Social influence

Simulates how the opinions of the actors change when they are influenced by their neighbours, under the rules compared by Flache et al. (2017).

Usage

social_influence(
  A,
  opinion,
  rule = c("assimilation", "bounded", "repulsion", "friedkin"),
  mu = 0.3,
  epsilon = 0.15,
  susceptibility = 0.5,
  steps = 50
)

Arguments

A

A square matrix of influence, which can be weighted. The rows are usually normalised so that the weights of each actor add up to one

opinion

A vector with the initial opinion of every actor, usually between zero and one

rule

The rule of influence: assimilation (default), bounded, repulsion or friedkin

mu

How much an actor moves at each step

epsilon

Maximum difference of opinion that still influences an actor, for the bounded rule

susceptibility

Weight given to the neighbours in the friedkin rule, as a number or a vector with one value per actor

steps

Number of steps

Value

This function returns the opinions of every actor at every step, the final opinions, and the number of groups of opinions at the end.

Details

Every actor starts with an opinion and updates it at each step:

assimilation: the actor moves towards the opinions of its neighbours, which leads the network to consensus (French, 1956; DeGroot, 1974).

bounded: the actor is only influenced by the neighbours whose opinion differs less than epsilon, which leads to fragmentation into groups that no longer influence each other (Hegselmann and Krause, 2002).

repulsion: the actor moves towards similar neighbours and away from those who are too different, which leads to bi-polarization. The opinions are kept between zero and one.

friedkin: the actor combines the opinions of its neighbours with the opinion it started with, and susceptibility is the weight given to the neighbours (Friedkin and Johnsen, 1990).

References

DeGroot, M. H. (1974). Reaching a consensus. Journal of the American Statistical Association, 69(345), 118–121. doi:10.1080/01621459.1974.10480137

Flache, A., Mas, M., Feliciani, T., Chattoe-Brown, E., Deffuant, G., Huet, S. and Lorenz, J. (2017). Models of social influence: Towards the next frontiers. Journal of Artificial Societies and Social Simulation, 20(4), 2. doi:10.18564/jasss.3521

French, J. R. P. (1956). A formal theory of social power. Psychological Review, 63(3), 181–194. doi:10.1037/h0046123

Friedkin, N. E. and Johnsen, E. C. (1990). Social influence and opinions. Journal of Mathematical Sociology, 15(3-4), 193–206. doi:10.1080/0022250X.1990.9990069

Hegselmann, R. and Krause, U. (2002). Opinion dynamics and bounded confidence models, analysis and simulation. Journal of Artificial Societies and Social Simulation, 5(3), 2.

Author

Alejandro Espinosa-Rada

Examples

A <- matrix(c(
  0, 1, 1, 0, 0, 0,
  1, 0, 1, 0, 0, 0,
  1, 1, 0, 1, 0, 0,
  0, 0, 1, 0, 1, 1,
  0, 0, 0, 1, 0, 1,
  0, 0, 0, 1, 1, 0
), byrow = TRUE, ncol = 6)
rownames(A) <- letters[1:nrow(A)]
colnames(A) <- rownames(A)
W <- A / rowSums(A)
opinion <- c(0.1, 0.2, 0.3, 0.7, 0.8, 0.9)

social_influence(W, opinion, rule = "assimilation", steps = 20)$final
#> [1] 0.4021102 0.4021108 0.4421799 0.5578201 0.5978892 0.5978898
social_influence(W, opinion, rule = "bounded", epsilon = 0.15, steps = 20)$groups
#> [1] 2