Biomedical Engineering Reference
In-Depth Information
Let a reaction function
R
be introduced, indicating the
dependence of the actual outcome
x
* on the program
manager's knowledge of the disseminated judgment (or
prediction) of
x
. This is given by:
x
* =
R
(
x
)
[12.2]
Given the relevant range [x(o), x(i)] we can represent the
reaction function by a two-dimensional diagram
(Figure 12.2).
With the variance of x through the range x(o) to x(i) will be
associated a variance of x* between x(o)* and x(i)*. If R(x) is
continuous over [x(o), x(i)], and if R(x) is bounded (i.e., 0 <
R(x) < F) then by the generalized Brouwer Fixed-point Theorem
there exists at least one x and one x* such that, x = x*. Also,
for x = x*, the system described by Eqns 1 and 2 is in equilibrium
(i.e., the manager will cease to react to x).
16
Thus, for x = x*, that value of x is the correct public
prediction, as well as the correct formative evaluative
judgment.
Figure 12.2
Reaction function for hypothetical program
