A study of social and economic evolution of human societies using methods of Statistical Mechanics and Information Theory

Abstract

This dissertation explores some applications of statistical mechanics and information theory tools to topics of interest in anthropology, social sciences, and economics. We intended to develop mathematical and computational models with empirical and theoretical bases aiming to identify important features of two problems: the transitions between egalitarian and hierarchical societies and the emergence of money in human societies. Anthropological data [1] suggest the existence of a correlation between the relative neocortex size and the average size of primates' groups, most of which are hierarchical. Recent theories [2] also suggest that social and evolutionary pressures are responsible for modi cations in the cognitive capacity of the individuals, what might have made possible the emergence of di erent types of social organization. Based on those observations, we studied a mathematical model that incorporates the hypothesis of cognitive costs, attributed for each cognitive social representation, to explain the variety of social structures in which humans may organize themselves. A Monte Carlo dynamics allows for the plotting of a phase diagram containing hierarchical, egalitarian, and intermediary regions. There are roughly three parameters responsible for that behavior: the cognitive capacity, the number of agents in the society, and the social and environmental pressure. The model also introduces a modi cation in the dynamics to account for a parameter representing the information exchange rate, which induces the correlations amongst the cognitive representations. Those correlations ultimately lead to the phase transition to a hierarchical society. Our results qualitatively agree with anthropological data [3] if the variables are interpreted as their social equivalents. The other model developed during this work tries to give insights into the problem of emergence of a unique medium of exchange, also called money. Predominant economical theories [4, 5], describe the emergence of money as the result of barter economies evolution. However, criticism [6] recently shed light on the lack of historical and anthropological evidence to corroborate the barter hypothesis, thus bringing out doubts about the mechanisms leading to money emergence and questions regarding the in uence of the social conguration. Recent studies [7] also suggest that money may be perceived by individuals as a perceptual drug and new money theories [8] have been developed aiming to explain the monetization of societies. By developing a computational model based on the previous dynamics for hierarchy emergence, we sought to simulate those phenomena using cognitive representations of economic networks containing information about the exchangeability of any two commodities. Similar mathematical frameworks have been used before [9], but no discussion about the e ects of the social network con guration was presented. The model developed in this dissertation is capable of employing the concept of cognitive representations and of assigning them costs as part of the dynamics. The new dynamics is capable of analyzing how the information exchange depends on the social structure. Our results show that centralized networks, such as star or scale-free structures, yield a higher probability of money emergence. The two models suggest, when observe together, that phase transitions in social organization might be essential factors for the money emergency phenomena, and thus cannot be ignored in future social and economical modeling.