Part II A General Heuristic Decision-Making Procedure
9.4 Decision Maxims for Overcoming Uncertainty
Inset 9.3 (continued)
is considered. The guaranteed amount of the first stage suggests a reference point for the second stage. In the second stage, the risky amounts are assessed, in each case based on another specific reference point from the first stage. In situation A, the reference point for the second step is EUR 1,000 and the additional amounts are therefore relative gains. In situation B, the reference point is EUR 2,000, and the risk evaluation deals with relative losses (see von Nitzsch2002, p. 114).
9.3.3 Problems with the Application of the Decision Maxims
• Wald’s minimax maxim,
• The maximax maxim,
• Laplace’s maxim of equal probability,
• Hurwicz’s optimism-pessimism-index maxim, as well as
• Niehans and Savage’s minimax-risk maxim.
In the following text, these five maxims will first be briefly presented and then their application will be explained using an example.
The minimax maxim compares options exclusively on the basis of their worst consequences. The option which is best among these worst consequence values is chosen. The application of the minimax rule corresponds to extreme risk-averse behavior, or to a worst case attitude.
The maximax maxim is exactly the opposite. It requires the actor to look only at the best consequence values for each option and to go for the alternative that displays the highest value.
The rule of equal probability represents a middle course between the minimax and maximax maxims. As its name suggests, it makes the assumption that all consequence values are equally likely. The maxim therefore provides that an average consequence value is determined for each option. The actor then chooses the option with the best of these values.
Like the maxim of equal probability, the optimism-pessimism-index maxim seeks a middle course between the extreme maximax and minimax rules. This maxim is applied in three steps:
1. First, the actor fixes a value for the optimism-pessimism-index between 0 and 1.
The higher the value, the more optimistic or risk-tolerant the actor is.
2. For each option, the best consequence value is multiplied by the index value and the worst consequence value is multiplied by the difference between the index value and 1.
3. Finally, the two products are added. The option with the best value is chosen.
The best value means the highest sum for positive consequences and the lowest sum for negative consequences.
Niehans and Savage’s minimax-risk maxim takes a different approach. Unlike the other four maxims, it does not consider the consequence values from a more or less pessimistic or optimistic viewpoint, but looks at the differences between the consequence values of the different options in a scenario: if the actor decides in favor of option A and scenario 1 then follows, the actor is interested in the difference between the consequence of option A and the consequence of the optimal option in scenario 1. If this difference is great, this means a correspondingly great regret. If the difference is small, the actor’s regret is smaller. If the best option for the occurring scenario was chosen, then there is no reason for regret. The maxim tries to minimize the regret as much as possible. It is applied in three steps:
102 9 Decision Maxims for Establishing the Overall Consequences. . .
1. First, the differences between the consequence values and the best consequence value are calculated for each scenario. They represent the possible regrets in the different scenarios.
2. Then, the highest possible regret for each option is identified.
3. Finally, the actor decides in favor of the option where the highest possible regret is the lowest.
The five maxims will now be illustrated in an example: An actor is given the general agency for products offered by three suppliers. Since the products are in competition with each other, only one of them can be included in the product range.
Figure 9.8 shows the contribution margins of each product in EUR after the deduction of all costs dependent on the decision.
According to the minimax maxim, product A should be chosen. The zero figure of option A is the best of the lowest consequence values of the three options.
If the maximax rule is used, then product B will be preferred. The 70 million EUR contribution margin represents the highest consequence value.
According to the equal probability maxim, the average consequences have to be calculated for all three options. They amount to:
• 15 million EUR for option A,
• 18.333 million EUR for option B and
• 20 million EUR for option C.
According to this maxim, product C should be chosen.
If the optimism-pessimism-index maxim is used, the result will depend on the optimism or risk-acceptance of the actor. The selection of an index value of 1/3 means that the actor is rather pessimistic or cautious. With this assumption, the following overall consequences are produced for the three options:
Criterion and scenarios
Options
Total contribution margin in millions of EUR
Poor economic situation
Average economic situation
Good economic situation
Product A 0 15 30
Product B -30 15 70
Product C -10 10 60
Fig. 9.8 Starting point for the application of the maxims for overcoming uncertainty
• Opt. A: 1/3 • 30 million EUR + 2/3 • 0 EUR¼10 million EUR
• Opt. B: 1/3 • 70 million EUR + 2/3 • (30) million EUR¼3.333 million EUR
• Opt. C: 1/3 • 60 million EUR + 2/3 • (10) million EUR¼13.333 million EUR Here, option C should be chosen.
Finally, Fig.9.9shows the result of the application of the minimax-risk rule. As can be seen from the figure, the maximum regret is the lowest with option C.
It should therefore be chosen.