Multiattribute Utility Theory

In making a decision, an individual evaluates the possible consequences and expected utility of various alternatives. Then, he or she chooses the course of action that provides the highest expected utility. The most common or traditional utility theory assumes that an individual’s utility is a function of a single attribute objective such as wealth or income.

However, most complex decision problems involve multiple, conflicting objectives.

Multiattribute utility theory can be used for decision analysis when a decision involves multiple attributes or objectives. Producers have different management objectives, financial status, risk preferences, demographic characteristics, and socioeconomic characteristics, which will cause

One can use multiattribute analysis to investigate the way in which a decision maker establishes tradeoffs between alternative attributes to maximize his utility. Attributes, in multiattribute decision analysis, refer to the various factors that can have a significant impact on a decision maker’s choice between alternative situations. If only one attribute is evaluated in a model when additional attributes are important to the decision maker, then the model will provide biased, inaccurate results. Therefore, it is important to consider all attributes that could influence an individual’s preference for a given situation when assessing utility (Keeney and Raiffa).

The general framework for a multiattribute decision problem assumes that an objectives hierarchy has been specified and that attributes x1, x2,...,xn have been determined to be appropriate for the problem. Let X represent a composite good (insurance product) with n attributes, where X = (xij,…,xnj) and xij represents the ith attribute level of the jth product profile.

The utility function for the jth multiattribute product can be written as follows:

[3]

úûù êëé çèæ ÷øö

=U xij xnj

j X ,...,

U

This utility function is analyzed over the n attributes, where there are a total of j alternative products.

An additive utility function implies additive independence of the attributes. “An attribute, Xi, is additive independent of attribute Xj when conditional preferences for attribute Xi

given Xj do not depend on the particular level of Xj” (Keeney and Raiffa). The additive utility function can be written as follows:

[4] U_j=b₁x_1j+ b₂x_2j +...+b_nx_nj

In this linear equation, bi represents the weight or part worth utility for each attribute for

attribute to obtain total utility for the profile. If interactions between attributes are found to be significant, another functional form will be specified.

3.1.2 Conjoint Analysis

Conjoint analysis (CA) offers a flexible methodology that can be applied in almost any area in which consumer decisions are being evaluated. Conjoint analysis is a multivariate technique that uses a survey-based approach to understand how respondents develop preferences for products or services. In a conjoint experiment, a product is decomposed into relevant factors or attributes that can be combined to fully describe the product. From the specified attributes and attribute levels, hypothetical products are constructed for respondents to evaluate. One is able to determine the importance of product attributes and their levels by allowing respondents to evaluate only a fraction of the possible product combinations.

Respondents evaluate the products through a realistic procedure that is very similar to making tradeoffs among products in everyday decision-making. Respondents to conjoint survey questions are asked to either rate or rank the different product profiles that are comprised of various levels of the pre-specified attributes. Respondents are provided a numerical scale, which is used to rate each profile, or they rank each of the profiles numerically from most to least preferred. Therefore, products that are given a higher overall rating or ranking provide more utility to the consumer.

Utility is the conceptual basis for assessing the value of a product or service with CA.

When the observed rankings or ratings are collected from respondents, they are used as the dependent variables, the specified attributes are the independent variables, and the part worth utility values are estimated econometrically. The respondent’s total utility for a product is determined from the combination of individual or part worth utility values for each attribute of

the product. The part worth utility estimates can be combined for any combination of attributes so that the total utility for a wide range of products can be determined. The part worth estimates can also be used as a method to segment the market (Green and Srinivasan). Individuals with similar estimates are clustered together to identify differences in characteristics.

From Equation 4, the utility, Uj, represents an observable utility measure. The judgmental values (ratings or rankings) that the respondent provides for a profile are the actual observable utility measures, and they represent the dependent variable for the model. The independent variables in the model, xij, are the attribute levels specified for each product attribute. The weights of the independent variables (part worth utilities), denoted by bi, are estimated econometrically. Thus, Equation 4 can be rewritten as follows:

[5] R_j=b₁x_1j+ b₂x_2j +...+b_nx_nj

Here, Rj represents the actual rating or ranking provided by the respondent.

Producers are assumed to select the combination of attributes that will maximize their utility subject to their individual objectives (Varian). This suggests that the decision maker will choose product j over j+1 only if Uj > Uj+1. The theoretical framework for estimating the marginal contribution of specific attributes of livestock revenue protection products is based on consumer demand theory developed by Lancaster. The Lancasterian theoretical framework is used, which suggests that goods are not the direct object of utility; rather, it is the characteristics of the goods from which utility is derived. The decision maker’s theoretical utility model can be expressed as follows:

[6] Uj = f(X1j, X2j, …Xnj; Z1, Z2…,Zn | Qⁿ) + e

In Equation 6, Uj represents the utility an individual receives from product j, Xij represents the ith attribute level for product j, Zi represents the socioeconomic profile for each individual (i

term. The variables x and Z are main effect variables for product attributes and individuals’

profiles, respectively.

The partial derivative of the consumer’s utility of the jth product with respect to the product characteristic, ∂U(x*)j/ ∂xnj, gives the value or part worth that the consumer assigns to the nth characteristic level of the jth product (Louviere). According to this formulation, the change in a cattle producer’s utility for an insurance product is determined by variations of the insurance attributes. The conceptual and empirical strength of conjoint analysis comes from the information gained from analysis of the trade-offs made among product attributes that can be used to establish the perceived preference for all available products (Gan and Luzar).

The contribution of each individual attribute to the respondents’ total utility defines the preference for the given product. Knowing the preference structure of producers provides a tremendous amount of flexibility in examining both individual and aggregate attitudes to a wide range of products. The part worth utility values provide the researcher the flexibility to perform the following tasks: 1) define the object with the optimum combination of features; 2) show the relative contributions of each attribute and each level to the overall evaluation of the object; 3) use estimates of consumer judgments to predict preferences among objects with differing sets of attributes; 4) isolate groups of potential consumers who place differing values on the attributes to define potential segments; and 5) identify marketing opportunities by exploring the market potential for attribute combinations not currently available (Hair et al.).