competitors, market shifts, and financial cycles. Some observers have suggested that venture capital investment decisions are primarily subjective assessments. While the question of risk in venture capital investing has been addressed on an ad hoc basis in several empirical studies, there has been little effort to develop a theoretical framework of risk perceptions and risk-reduction strategies. Despite differences in investor experience, investment preferences, and tolerance for risk, venture capital managers share many common perceptions of the risks involved in investing in new ventures and the distribution of those risks over the venture-capital-funded phase of development. Venture capital managers also utilize many common behaviors and strategies in adapting to these risks. These perceptions and reactions to risk in investing, and strategies for controlling risk can, in theory, be used to construct a behavioral framework that can predict how venture capital managers will behave in choosing between various investment opportunities in order to minimize risk and to maximize potential returns. In an attempt to begin to identify various elements of such a behavioral framework of venture capital reactions to risk, the authors have drawn upon psychological risk theory of decision-making under uncertainty, including classic expected utility theory, later modifications to that theory by Kahneman and Tversky (1979). and Coombs and Huang's (1970) “portfolio approach” to risk, that are applicable to venture capital investing. These expected behaviors to risk have been used in conjunction with empirical studies of venture capital investment and portfolio outcomes, distributions of investments within portfolios, and venture capitalist perceptions of risk, to propose nine hypotheses about how venture capital managers behave in making investment decisions. These hypotheses include differences in variation and magnitude of returns for early-stage versus later-stage ventures, explanations of how risk distributions change over the stagewise development of new ventures, differences in the behavior of “aggressive” versus “conservative” investors in screening investment prospects, and strategies utilizing a lower “ideal level of risk” to reduce the chances of achieving negative or sub-normal final portfolio returns.

Taxpayer attitudes toward tax audit risk

Theoretical analyses on tax evasion usually assume that the taxpayer's behavior conforms to the Von Neumann-Morgenstern axioms for behavior under uncertainty, namely that the taxpayer is generally risk averse. This study found that the taxpayers' attitudes toward risk could be affected by (1) whether taxpayers perceive a tax payment as reduced income or as a loss; and (2) the magnitude of the tax savings and penalty structure. The findings, in general, agree more with the prospect theory than with the classical expected utility theory.