The Problem of Quantifying Utility
Authors: Romanchak V. M. 
Published: July 2021

Purpose of the study. Analysis of the literature shows that the ordinal theory of utility is widespread in the theory of consumer behavior. To analyze consumer preferences, a utility function is used, which characterizes the value of the utility of the consumed goods and services on a scale of order. Moreover, to find the marginal utility of a product, arithmetic operations are used, which are impossible on a scale of order. To allow arithmetic operations, a quantitative analysis of the utility function is required. Consequently, the problem of quantitative measurement of the utility function is relevant.

The measurement problem also arises in decision theory. For example, the hierarchy analysis method is a popular method for solving multicriteria problems, but contains an erroneous model of subjective measurement. For this reason, other methods appear in decision-making theory that should replace the method of analyzing hierarchies. The theory of the importance of criteria is being actively developed. However, the theory of the importance of criteria also does not solve the problem of quantitative measurement.

For a long time, the problem of measurement has also existed in psychophysics. The existence of two mismatched psychophysical laws contradicts the classical theory of measurements. Recently, a rating solution has been proposed. The equivalence of the basic laws of psychophysics has been proved. In this paper, it is proposed to use the rating method to measure preferences in utility theory and in decision theory.

Materials and methods. The domain of the rating is the set of ordered pairs of objects. Moreover, the composition (operation of addition) of objects is defined on the set of ordered pairs. A rating is a number that is assigned during a measurement to an ordered pair of objects.

The rating is assumed to preserve the operation of composition of ordered pairs.

An arithmetic operation is selected to carry out the measurement. The measurement result must match the result of the arithmetic operation. The result of an arithmetic operation is the difference or ratio of the values of the quantity. The rating values coincide with the result of the arithmetic operation (up to isomorphism).

The additivity of the rating is used to check the adequacy of the measurement results. For this, it is assumed that the rating is independent of the measurement method. The theoretical justification for independence is the isomorphism condition. The empirical confirmation of independence is the equivalence of the basic psychophysical laws.

Results. The paper presents an axiomatic approach to the measurement problem. Measurement can be carried out in both objective and subjective ways. The axiomatic and classical definition of the rating has been formulated. The axiomatic definition implies the classical definition for a special set of objects. The classic definition is constructive. To check the adequacy of the measurement results, it is enough to compare the ratings obtained by different measurement methods (method of alternatives).

Conclusion. The rating method is a quantitative measurement method. The rating method can be used to construct a model of consumer behavior and in decision-making theory.