Mexican voter network as a dynamic complex system

One of the most important properties in the systems is complexity. When a great level of complexity exists in a system, it is considered as a complex system. The complex systems can be soft systems and hard systems. In hard systems when their elements are interrelated in a non-linear way, they are considered as complex systems, that is to say, complex systems are those that contain a great number of elements interacting in a non-linear way. To try to understand the behavior of this type of systems diverse mathematical tools have been developed. A new scientific discipline with great impact in the analysis of the complex systems has been developed in recent years; we refer to the fractal analysis. Voting data from Mexican federal deputy elections are analyzed and considered as a response function of a social system with underlying dynamics leading to complex behavior. It was found that voting distributions among candidates, as well as political parties behave as a fat-tail Levy stable distribution, associated with fractal structure of electoral network. Specifically, it is shown that the distribution of voter preferences follows the shifted Pareto distribution with scaling exponent a which shows only a few variations from state to state and it is essentially the same for all federal elections from 1991 to 2003. Furthermore, it is shown that Mexican voter network can be modeled by hierarchical pseudo-fractal network characterized by two different fractal dimensions. The identified hierarchical architecture of voter network offers a new perspective on the analysis, modeling and forecasting of elections.