Abstract: Decision making is one of the most human acts and seems to be the most difficult area to formalize into a theory of behaviors that are causal and deterministic. In fact one might think that the very nature of decision-making is one of chance and uncertainty. One issue we think relevant is the general lack of understanding of causal theories and how they deal with uncertainty. Moreover, in our view, there is insufficient appreciation of the sensitivity of the initial conditions that determine future behaviors. When these issues are taken into account, it becomes easier to see the possibility for causal formal theories of human decision-making.
In this appendix, we explore the sensitivity of decisions on initial conditions and its relationship to chaos. We provide the driven pendulum from physics where the dynamic mechanisms are well understood. On many machines you can explore the behavior of the following Mathematica CDF file using the free CDF reader:
To help understanding, we illustrate the decision-making process using a simplified decision process theory model and supply a Mathematica CDF notebook for you to download and experiment with: Decision making, chaos and determinism. The free CDF reader is not sufficient; you will need Mathematica version 9.0.1 or later. However the main results are in the following PDF. The CDF reader will allow you to understand exactly what formulas were used and what parameters were used in the calculations, but the sliders won’t work properly in the reader because the computations are more complex than for the pendulum.