The Life of Concepts: An ABM of Conceptual Drift in Social Groups - Agents and Artificial Intelligence - page 273

combinations of those parameters, we observed a bifurcation. Interestingly, note that
the combinations for p(a1) and p(a2) , for which we obtain a bifurcation,
approximately lie on a line connecting the lower right corner of the graph with the
upper left one. Moreover, see that the zone where we get the bifurcation gets wider at
the upper left corner. That means that at the lower right corner ( p(a1) >> p(a2) ), the
dynamics of the ABM gets more sensitive to the combination of p(a1) and p(a2) than
at the opposite corner ( p(a1) << p(a2) ). Since that behaviour of the ABM was quite
intriguing, we developed another model to try to explain such behaviour.

5 Probabilistic and Markov Chain Model

To begin to validate the ABM results, and more formally explain the conditions under
which the three dynamics appeared, we developed a simple probabilistic model. This
initial model justified why the bifurcation emerged when the values for p(a1) and
p(a2) roughly lie on a line connecting the lower right corner of the graph with the
upper left one, as shown in Figure 4.

5.1 Simple Conditional Probability Model

To explain the three different types of dynamics that emerge from the ABM, we use a
simple conditional probability model to calculate an initial probability that a concept
will strengthen ( p if ). If p if is small, then most probably, the coefficient, which
represents the concept, will decrease. On the other hand, if p if is large, the coefficient
will increase. If p if is about 0.5, then we obtain the ideal situation under which a
bifurcation might occur, i.e. each coefficient will have a 50% chance of decreasing
and a 50% chance of increasing, thus making it possible that about half of them will
diminish and half of them will augment. Figure 5 shows a conditional probability tree
that helps calculate p if .

Fig. 5. Conditional probability tree for calculating p if