Complexity in Spatial Dynamics: the Emergence of Homogeneity/Heterogeneity in Culture

1. Complexity in Spatial Dynamics: the Emergenceof Homogeneity/Heterogeneity in Culture Paul Ormerod, Camila Caiado, Alex Bentley Launch of WP3, Tipping Points, 14 September 2012

2. Purpose • Spatial homogeneity/heterogeneity of cultural choices across a population based in different locations is an important policy issue e.g. linguistic divisions, ideological divisions, assimilation of minorities • A population is allocated across k different locations and selects from a range of different attributes • If each location only pays attention to choices made there, or if each location pays attention to choices made everywhere else, we will clearly have cultural hetero/homogeneity • How willing do people have to be to take into account the preferences of other locations for cultural homogeneity to emerge?

3. Behavioural choice • Agents do not have fixed preferences • Preferences evolve according to the choices made by others • The basic choice rule is preferential attachment plus a small element of random innovation • Bentley, Ormerod, Batty, Behavioral Ecology and Sociobiology, 2011 • Many outcomes are highly non-Gaussian and exhibit turnover in time across the rankings of popularity

7. The model • There are K locations. Agents enter the model and choose a location using the principle of preferential attachment • The agent then uses preferential attachment plus innovation to select amongst the various choices • There are 2 parameters in the basic model: the innovation rate; the ‘memory’ i.e. How far back do you go when considering the choices which have already been made • We introduce a third parameter: how much weight do you give to the choices made at other locations?

8. The algorithm • Start with N agents, locate each agent at one of the k available locations and for each agent choose one of the p available products at random. • For each time step t, create n new agents and locate them using preferential attachment. . In our example, N=1000, k=100, p=10 and n=1000. • Each new agent makes a product choice based on the choices of previous agents that entered the model in the past m steps and weighs each choice based on location according to an ‘affinity’ constant λ.