Information Technology Reference
In-Depth Information
Distribution of Belief for Actors
0.6
Series1
Series2
Series3
Series4
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
7
8
9
Hypotheses of value
Fig. 14.5
The change of belief of a scale value for actor 2 as perceived by actor 1 after 300 cycles
Expectation E(x) is the expected or average value of the scale over an imaginary
time period (n), which in this model is taken to be in the order of four events. It is
'imaginary' because it is in practice calculated in terms of an accumulation of effects
such that events occurring further back in time have an exponentially decreasing
weight on the current value. The equivalent time period in this case is in the order of
four events (see Chap. 7). The consequence of making this time window larger is to
reduce the response of the belief value to change, so we have:
3
.
Flexibility f(p
x
)
=
1
/
n
Figure
14.5
shows the differences in belief over the range of scales after 300 model
cycles. Considering that the beliefs are independent, the smoothness of the curve is
comforting. From Table
14.1
we can see that, for Series 1 and 2, the believed values
are well defined being 8 or 9 and 0 or 1. For series 3 and 4 the believed values are
more spread out, covering a range of five mid range values in both cases. What is
plotted in Fig.
14.4
is the expected value rather than the 'believed' values.
Table
14.2
results are subjected to the z-score normalisation process to make
them comparable with observed results derived from the experiment. We then get
the results shown in Table
14.3
:
Then the evaluation distances are calculated by plotting these data sets in four-
dimensional space. The distance between each pair of points in 4D space is given
indicating how closely allied the other actors are placed in terms of music order in
the model.
It should be noted that because each actor has a sub-model of the other actors that
is expected to be different. So actor 1's perception of distance from actor 2 is likely
