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success
U(X) p+
to do by herself
U(X) p-
failure
success
U(X) d+
delegation
U(X) d-
failure
Figure 3.5
Simplified Decision Tree for Trust-based Delegation
where it is supposed that it is possible to attribute a quantitative value (importance) to the goals
and where the values of the actions (delegation and performance) are supposed to be negative
(having costs: energies and resources committed in the enterprise).
We have called Additional Damage for Failure the negative results of both the failures (direct
performance and delegation): they represent not only the frustration of the missed achievement
of the goal but also the potential additional damages coming from these failures (in terms of
compromising other goals, interests, resources, and so on): in particular, in the case of trusting
Y there are all the risks of reduced control in the situation following the delegation act.
From the formula (3.4) we obtain:
A
DoT XY τ >
DoT XX τ
+
B
(3.5)
where:
where
A
=
(U(X) p +
U(X) p ) / (U(X) d +
U(X) d )
B
=
(U(X) p
U(X) d ) / (U(X) d +
U(X) d )
Let us consider now, the two terms A and B separately.
As for term A , (considering B
0 , that means that the trustor has the same damage in terms
of cost in the case of the failure of the direct performance and in the case of the failure of
action delegated to Y )if:
=
A = 1 (the differences between success utility and failure utility in the case of X 's direct
performance and in the case of delegation to Y are the same):
then the formula (3.5) becames, DoT XY τ >
DoT XX τ
in practice, in this case (B
=
0 and A
=
1)
it is necessary more trust in Y than in herself for X's delegation .
This (A
=
1, B
=
0) is a clear and rational result: in the case in which:
1) the utility's difference between success and failure is the same (in performing the task by
themselves or delegating the task to the trustee)(A
1); and
2) the failure of X's performance has the same damage of the failure of the Y's delegated
performance; then
X has to trust Y more than herself for delegating to him that task: for X is rational to delegate
to Y for any value greater than zero between these two trust values (DoT XY τ
=
DoT XX τ >
0).
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