Preferences over characteristics and utility functions over commodities

Following Lancaster, preferences are defined over a set of characteristics, while commodities vectors are transformed into characteristics by a production function. We assume that both the preferences over the characteristics and the production functions are “neoclassical” and we characterize the set utility functions over the consumption space derived as the composition of preferences over characteristics and production functions. We prove that, under regularity conditions, any function can be derived by such a composition. Thus, the theories of characteristics does not impose any restrictions on derived utility functions. We thank an anonymous referee for helpful suggestions. The research of Aldo Rustichini was supported by the NSF grant NSF/SES-0136556. Paolo Siconolfi acknowledges the support of the Graduate School of Business, Columbia University.     

Characterizing stochastically monotone functions by multiattribute utility theory

The research of Peter Wakker has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences.     

Subjective ambiguity, expected utility and Choquet expected utility

Summary. Using the Savage set up, this paper provides a simple axiomatization of the Choquet Expected Utility model where the capacity is an inner measure. Two attractive features of the model are its specificity and the transparency of its axioms. The key axiom states that the decision-maker uses unambiguous acts to approximate ambiguous ones. In addition, the notion of ‘ambiguity’ is subjective and derived from preferences. Received: March 23, 2000; revised version: April 24, 2001     

Differentiable von Neumann-Morgenstern utility

Summary. Differentiability is a convenient property of von Neumann-Morgenstern utility functions which is almost always imposed but has not been translated into behavioral terms. In applications, expected utility is usually maximized subject to a constraint, and the maximization is carried out by differentiating the utility function. This paper presents two sets of necessary and sufficient conditions for a risk averse von Neumann-Morgenstern utility function to be differentiable. The first of them is formulated in terms of the equivalent risk premia of small gambles. It says, in brief, that the equivalent risk premium is of a smaller order of magnitude than the risk itself, as measured by the expectation of the absolute value of the risk. The second set of necessary and sufficient conditions is formulated in terms of the probability premium of small lotteries. It says, essentially, that the probability premium for small binary lotteries goes to zero as the size of the lottery goes to zero. Received: May 11, 1997; revised version: May 14, 1998     

Expected utility theory and prospect theory: one wedding and a decent funeral

Choice behavior is typically evaluated by assuming that the data is generated by one latent decision-making process or another. What if there are two (or more) latent decision-making processes generating the observed choices? Some choices might then be better characterized as being generated by one process, and other choices by the other process. A finite mixture model can be used to estimate the parameters of each decision process while simultaneously estimating the probability that each process applies to the sample. We consider the canonical case of lottery choices in a laboratory experiment and assume that the data is generated by expected utility theory and prospect theory decision rules. We jointly estimate the parameters of each theory as well as the fraction of choices characterized by each. The methodology provides the wedding invitation, and the data consummates the ceremony followed by a decent funeral for the representative agent model that assumes only one type of decision process. The evidence suggests support for each theory, and goes further to identify under what demographic domains one can expect to see one theory perform better than the other. We therefore propose a reconciliation of the debate over two of the dominant theories of choice under risk, at least for the tasks and samples we consider. The methodology is broadly applicable to a range of debates over competing theories generated by experimental and non-experimental data.     

Upper and lower bounds for expected utility

Summary.   The decision-theoretic literature has developed very few techniques to bound the expected utility of a random variable when only simple statistics like its median or mode or mean are known. One reason for this lack of results is that we are missing a convenient way to link probability theory and expected utility. This paper is written to demonstrate a general (and genuinely probabilistic) technique to obtain upper and lower bounds for the expected utility of a lottery. Received: December 14, 1999; revised version: March 8, 2000     

On the characterization of excess demand functions

Summary. In this paper, we give the necessary and sufficient conditions that characterize the individual excess demand function when it depends smoothly on prices and endowments. A given function is an excess demand function if and only if it satisfies, in addition to Walras law and zero homogeneity in prices, a set of first order partial differential equations, its substitution matrix is symmetric and negative semidefinite. Moreover, we show that these conditions are equivalent to the symmetry and negative semidefiniteness of Slutsky matrix, Walras law and zero homogeneity of Marshallian demand functions.Received: 25 November 2002, Revised: 11 March 2004, JEL Classification Numbers: D11.Marwan Aloqeili: I would like to thank an anonymous referee for helpful comments.     

Remarks concerning concave utility functions on finite sets

Summary. A direct construction of concave utility functions representing convex preferences on finite sets is presented. An alternative construction in which at first directions of supergradients (prices) are found, and then utility levels and lengths of those supergradients are computed, is exhibited as well. The concept of a least concave utility function is problematic in this context.Received: 28 November 2002, Revised: 28 June 2004, JEL Classification Numbers: D11, C60.I am indebted to an anonymous referee, Marcel K. Richter and Kam-Chau Wong, for many valuable remarks and suggestions.     

A note on linear utility

Summary We show that any complete, lower-semicontinuous, and translation-invariant preorder defined on a topological vector space admits a linear and continuous utility representation.Thanks are given to an anonymous referee for his/her valuable suggestions and comments.     

A new approach to modeling decision-making under uncertainty

This paper presents two axiomatic models of decision making under uncertainty that avoid the use of a state space. The first is a subjective expected utility model with action-dependent subjective probabilities and effect-dependent preferences (the case of effect-independent preferences is obtained as a special instance). The second is a nonexpected utility model involving well-defined families of action-dependent subjective probabilities on effects and a utility representation that is not necessarily linear in these probabilities (a probabilistic sophistication version of this model, with action-dependent subjective probabilities is obtained as a special case). The hospitality of EUREQua, University of Paris 1, and financial support by the National Science Foundation grant SES-0314249 are gratefully acknowledged.     

Stability of risk preference parameter estimates within the Becker-DeGroot-Marschak procedure

This paper reports new data from both selling and buying versions of the Becker-DeGroot-Marschak (BDM) procedure. First, when using the selling version of BDM, the cross-sectional mean of CRRA risk preference parameter estimates shifts from a value consistent with “as if” risk-seeking behavior in the early baseline to a value closer to “as if” risk neutrality in the late baseline. Second, when using the buying version of BDM, the cross-sectional mean of CRRA risk preference parameter estimates does not appear to change over time in a statistically significant manner. The cross-sectional mean from the late baseline of the buying version of BDM is closer to “as if” risk neutrality and to the late baseline estimates from the selling version of BDM than it is to either early baseline estimates from the selling version of BDM or typical estimates from the first price auction. Use of dominated offers is correlated with deviations from “as if” risk neutrality; this suggests the possibility that the early deviations from “as if” risk neutrality reflect errors. Electronic Supplementary Material Supplementary material is available in the online version of this article at . JEL Classification D80     

On the existence of expected multi-utility representations

We prove the following facts related to the expected multi-utility representation of an affine preorder: If the prize space is not compact and if the lottery set consists of all probabilities on the prize space, standard independence and continuity axioms do not guarantee the existence of a (continuous) representation. If the prize space is σ-compact and lotteries have compact support, a representation exists. When the preorder in question is bounded, this result extends to the set of lotteries that consists of all probabilities on the prize space. For the case of monetary lotteries, the boundedness assumption in this last result can be dropped, provided that the preference relation at hand is monotone and risk-averse.     

Subjective recursive expected utility

We axiomatize a subjective version of the recursive expected utility model. This development extends the seminal results of Kreps and Porteus (Econometrica 46:185–200 (1978)) to a subjective framework and provides foundations that are easy to relate to axioms familiar from timeless models of decision making under uncertainty. Our analysis also clarifies what is needed in going from a represention that applies within a single filtration to an across filtration representation.Part of this research was conducted when Ozdenoren visited MEDS in Fall 2003. We thank Tapas Kundu, Costis Skiadas, Jean-Marc Tallon and Tan Wang for helpful discussions and also thank audiences at Koc University, Northwestern University, the CERMSEM conference “ Mathematical Models in Decision Theory” at Universite Paris I, and the FUR XI conference on foundations and applications of utility, risk and decision theory     

Theories of choice under risk: Insights from financial markets

To date, the plausibility of theories of choice under risk hinges are mainly on experimental evidence. This paper devises and implements an approach amenable of assessing the performance of three families of models (expected utility, rank-dependent expected utility, and the cumulative prospect theory) using information from financial asset markets. Our findings unequivocally support reference-point dependence, diminishing marginal sensitivity, loss aversion, and nonlinear weighting of (gain and loss) physical probabilities. The empirical observations are found to be robust to, inter alia, the parameterization of the utility and probability weighting functions, “day-of-the-week effects”, the choice of a reference point, and the introduction of possible, low-probability market crashes (peso component).     

Option price without expected utility

We consider the meaning of the option price, commonly acknowledged as the preferred ex ante welfare measure, in the rank-dependent expected utility (RDEU) framework. The importance of this pertains to performing benefit-cost analysis when RDEU maximizers are prevalent in society.     

A simple axiomatization and constructive representation proof for choquet expected utility

>P>Summary. We provide a set of simple and intuitive set of axioms that allow for a direct and constructive proof of the Choquet Expected Utility representation for decision making under uncertainty. Received: October 29, 2002; revised version: November 13, 2002 RID="*" ID="*" We thank Matthew Ryan for very useful comments and suggestions on related work and for encouraging us to write this note. Correspondence to: S. Grant     

Saving under rank-dependent utility

Summary. In this note we use the rank-dependent utility (RDU) model to analyze saving decisions. The RDU model enables us to separate the effects of pessimism and optimism on saving from that of concavity of the utility function. While pessimism induces more saving, the importance of this effect is shown to depend upon properties of the utility function such as prudence and temperance.JEL Classification Numbers: D11, D81.An anonymous referee provided helpful comments. Han Bleichrodts research was made possible by a grant from the Netherlands Organisation for Scientific Research (NWO). Louis Eeckhoudt acknowledges support from the Interuniversity Attraction Poles Programme - Belgian State - Federal Office for Scientific, Technical, and Cultural Affairs.     

Expected utility theory and experimental utility measurement, 1950–1985. From confidence to scepticism

Abstract

The paper reconstructs the history of the experimental attempts to measure the cardinal utility of money between 1950 and 1985 within the framework provided by expected utility theory (EUT). It is shown that this history displays a definite trajectory: from the confidence in EUT and the EUT-based measurement of utility of the 1950s to the scepticism that, from the mid-1970s, haunted the validity of EUT as well as the significance of the utility measures obtained through it. By exploring the diverse aspects and causes of this trajectory, the paper covers new ground in the history of both decision theory and utility measurement.