Complexity in spatial dynamics the emergence of homogeneity heterogeneity in culture
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Complexity in Spatial Dynamics: the Emergence of Homogeneity/Heterogeneity in Culture. Paul Ormerod, Camila Caiado, Alex Bentley Launch of WP3, Tipping Points, 14 September 2012. Purpose.

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

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Complexity in spatial dynamics the emergence of homogeneity heterogeneity in culture

Complexity in Spatial Dynamics: the Emergenceof Homogeneity/Heterogeneity in Culture

Paul Ormerod, Camila Caiado, Alex Bentley

Launch of WP3, Tipping Points, 14 September 2012


Purpose

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?


Behavioural choice

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


The model

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?


The algorithm

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.


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