Part II A General Heuristic Decision-Making Procedure
9.2 Decision Maxims for Overcoming Polyvalence
9.2.1 Utility Value Maxim
The application of the utility value maxim (see Bamberg and Coenenberg 2002, pp. 47 ff.; Eisenfu¨hr and Weber2003, pp. 115 ff.; Rommelfanger and Eickemeier 2002, pp. 140 ff.) includes the following sub-tasks:
Criteria Environ-
mental scenarios
Decision under univalence
Decision under polyvalence
Decision under cer- tainty
No decision maxims necessary
Utility value Quasi-univalent decision
Decision under risk
Expectation value Utility expectation value
Combined application
Decision under uncertainty
Minimax Maximax Equal probability Optimism- pessimism-index Minimax-risk
Combined application
= Fully applicable
= Only applicable if information is ignored Fig. 9.1 The decision maxims and their application
88 9 Decision Maxims for Establishing the Overall Consequences. . .
1. First, the consequence values are transformed into utility values. This is done in parallel for each consequence type. In order to avoid indirectly weighting the consequence values, each consequence type receives the same sum of utility values. It is recommended to choose the value “1” as the sum of the utility values of a consequence type. This means that for each consequence type, the utility values of the options lie between 0 and 1. It is also useful to award the highest utility value to the most favorable consequence and the lowest utility value to the most unfavorable consequence. With the purchase of a machine, for example, this would mean that, in reference to price, the machine with the lowest price receives the highest utility value.
2. The second step consists in the weighting of the consequence types. The weightings based on subjective judgments should reflect the relative importance of the criteria for the attainment of the goals. To standardize the weighting of the consequence types, it is proposed to choose the value 1 for the sum of all weightings.
3. Now that the consequence values have been transformed into utility values and the weightings for the decision criteria/consequence types have been determined, the overall consequences can be established. To do this, the utility values are multiplied by their weightings and the weighted utility values are added.
The most difficult and costly step in the application of the utility value maxim is the first step. Inset 9.1 shows how the transformation of the consequence values into utility values can be carried out for different categories of decision criteria/conse- quence types.
For a better understanding, the utility value maxim is now applied in an example:
A company has to choose from three offices in a new market. Figure9.2shows the decision matrix with three consequence types. The three consequence types have different qualities:
Criteria Options
Rent
in Swiss francs
Surface in m2
Situation
Office A 1,000 120 Good
Office B 1,100 120 Excellent
Office C 800 90 Satisfactory
Fig. 9.2 Starting point of the example on the application of the utility value maxim
• Rent is a quantitative, negative consequence.
• Surface is a quantitative, positive consequence.
• Finally, the situation represents a qualitative, positive consequence.
Figure9.3shows the result of the application of the procedure:
• First, the consequence values are transformed into utility values. The sum of the utility values of a consequence type is 1.
• Next, the consequence types are weighted.
• Finally, the weighted utility values are calculated and added. Since the sum of the utility values of each consequence type is 1 and the weightings also total 1, the sum of the weighted utility values of all three options is also 1.
On the basis of the sum of the weighted utility values, office B should be chosen.
Inset 9.1: Transforming Consequence Values into Utility Values
When transforming consequence values into utility values, four different categories of consequence types are distinguished:
• Quantitative consequence types where a high value is positive, such as the contribution margin
• Quantitative consequence types where a high value is negative, such as costs
• Qualitative consequence types where a high evaluation is positive, such as aesthetics.
(continued) Criteria and
weigh- tings
Options
Rent in Swiss francs
Surface in m2
Situation Total of the weighted utility values
0.5 0.3 0.2
Office A 0.32 0.16
0.36 0.11
0.29 0.06
– 0.33 Office B 0.29
0.14
0.36 0.11
0.57 0.11
– 0.36 Office C 0.39
0.20
0.28 0.08
0.14 0.03
– 0.31
Total 1.00
0.5
1.00 0.3
1.00 0.2
– 1.00 Upper figures = Utility values
Lower figures = Weighted utility values
Fig. 9.3 Example of the application of the utility value maxim
90 9 Decision Maxims for Establishing the Overall Consequences. . .
Inset 9.1 (continued)
• Qualitative consequence types where a high evaluation is negative, such as offensive odors.
In the main text, it is recommended, when transforming the consequence values of a consequence type into utility values, to use 1 as the sum of the utility values. In this way, no indirect weighting of the different consequence types occurs.
The transformation of utility values is done in the following way for each of the four consequence types:
• Quantitative positive consequence types, like profit, are transformed into utility values by expressing the individual consequence values as a pro- portion of the sum of all consequence values.
• Quantitative negative consequence types, such as costs, are transformed into utility values by first determining the reciprocal for each consequence value. The reciprocals are then expressed as a proportion of the sum of all reciprocals. The procedure can be illustrated with the following example:
A company is looking for an office in a new market and has three options to choose from. The monthly rent is a decision criterion and therefore a consequence type. The following figure shows the three figures for rent and their transformation into utility values. In this procedure, the space with the lowest rent has the highest utility value and the space with the highest rent has the lowest utility value.
Options Rent
in Swiss francs
Reciprocal of the rent
Utility values
Office A 1'000 0.001 0.32
Office B 1'100 0.000909 0.29
Office C 800 0.00125 0.39
Total – 0.003159 1.00
Transformation of quantitative negative consequences into utility values
• Qualitative positive consequence types, such as aesthetics, are first trans- formed into quantitative consequence values by using a defined scale. The transformation must reflect the “distances” between the verbal consequence
(continued)
Inset 9.1 (continued)
values as precisely as possible. Utility values can then be calculated in the same way as for quantitative, positive consequence values. The procedure will be illustrated again with the example of the decision on office space:
Alongside rental costs, the company has chosen the situation as a further decision criterion and has rated the three options on a qualitative scale with four values: “excellent”, “very good”, “good” and “satisfactory”. The next figure gives the evaluations and their subsequent transformation into utility values. As the figure shows, the evaluation of the situation is based on a four-point scale. However, none of the offices was given the value “very good” in the evaluation. This fact must be taken into account when converting the verbal consequences into numerical values, because the distance between “excellent” and “good” is twice as far as the distance between “good” and “satisfactory”.
• Qualitative negative consequence types, such as offensive odors, are also first converted into quantitative values using a scale. In this case, however, the negative consequence type is at the same time transformed into a positive consequence type. The most disadvantageous verbal consequence for the actor is assigned the smallest quantitative value and the most advantageous the largest quantitative value. Here too one should make sure that the “distances” between values are represented satisfactorily.
The transformation into utility values can afterwards be carried out in the same way as for quantitative, positive consequence types.
Options Situation* Quantitative value of the situation
Utility values
Office A Good 2 0.29
Office B Excellent 4 0.57
Office C Satisfactory 1 0.14
Total – 7 1.00
* Measured on the scale: excellent, very good, good, satisfactory Transformation of qualitative positive consequences into utility values
(continued) 92 9 Decision Maxims for Establishing the Overall Consequences. . .
Inset 9.1 (continued)
With quantitative consequence types, the consequence values may extend from negative values through zero to positive values. This is possible, for example, with a consequence type such as return on investment (ROI). In this case, the conversion into utility values, as proposed above, is impossible.
Therefore, the consequence values must be transformed into a value area0 before they are converted into utility values. This is possible by adding a constant to all consequence values (This increase in consequence values by a constant amount is technically unproblematic, because the utility values, independently of this operation, merely represent an interval scale in each case). The next figure provides an example of the proposed approach: Four potential acquisitions are assessed, among other things, on the basis of their ROI for the previous year. The spectrum ranges from negative to positive values. The figure now shows how these ROI values are transformed into utility values.
Options ROI Transformed ROI Utility values
Acquisition A 8% 10% 0.53
Acquisition B - 2% 0% 0.00
Acquisition C 0% 2% 0.10
Acquisition D 5% 7% 0.37
Total – 19% 1.00
Transformation of positive and negative values into utility values