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Center for Nonlinear Studies |
We model the dynamics of social structure by a simple interacting particle system. The social standing of an individual agent is represented by an integer-valued fitness that changes via two offsetting processes. When two agents interact one advances: the fitter with probability p and the less fit with upset probability q=1-p. The fitness of an agent may also decline with rate r. From a scaling analysis of the underlying master equations for the fitness distribution of the population, we find four distinct social structures as a function of p and r: a static lower-class society, an upwardly-mobile middle-class society, a hierarchical society and an egalitarian society. We use this model to quantify competitiveness among teams in five different major leagues. We analyze the results of over 300,000 professional games played over the last century and find that British soccer and Baseball are the most competitive sports while American Football is the least competitive one.