Simulating the Social Processes of Science Leiden| 9 April 2014

INGENIO [CSIC-UPV] Ciudad Politécnica de la Innovación | Edif 8E 4º Camino de Vera s/n 46022 Valencia

tel +34 963 877 048 fax +34 963 877 991

DIFFUSION OF SCIENTIFIC KNOWLEDGE:

A PERCOLATION MODEL 

Elena M. Tur

With P Zeppini and K Frenken

www.ingenio.upv.es

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• How do social pressure and assortativity affect the process of diffusion?

• How do their effect interact with the social network structure?

• How do local effects dictate global diffusion through the overall network structure?

• Main contribution: introducing social pressure in a model of diffusion with different network structures

Focus

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• Spread of rumors (Zanette, 2002)• Online spreading of behavior (Centola, 2010)• Opinion dynamics (Shao et al., 2009)• Paradigm shift in science (Brock and Durlauf, 1999)

• How to approach the problem (Zeppini and Frenken, 2013)• Heterogeneity of agents• Externalities• Social network• Percolation (Solomon et al., 2000)

Diffusion of ideas

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• : value of the idea• : minimum quality requirement of agent

Agent adopts the idea at time if:• has not adopted before • is informed: a neighbor has adopted at time • is willing to adopt:

Percolation in a social network

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Percolation in a social network

𝑞𝑖∼𝑈 [0,1 ]→𝑞𝑖≤𝑣0?

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Percolation in a social network

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• Small world (Watts and Strogatz, 1998)Starting with a regular lattice, with nodes and 𝑛 𝑘edges per node, rewire each edge at random with probability 𝑝

• High clustering coefficient, low average path length

Social network

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• Upper bound to diffusion: 45º line (well-mixed population)

• Diffusion increases with • Phase changes: from a

non-diffusion to a diffusion regime

• Percolation thresholds decrease with

Percolation without social pressure

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SOCIAL PRESSURE

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• The unwilling to adopt can be persuaded • Network externalities: shared language, shared

experiences, shared beliefs…• Increasing amount of evidence• Conformity (Asch,1958)

• Weariness

Why social pressure?

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• : # neighbors of agent that have adopted at time • : social pressure intensity

• is decreasing in the number of adopting neighbors • is decreasing in the social pressure intensity• if • if

Modelling social Pressure

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• agents• original neighbors in the small world algorithm• seeds or original adopters• time periods• runs of Monte Carlo simulations

• iid• Social networks: lattice, small world, Poisson network

Parameters for the simulations

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Percolation with social pressure

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Clustering with social pressure

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ASSORTATIVITY People tend to be friends with similar people

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Modelling assortativity

Most unwilling to adopt

Most willing to adopt

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• No critical transition from non-diffusion to diffusion

• Diffusion size scales linearly with diffusion size

• No effect of the network structure (well-mixed population)

Percolation with assortativity

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Percolation with social pressure and assortativity

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Does assortativity help diffusion?

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Does assortativity help diffusion? (2)

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CONCLUSIONS

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• Social pressure changes the behavior of the percolation process: higher diffusion size, lower percolation thresholds

• The effect of social pressure is different for different network structures: critical transition in small worlds and lattices

• With social pressure, clustering becomes beneficial for diffusion: reduced differences between networks

• Assortativity removes the effect of the network structure: all behave as a well-mixed population

• Assortativity can help or hamper diffusion depending on the setting

Conclusions

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• Other social network structures: scale-free networks (Barábasi and Albert, 1999)

• Evolving endogenous social network• Re-think the social pressure implementation: always

possitive efffect?• Different minimum quality requirement distributions,

Future work and limitations

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THANK YOUINGENIO [CSIC-UPV] Ciudad Politécnica de la Innovación | Edif 8E 4º Camino de Vera s/n 46022 Valencia

tel +34 963 877 048 fax +34 963 877 991