Revisiting the Expected Utility Theory and the Consumption CAPM
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Journal of Risk and Financial Management Article The Standard Model of Rational Risky Decision-Making Kazem Falahati Glasgow School for Business and Society, Glasgow Caledonian University, 70 Cowcaddens Road, Glasgow G4 0BA, UK; [email protected]; Tel.: +44-141-331-3708 Abstract: Expected utility theory (EUT) is currently the standard framework which formally defines rational decision-making under risky conditions. EUT uses a theoretical device called von Neumann– Morgenstern utility function, where concepts of function and random variable are employed in their pre-set-theoretic senses. Any von Neumann–Morgenstern utility function thus derived is claimed to transform a non-degenerate random variable into its certainty equivalent. However, there can be no certainty equivalent for a non-degenerate random variable by the set-theoretic definition of a random variable, whilst the continuity axiom of EUT implies the existence of such a certainty equivalent. This paper also demonstrates that rational behaviour under utility theory is incompatible with scarcity of resources, making behaviour consistent with EUT irrational and justifying persistent external inconsistencies of EUT. A brief description of a new paradigm which can resolve the problems of the standard paradigm is presented. These include resolutions of such anomalies as instant endowment effect, asymmetric valuation of gains and losses, intransitivity of preferences, profit puzzle as well as the St. Petersburg paradox. Keywords: decision-making; rationality; risk; expected utility; behavioural puzzles MSC Codes: 62Cxx; 90B50; 91A26; 91B02; 91B06; 91B16; 91B30 Citation: Falahati, Kazem. 2021. The JEL Codes: C00; D01; D81 Standard Model of Rational Risky Decision-Making. Journal of Risk and Financial Management 14: 158. -
Updating Rules for Non-Bayesian Preferences
Updating Rules for Non-Bayesian Preferences. Tan Wang∗ December, 1999 Abstract We axiomatize updating rules for preferences that are not necessarily in the expected utility class. Two sets of results are presented. The first is the axiomatization and representation of conditional preferences. The second consists of the axiomatization of three updating rules: the traditional Bayesian rule, the Dempster-Shafer rule, and the generalized Bayesian rule. The last rule can be regarded as the updating rule for the multi-prior expected utility (Gilboa and Schmeidler (1989)). The operational merit of it is that it is equivalent to updating each prior by the traditional Bayesian rule. ∗Tan Wang is with the Faculty of Commerce and Business Administration, University of British Columbia, Van- couver, British Columbia, Canada, V6T 1Z2. [email protected]. The author is grateful to the Social Sciences and Humanities Research Council of Canada for financial support. 1 Introduction The traditional approach to updating is the Bayesian rule. This approach is justified by the ax- iomatic treatment of Savage (1954), where it is shown that, in situations of uncertainty, if a decision maker’s preference satisfies a certain set of axioms, his preference can be represented by an expected utility with respect to a subjective probability measure and that probability measure represents the decision maker’s belief about the likelihood of events. Moreover, in light of new information, the decision maker updates his belief according the Bayesian rule. This Savage paradigm has been the foundation of much of the economic theories under uncertainty. At the same time, however, the Savage paradigm has been challenged by behavior exhibited in Ellsberg paradox (Ellsberg (1961)), which seems to question the very notion of representing a decision maker’s belief by a probability measure and hence by implication the validity of the Bayesian rule. -
Economics 142: Choice Under Uncertainty (Or Certainty) Winter 2008 Vincent Crawford (With Very Large Debts to Matthew Rabin and Especially Botond Koszegi)
Economics 142: Choice under Uncertainty (or Certainty) Winter 2008 Vincent Crawford (with very large debts to Matthew Rabin and especially Botond Koszegi) Background: Classical theory of choice under certainty Rational choice (complete, transitive, and continuous preferences) over certain outcomes and representation of preferences via maximization of an ordinal utility function of outcomes. The individual makes choices “as if” to maximize the utility function; utility maximization is just a compact, tractable way for us to describe the individual’s choices in various settings. We can view the utility function as a compact way of storing intuition about behavior from simple experiments or though-experiments and transporting it to new situations. The preferences represented can be anything—self-interested or not, increasing in intuitive directions (more income or consumption) or not—although there are strong conventions in mainstream economics about what they are normally defined over—own income or consumption rather than both own and others’, levels of final outcomes rather than changes. Thus if you think the mainstream approach is narrow or wrong-headed, it may make as much or more sense to complain about those conventions than about the idea of rationality per se. Background: Classical “expected utility” theory of choice under uncertainty This is the standard way to describe people’s preferences over uncertain outcomes. The Marschak reading on the reading list, linked on the course page, is a readable introduction. The basic idea is that -
Behavioral Economics Comes of Age
Behavioral Economics Comes of Age Wolfgang Pesendorfer† Princeton University May 2006 † I am grateful to Markus Brunnermeier, Drew Fudenberg, Faruk Gul and Wei Xiong for helpful comments. 1. Introduction The publication of “Advances in Behavioral Economics” is a testament to the success of behavioral economics. The book contains important second-generation contributions to behavioral economics that build on the seminal work by Kahnemann, Tversky, Thaler, Strotz and others. Behavioral economics is organized around experimental findings that suggest inade- quacies of standard economic theories. The most celebrated of those are (i) failures of expected utility theory; (ii) the endowment effect; (iii) hyperbolic discounting and (iv) social preferences. Most of the articles collected in Advances deal with one of these four topics. Expected Utility: Expected utility theory assumes the independence axiom. The (stochastic version of the) independence axiom says that the frequency with which a pool of subjects chooses lottery p over q doesnotchangewhenbothlotteriesaremixedwithsome common lottery r. Experiments by Allais, Kahnemann and Tversky and others demon- strate systematic failures of the independence axiom. Chapter 4 in the book discusses this experimental evidence and the theories that address it. Kahnemann and Tversky (1979) develop prospect theory to address the failures of expected utility theory. They argue that when analyzing choice under uncertainty it is not enough to know the lotteries an agent is choosing over. Rather, we must know more about thesubject’ssituationatthetimehemakeshischoice.Prospecttheorydistinguishes between gains and losses from a situation-specific reference point. The agent evaluates gains and losses differently and exhibits first-order risk aversion locally around the reference point. The Endowment Effect: In standard consumer theory, demand is a function of wealth and prices but does not depend on the composition of the endowment. -
Welfare Goal in Antitrust Journals.Sagepub.Com/Home/Abx
The Antitrust Bulletin 1-39 ª The Author(s) 2018 The Unsound Theory Behind Article reuse guidelines: sagepub.com/journals-permissions the Consumer (and Total) DOI: 10.1177/0003603X18807802 Welfare Goal in Antitrust journals.sagepub.com/home/abx Mark Glick* Abstract This is the first installment of a two-part commentary on the New Brandeis School (the “New Brandeisians”) in Antitrust. In this first part, I examine why the New Brandeisians are correct to reject the consumer welfare standard. Instead of arguing, as the New Brandeisians do, that the consumer welfare standard leads to unacceptable outcomes, I argue that the consumer or total welfare standard was theoretically flawed and unrigorous from the start. My basic argument is that antitrust law addresses the impact of business strategies in markets where there are winners and losers. For example, in the classical exclusionary monopolist case, the monopolist’s conduct is enjoined to increase competition in the affected market or markets. As a result of the intervention, consumers benefit, but the monopolist is worse off. One hundred years of analysis by the welfare economists themselves shows that in such situations “welfare” or “consumer welfare” cannot be used as a reliable guide to assess the results of antitrust policy. Pareto Optimality does not apply in these situations because there are losers. Absent an ability to divine “cardinal utility” from obser- vations of market behavior, other approaches such as consumer surplus, and compensating and equivalent variation cannot be coherently extended from the individual level to markets. The Kaldor-Hicks compensation principle that is in standard use in law and economics was created to address problems of interpersonal comparisons of utility and the existence of winners and losers. -
Prospect Theory
Prospect Theory Warwick Economics Summer School Prospect Theory Eugenio Proto University of Warwick, Department of Economics July 19, 2016 Prospect Theory, 1 of 44 Prospect Theory Outline 1 General Introduction 2 The Expected Utility Theory 3 Main Departures from Expected Utility 4 Prospect Theory 5 Empirical Evidence Finance Economic Development Housing Markets Labor Market Domestic Violence 6 Summary Prospect Theory, 2 of 44 Prospect Theory General Introduction Behavioral Economics Economics and Psychology were not separated Adam Smith: The theory of Moral Sentiments Jeremy Bentham, the psychological underpinnings of Utility Francis Edgeworth, concept of envy in Utility Functions Prospect Theory, 3 of 44 Prospect Theory General Introduction Behavioral Economics, cont'd Neoclassical Revolution separated clearly Psychology and Economics Economics like a natural (and not a social) science Psychology has too unsteady foundations Utility can be defined as an ordinal (and not a cardinal) object Rejection of the hedonistic assumptions of Benthamite Utility Neoclassical economists expunged the psychology from economics Prospect Theory, 4 of 44 Prospect Theory General Introduction Behavioral Economics, cont'd Some early Criticism to the neoclassical economy from Irwing Fisher, J.M. Keynes,, Herbert Simon More from Allais (1953), Ellsberg (1961), Markowitz (1952), Strotz (1955), following the Expected Utility Theory and the discounted utility models Kahneman and Tversky (1979) on expected utility, Thaler (1981) and Loewenstain and Prelec (1992) -
Economic Theory, Ideal Types, and Rationality
Lansana Keita Economic Theory, Ideal Types, and Rationality Abstract: Contemporary economic theory is generally regarded as a scien tific or at least potentially so. The replacing of the cardinal theory of utility measurement by the ordinal theory was supposed to prepare the groundwork for economics as a genuine science. But in adopting the ordinal approach, theorists saw fit to anchor ordinal theory to axioms of choice founded on principles of rational behavior. Behavior according to these axioms was embodied in the ideal type model of rational economic man. This model served the basis for scientific explanation of the choices made by actual economic agents. I argue though that the postulate of rationality is a normative principle and that this compromises the scientific pre tensions of economic theory. Yet the theorist must rely on this principle to formulate predictive and explanatory theories. This raises questions as to whether it is possible that economic theory satisfy the same kind of scientific criteria set down for research in the natural sciences. I. It is generally assumed that of all the social sciences, econom ics is the most promising candidate for acceptance as a science. Theories in economics conform to the formal requirements de manded of theories in natural science in the sense that they possess basic postulates, axioms and laws whose function is to describe at a fundamental level some segment of the empir ical world particular to the discipline itself. Predictive and explanatory theories are then constructed from these posited axioms and postulates. For example, microeconomic theory which is founded on a set of axioms of choice purports to predict and explain the behavior of the consumer and that of the entre preneur. -
Ordinal Utility and the Traditional Theory of Consumer Demand1 Donald W
real-world economics review, issue no. 67 subscribe for free Ordinal utility and the traditional theory of consumer demand1 Donald W. Katzner [University of Massachusetts/Amherst, USA] Copyright: Donald W. Katzner, 2014 You may post comments on this paper at http://rwer.wordpress.com/comments-on-rwer-issue-no-67/ In an earlier issue of this Journal, Jonathan Barzilai, in a paper entitled, “Inapplicable Operations on Ordinal, Cardinal, and Expected Utility” [see reference 2], has raised important issues regarding ordinal utility, and correctly clarified the meaning of the general notion of ordinality in terms of the mathematical theory of measurement. In that process, he has also subjected the traditional theory of consumer demand to serious attack. Barzilai's assault on traditional consumer theory, which is based on the mathematical theory of measurement, is useful because it brings to the fore the fact that, for economists, there is a second notion of ordinal utility, older than and independent of the mathematical-theory-of-measurement concept, and which is the relevant one for the traditional theory of consumer demand. That older approach seems to have had widespread acceptance among economists before the newer mathematical approach was known to them. The essence of Barzilai's attack consists of the claims that: 1. The function values of the utility function in that theory are ordinal and cannot, according to the mathematical theory of measurement, be subjected to arithmetic operations. This means that, since the reckoning of derivatives requires subtraction and division of function values, the derivatives of the ordinal utility function cannot be calculated. -
How Prospect Theory Can Improve Legal Counseling
University of Arkansas at Little Rock Law Review Volume 24 Issue 1 The Ben J. Altheimer Symposium: The Article 4 Impact of Science on Legal Decisions 2001 How Prospect Theory Can Improve Legal Counseling John M.A. DiPippa University of Arkansas at Little Rock William H. Bowen School of Law, [email protected] Follow this and additional works at: https://lawrepository.ualr.edu/lawreview Part of the Law and Society Commons, Legal History Commons, and the Legal Profession Commons Recommended Citation John M.A. DiPippa, How Prospect Theory Can Improve Legal Counseling, 24 U. ARK. LITTLE ROCK L. REV. 81 (2001). Available at: https://lawrepository.ualr.edu/lawreview/vol24/iss1/4 This Essay is brought to you for free and open access by Bowen Law Repository: Scholarship & Archives. It has been accepted for inclusion in University of Arkansas at Little Rock Law Review by an authorized editor of Bowen Law Repository: Scholarship & Archives. For more information, please contact [email protected]. HOW PROSPECT THEORY CAN IMPROVE LEGAL COUNSELING John MA. DiPippa" I. INTRODUCTION Rational choice is the law's predominate model.' The law believes that (1) clients are rational, and (2) they will act rationally by choosing the path that leads to maximum utility, and (3) lawyers act profession- ally when they base their professional behavior on these assumptions. Clients need the information that will allow them (or their lawyer) to calculate the costs and benefits of each decision. In essence, law transplants the assumptions of classical economics into the realm of lawyer-client decision making.' Recent research casts doubt on the rational choice model of decision making. -
Bounded Rationality Till Grüne-Yanoff* Royal Institute of Technology, Stockholm, Sweden
Philosophy Compass 2/3 (2007): 534–563, 10.1111/j.1747-9991.2007.00074.x Bounded Rationality Till Grüne-Yanoff* Royal Institute of Technology, Stockholm, Sweden Abstract The notion of bounded rationality has recently gained considerable popularity in the behavioural and social sciences. This article surveys the different usages of the term, in particular the way ‘anomalous’ behavioural phenomena are elicited, how these phenomena are incorporated in model building, and what sort of new theories of behaviour have been developed to account for bounded rationality in choice and in deliberation. It also discusses the normative relevance of bounded rationality, in particular as a justifier of non-standard reasoning and deliberation heuristics. For each of these usages, the overview discusses the central methodological problems. Introduction The behavioural sciences, in particular economics, have for a long time relied on principles of rationality to model human behaviour. Rationality, however, is traditionally construed as a normative concept: it recommends certain actions, or even decrees how one ought to act. It may therefore not surprise that these principles of rationality are not universally obeyed in everyday choices. Observing such rationality-violating choices, increasing numbers of behavioural scientists have concluded that their models and theories stand to gain from tinkering with the underlying rationality principles themselves. This line of research is today commonly known under the name ‘bounded rationality’. In all likelihood, the term ‘bounded rationality’ first appeared in print in Models of Man (Simon 198). It had various terminological precursors, notably Edgeworth’s ‘limited intelligence’ (467) and ‘limited rationality’ (Almond; Simon, ‘Behavioral Model of Rational Choice’).1 Conceptually, Simon (‘Bounded Rationality in Social Science’) even traces the idea of bounded rationality back to Adam Smith. -
On Ordinal Utility, Cardinal Utility, and Random Utility
This is a repository copy of On ordinal utility, cardinal utility, and random utility . White Rose Research Online URL for this paper: http://eprints.whiterose.ac.uk/2544/ Article: Batley, R. (2007) On ordinal utility, cardinal utility, and random utility. Theory and Decision, Online. ISSN 1573-7187 https://doi.org/10.1007/s11238-007-9046-2 Reuse See Attached Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the reason for the withdrawal request. [email protected] https://eprints.whiterose.ac.uk/ White Rose Research Online http://eprints.whiterose.ac.uk/ Institute of Transport Studies University of Leeds This is an author produced version of a paper published in Theory and Decision Journal. It has been peer reviewed but does not include the final publishers formatting and pagination. White Rose Repository URL for this paper: http://eprints.whiterose.ac.uk/2544/ Published paper Batley, Richard (2007) On ordinal utility, cardinal utility, and random utility. Theory and Decision, Online First, May 2007 White Rose Consortium ePrints Repository [email protected] Onordinalutility,cardinalutility,andrandomutility RichardBatley InstituteforTransportStudies,UniversityofLeeds,UK [email protected] ABSTRACT ThoughtheRandomUtilityModel(RUM)wasconceivedentirelyintermsof ordinal utility, the apparatus through which it is widely practised exhibits properties of cardinal utility.The adoption of cardinal utility as a working operation of ordinal is perfectly valid, provided interpretations drawnfrom thatoperationremainfaithfultoordinalutility.Thepaperconsiderswhether the latter requirement holds true for several measurements commonly derivedfromRUM.Inparticularitisfoundthatmeasurementsofconsumer surplus change may depart from ordinal utility, and exploit the cardinality inherentinthepracticalapparatus. -
Direct Tests of Cumulative Prospect Theory⇤
Direct Tests of Cumulative Prospect Theory⇤ B. Douglas Bernheim † Charles Sprenger‡ Stanford University and NBER UC San Diego First Draft: December 1, 2014 This Version: November 8, 2016 Abstract Cumulative Prospect Theory (CPT), the leading behavioral account of decision making under uncertainty, assumes that the probability weight applied to a given outcome depends on its ranking. This assumption is needed to avoid the violations of dominance implied by Prospect Theory (PT). We devise a simple test involving three-outcome lotteries, based on the implication that compensating adjustments to the payo↵s in two states should depend on their rankings compared with payo↵s in a third state. In an experiment, we are unable to find any support for the assumption of rank dependence. We separately elicit probability weighting functions for the same subjects through conventional techniques involving binary lotteries. These functions imply that changes in payo↵rank should change the compensating adjustments in our three-outcome lotteries by 20-40%, yet we can rule out any change larger than 7% at standard confidence levels. Additional tests nevertheless indicate that the dominance patterns predicted by PT do not arise. We reconcile these findings by positing a form of complexity aversion that generalizes the well-known certainty e↵ect. JEL classification: D81, D90 Keywords:ProspectTheory,CumulativeProspectTheory,RankDependence,CertaintyEquiv- alents. ⇤We are grateful to Ted O’Donoghue, Colin Camerer, Nick Barberis, Kota Saito, and seminar participants at Cornell, Caltech, and Gary’s Conference (UC Santa Barbara) for helpful and thoughtful discussions. Fulya Ersoy, Vincent Leah-Martin, Seung-Keun Martinez, and Alex Kellogg all provided valuable research assistance.