Seeking Allies - Natural and Artificial Reasoning - page 186

Table 14.2 Actor 1's range of expected values for other actors in the group
Series 1 Series 2 Series 3 Series 4 Actor 1 Model description

6.00 8.00 8.00 9.00 Models himself

7.18 1.09 4.72 3.52 Models actor 2

1.61 4.15 6.02 7.81 Models actor 3

0.86 3.5 5.05 6.96 Models actor 4

Table 14.3 Actor 1's normalised expected values and normalised distances
Series 1 Series 2 Series 3 Series 4 Distance in 4D

space

Actor 1 Model
description

− 1.61 0.23 0.23 1.15 0.00 Models himself

1.39 − 1.38 0.27 − 0.28 3.69 Models actor 2

− 1.43 − 0.33 0.49 1.27 0.65 Models actor 3

− 1.45 − 0.27 0.43 1.29 0.57 Models actor 4

to be different from actor 2's distance from actor 1. So in comparing the distances
derived from the model with the results obtained from the experiments (shown in
Table 14.4 ) we can make some predictions from the relative z-score distance between
two subjects' choice of ally. Note that the results in Table 14.4 are 500 runs instead of
300 as shown previously. This accounts for the first line of Table 14.4 being slightly
different from the fifth column of Table 14.3 .

14.7 Assessing the Results

We can measure the predictive power of the model in terms of the improved infor-
mation over the null hypothesis. The null hypothesis is where the choice of order is
made randomly compared with model differences. The model has simulated a con-
versational process that allows internal sub-models to be constructed that provides
an actor centred view. In Table 14.4 we have scored a successful prediction of order
by assigning 1.0 and a partial order as 0.5 only where, due to lack of information,
there is 0.5 probability of the answer being correct (rounded to 2 decimal places).
All other orderings have been scored 0. So we have:

• Probability of guessing order correctly if random = 1/3! = 1/6 = 0.17

• Random Hypothesis Entropy =− Log 2 (0.17) = 2.56

• Observed Entropy =− Log 2 (0.40) = 1.32

The numeric value of the prediction from the model is the difference of the two
hypotheses. This is about 1.2 bits, which means that you roughly double your chance
of guessing correctly by running and using the model.