Political Power and Socio-Economic Inequality

This was the topic of my master's thesis in mathematics, and since I defended it successfully on July 25th, 2012, I now want to make it available here. Below are some remarks about the topic, but of course you're invited to read the thesis itself for the most elaborate and hopefully best discussion of the subject!

My motivation for this work was the clearly omnipresent phenomenon of social inequality. In my interpretation, one of the main reasons for the inequality in a society may be uneven distribution of political power (unequal distribution of economic means and in particular capital is more commonly studied, but I believe power takes also a key role).

Another motivation was the idea to apply thermodynamics to social sciences, since also in a society, macroscopic phenomena are built from microbehaviour of individuals. Although I did not know this in the beginning, this is already an existing topic usually called econophysics. While econophyics in general also deals with problems of modelling for instance stock market behaviour, I applied it to political economy which is a topic I'm very interested in.

The results of my modelling are quite interesting, as the combination of political power and economic variables inevitably leads to total inequality in what is the ground state in physical terms, and the system shows a first-order phase transition which breaks permutation symmetry between the individuals spontaneously between a phase of equality and one of inequality (with a single privileged individual that holds almost all power and almost all wealth).

Of course, I have available all the program code written for the simulation as well as the raw result data and the literature cited. Feel free to contact me both if you have any comments or questions, and also if you are interested in this additional material!

Thesis: The actual thesis in the "official" version.
Presentation Slides: Some slides I prepared for my presentation of the topic during the defense.
Evolution of Configurations: This is a movie that shows one particular time-series of configurations as generated by my Monte-Carlo algorithm for a system at the critical temperature where the phase transition happens. In the upper half, an observable termed "uprising", which can be used as order parameter for the phase transition and measures inequality in some sense, is shown (and in addition, the audio channel also reflects this value). In the bottom, the actual configuration made up of individuals is shown in my social space, where one individual is marked throughout the movie. One can see that the system over the course of the simulation is in both phases, and one also sees the connection between a jump in uprising and the phase transition. Finally, the movie shows that the privileged individual is chosen randomly (and is of course not always the same) at the transition.
Energy Histogram: Basically an animated version of Figure 8 on page 51 of the printed thesis, this shows how the energy histogram evolves when the temperature is changed around the critical value. The red line depicts the current mean energy calculated from all the values, and the audio channel also presents this value. The shown curve is an interpolated version of the histogram (thus a little wobbly sometimes), normalised to represent a probability density.
Low Temperature Limit: In this movie, the behaviour of the system (random configurations) is shown for the limit of temperature going to zero. One can basically see two nice things: First, for low temperatures the Monte-Carlo configurations converge towards the theoretical ground state, which is marked with the red crosses. This confirms both my analysis and numerics. Second, at about half the time of the animation, the critical temperature is crossed and the phase transition takes place. One can very strikingly see how suddenly one individual becomes privileged and all others have almost no power afterwards. This is accompanied by a jump in the energy (which is plotted in the upper half) as well as the uprising (which the audio channel represents). See also Subsection 4.3.2 and Figure 6 in the thesis.