Delegation value

The delegation value is a concept of decision- oriented organizational theory that deals with the question of when a task holder (in the context of the delegation value theory referred to as an authority , e.g. a manager ) is better to decide a problem himself and when it is better to pass this decision on to you delegated to other decision-makers (e.g. employees or consultancies ) .

initial situation

The following situation is considered:

1. An instance is facing an object decision problem (what should be done). The alternatives up to are available to you. The consequences of these alternatives also depend on the incoming in the future environmental conditions up from. ${\displaystyle A_{1}}$ ${\displaystyle A_{A}}$ ${\displaystyle S_{1}}$ ${\displaystyle S_{S}}$
2. The instance wants to maximize the expected profit.
3. The instance can now delegate this object decision problem to someone and has to decide whether it does this and to whom it is delegating ( organizational decision problem ).
4. The instance has already structured the object decision problem in the form of a result matrix. It can therefore indicate a probability of occurrence for each environmental condition and indicate the corresponding profit for all alternatives and environmental conditions. This assumption is restrictive, but if the instance has no ideas about the object problem, it also lacks the basis for deciding on the delegation. ${\displaystyle W(S_{S})}$
5. The instance makes its decision based on the expected profit value . The possibility of obtaining additional information is neglected.
6. The authority is considering the delegation because it suspects that the possible decision-makers have or can obtain more / better information about the probabilities of occurrence or can better forecast them.
7. The following delegations are possible
   1. Delegation to a single decision maker (possibly supported by a staff)
   2. Breakdown of the problem into sub-problems and delegation to several decision makers.
   3. Delegation to a body , with the instance itself determining the voting rule.
8. The instance gives as a goal to maximize the expected profit.
9. The instance can change the results of the alternatives, e.g. B. by granting success bonuses
10. The delegation generally incurs costs in the form of expenses or opportunity costs . The costs are seldom known for certain; however, it is assumed that at least its expected value can be specified.

Decision by the instance

If the authority decides itself, it chooses the alternative that has the highest expected profit value E.

${\displaystyle E=\sum _{s=1}^{S}w(S_{s})G_{{\hat {a}}s}=\max _{a}\sum _{s=1}^{S}w(S_{s})G_{as}}$

-G _as is the gain of the alternative a, if the environmental state s occurs

-â is the index of the alternative with the highest expected profit value

Worth of delegation

For a positive delegation value it is necessary (but not sufficient) that the potential decision maker makes his decision dependent on the probabilities of the environmental conditions. If he chooses a certain alternative with certainty, the instance can choose this alternative itself. If the potential decision maker randomly chooses between the alternatives, choosing the first alternative with the probability and the second , the instance will achieve the same expected value if it decides according to a random mechanism that provides the same probabilities. ${\displaystyle w_{1}}$ ${\displaystyle w_{2}}$

The delegation value is calculated using the following formula:

${\displaystyle WD=ED-E}$

WD - delegation value

ED - expected value at delegation

E - expected value in the event of a decision by the instance

In order to calculate the expected value for delegation (ED), the conditional probabilities must first be introduced:

${\displaystyle p(A_{a}|S_{S}):=}$Probability (in the judgment of the instance) that the delegation will choose the alternative if the environmental condition occurs in the future . ${\displaystyle A_{a}}$ ${\displaystyle S_{s}}$

If the environmental condition occurs, the following expected profit (before deduction of costs) is achieved with delegation: ${\displaystyle S_{s}}$

${\displaystyle ED(S_{s})=\sum _{a=1}^{A}p(A_{a}|S_{s})G_{as}}$

In general, the expected profit value for delegation (before deduction of costs) then applies

${\displaystyle ED=\sum _{s=1}^{S}w(S_{s})ED(S_{s})}$ what can be formed

${\displaystyle ED=\sum _{s=1}^{S}w(S_{s})\sum _{a=1}^{A}p(A_{a}|S_{S})G_{as}}$

It follows:

${\displaystyle WD=\sum _{s=1}^{S}w(S_{s})[\sum _{a=1}^{A}p(A_{a}|S_{s})G_{as}-G_{{\hat {a}}s}]}$

In square brackets is the positive or negative increase in the expected profit value in the case of delegation compared to the decision by the instance.

Individual evidence

1. ↑ Laux, Liermann: Fundamentals of the organization: The control of decisions as a basic problem of business administration 6th edition, Springer, Berlin, 2005, pp. 214-216
2. ↑ Laux, Liermann: Fundamentals of the organization: The control of decisions as a basic problem in business administration 6th edition, Springer, Berlin, 2005, p. 216f.
3. ↑ Laux, Liermann: Fundamentals of the organization: The control of decisions as a basic problem of business administration 6th edition, Springer, Berlin, 2005, p. 220