Decision Maker's Utility Function Research Articles

Decisions with Estimation Uncertainty

This paper provides necessary and sufficient conditions for it to be optimal to base decisions on estimates of the parameters that characterize a decision problem (e.g., profit maximization with an estimated price elasticity of demand). We show that the separation of parameter estimation from decision making generally yields lower utility than an integrated approach which takes account of estimation uncertainty. We evaluate the decision in the parameter estimation method and show that the resulting utility loss can be substantial. MANY ACTUAL DECISIONS are based on statistical estimates of parameters that help to characterize the decision environment. For example, a firm maximizing the expected utility of profit might find that its input and output decisions depend on unknown parameters of its demand function. Econometric estimates of such parameters might then be derived and utilized in making these decisions. The first purpose of this paper is to rigorously investigate whether it is correct to make decisions in this manner; in general, it is not. The second purpose is to investigate the decis'ion bias in decisions based on commonly employed parameter estimates. We will determine, for example, whether a price setting monopolist is mistakenly setting prices too high or too low when he bases his pricing decision on the maximum likelihood estimate of his demand equation. Finally, we provide a detailed numerical example to show that basing decisions on conventional parameter estimates can lead to large losses of utility. In Section 2, we introduce all notation, explain the procedure commonly used when basing decisions on values of unknown underlying parameters, and exhibit the decision-theoretic correct alternative procedure. When the optimal decisions under these two procedures are identical, we call the proper. We use the term summary value to refer not only to standard parameter estimates but to any single substituted for an unknown parameter in order to make decisions. This generalized concept is necessary because a that is appropriate for making decisions, in a sense defined below, need not have any of the properties of conventional parameter estimators. In Section 3, we derive under general assumptions necessary and sufficient conditions for the existence of proper values that are independent of the decision maker's utility function, U( ). This independence restriction is

Comment on “Budgetary Responses of Individual Governmental Units to Federal Grants”

In a recent issue of Public Finance Quarterly, Hardy (1976) presented results of a study of the effect of conditional and unconditional grants on various categories of expenditures of the provinces of Ontario and New Brunswick. It is the purpose of this comment to point out several shortcomings of this paper with respect to the formulation of the provincial decision maker's utility function and his constraints with respect to conditional grants.

An interactive algorithm for optimal control of a system with multiple criteria

An interactive approach is proposed for the optimization of deterministic systems with multiple criteria. This approach does not require an explicit knowledge of the decision maker's utility function, but it is assumed that the decision maker can provide local information about this function at each interation The use of this interactive approach is then illustrated by applying it to the satellite attitude control problem and results are presented

A note on Marshallian and von Neumann-Morgenstern utility

The curvature of a decision maker's utility function is often used to measure his risk preference. In order to comprehensively describe an individual's decision making behaviour, however, it would also seem desirable to measure the gain in utility from an increase in wealth or income before accounting for risk. If a small increase in wealth leads to a large utility gain, then it could be said that the individual's aspiration to achieve the wealth increase would be high. This aspiration, however, may be more than offset by the risk involved in obtaining this extra wealth and the individual's attitude towards risk. In the following paper it is shown how the marginal utility of Marshall can be used in a measure of aspiration with this measure then combined with the usual measure of risk preference to explain the shape of any individuals utility curve. Using these measures, a general utility curve for all income or wealth classes is postulated.

A Procedure for Selecting Educational Goal Areas for Emphasis

This paper presents a description of a procedure for identifying educational goal areas to be emphasized in elementary schools; it produces an index number for each goal area that approximates the incremental increase in the decision-maker's utility function arising from emphasizing it. This utility function is defined on performance measures for a group of students. The procedure has been simplified to the extent that elementary school principals can be expected to perform the required computations without assistance.

A Generalization of Some Distribution Aspects of Chance-Constrained Linear Programming

AN ORDINARY LINEAR PROGRAMMING MODEL is said to be chance-constrained if its linear constraints are associated with a set of probability measures indicating the extent of violation of the constraints. When partial violation of the constraints is allowed for, the chance-constrained approach may be viewed as a method for providing appropriate safety margins. This approach has been generalized [9] in recent years in several directions. of which two are specially worth mentioning. First, although for reasons of simplicity solutions restricted to linear decision rules only have often been employed in chance-constrained programming, it is now possible to have solutions of a more general functional form, and this considerably enhances the scope of application of the chance-constrained approach in dynamic models with nonlinear objective functions. Second, it is not necessary in the chance-constrained approach to make the assumption that the decision maker's utility function is quadratic (or of a specific form), as it is required, for example, in the portfolio selection studies by Markowitz and others who base the analysis on the mean and variance of the probability distribution of net returns. Although the extent of violation of the constraints that would be tolerated is preassigned subjectively in this approach by the decision maker before the: actual solutions are computed, the tolerance measure may be parametrically varied, as in the revealed preference theory, and the resulting optimal solutions may help the decision maker move to the most preferred solution. This. formulation (see [8], [19]) also considerably helps the scope of applicability of the chance-constrained approach by developing suitable criteria for decisions under risk. Our objective here is to analyze the implications of a non-normal distribution of the random elements (A, b, c) of a linear program in the framework of probabilistic linear programming, where only the two approaches of chance-constrained programming (CCP) and stochastic linear programming (SLP) are considered. It is interesting to note that although the CCP and the SLP approaches are developed with different objectives in mind, they have frequently been applied under the assumption of normality of relevant