Incorporating wealth information into a multiple criteria decision making model

Abstract

We describe how a multiple criteria decision making (MCDM) modelling framework can be extended to account for one of the behavioral ramifications of a decision making activity, namely, the decision maker’s (DM’s) perception of his/her current wealth status, referred to as decisional wealth. Within the MCDM framework, decisional wealth reflects the relative achievements of each of the objectives in a given efficient solution. It is our argument that a DM’s preferences and the importance of his/her objectives, vary depending on the decisional wealth. Therefore, we use the wealth information and trade-off analysis to guide the search for preferred outcomes. We identify efficient solutions that satisfy a DM’s wealth-dependent preferences, and we illustrate the proposed modelling framework with an example.

Introduction

The purpose of this paper is to present a methodological framework that incorporates information about the relative wealth of a decision maker (DM) into a multiple criteria decision making (MCDM) model, and guides the DM in the decision making process by considering his/her wealth-dependent attitudes. The issues we consider can be illustrated with the following example. Imagine a person who has spent an afternoon at the race track and has already lost $140. Would such a person bet $10 on a 15:1 long shot in the last race? There may be two ways to frame this decision. One may view the status quo as the reference point, and frame the outcomes as a chance to further increase a loss to $150. Thus, one may not be willing to take the bet. On the other hand, one may view the present state as a loss of $140 for the betting day, and frame the last bet as a chance to recover it and return to the starting point. The latter frame produces more willingness to take the bet (Tversky and Kahneman, 1981).

This example illustrates how the framing of outcomes changes depending on the current perception of the reference points. It shows that the outcomes of a decision can be perceived either as gains or losses relative to the status quo, or as asset positions incorporating initial wealth.

Kahneman and Tversky (1983) argue that prior outcomes can influence the reference points, and a change of reference point alters the framing of the decisions and the preferences of the DM.

Thaler and Johnson (1990) investigate the influences of prior outcomes (gains or losses) on the choices of the DM. They argue that prior losses can increase the DM’s willingness to accept outcomes that offer the opportunity to break-even. Viewing the last race in the context of earlier losses is an example of such a situation. Similarly, the evidence supports an observation that bets on long shots are more popular on the last race of the day (Tversky and Kahneman, 1981).

In this paper we attempt to model a situation where the DM’s choices depend on the wealth of a DM that is reflected by the outcomes associated with a current decision (and that it can be measured through the values of the objective functions in the MCDM model). Such a wealth status clearly has an impact on the DM’s perception of gains and losses and his/her framing of a reference point. Following the recommendations of behavioral research, such information should be incorporated into the MCDM framework where the search for a preferred outcome is conducted in an interactive manner (see Steuer, 1986 for information about interactive MCDM approaches). We propose to frame the search process within the MCDM model in terms of the achieved wealth (level of the objective functions) relative to the maximum attainable wealth (ideal values). This helps us to capture changes in the DM’s preferences depending on the currently achieved outcomes. We propose to measure the DM’s wealth with a new index, which we call decisional wealth index. This index captures the relative wealth position of a DM in terms of the current levels of outcomes, and it is used as a proxy measure for the DM’s choice attitudes. There were attempts to describe efficient solutions of the MCDM models with additional measures (see Xanthopulos et al., 2000), but they were not used in a proactive way to guide the DM’s decision making process and generate potentially better solutions that reflect the wealth-dependent preferences of the DM.

As argued by Vincke et al. (1992), the MCDM models should provide support to the DM and aim at guiding his/her search for improved outcomes. Despite the obvious implications of the decisional wealth on the DM’s search attitude, to our knowledge there are no methodological approaches that incorporate this behavioral notion into an MCDM modelling framework.

The organization of the paper is as follows: In Section 2, we provide a background for our study. In Section 3, we define the MCDM problem addressed in this paper, and define the notions of decisional wealth and trade-offs. In Section 4, we illustrate how the notion of decisional wealth should be incorporated into an MCDM framework. In Section 5, we give the theoretical foundations of the proposed framework. The paper concludes with a discussion.