Evolving social influence in large populations

Darwinian studies of collective human behaviour, which deal fluently with change and are grounded in the details of social influence among individuals, have much to offer "social" models from the physical sciences which have elegant statistical regularities. Although Darwinian evolution is often associated with selection and adaptation, "neutral" models of drift are equally relevant. Building on established neutral models, we present a general, yet highly parsimonious, stochastic model, which generates an entire family of real-world, right-skew socio-economic distributions, including exponential, winner-take-all, power law tails of varying exponents, and power laws across the whole data. The widely used Barabasi and Albert (1999) Science 286: 509-512 "B-A" model of preferential attachment is a special case of this general model. In addition, the model produces the continuous turnover observed empirically within these distributions. Previous preferential attachment models have generated specific distributions with turnover using arbitrary add-on rules, but turnover is an inherent feature of our model. The model also replicates an intriguing new relationship, observed across a range of empirical studies, between the power law exponent and the proportion of data represented in the distribution.