Policy and Complex Systems
of interconnections corresponds to two Renyi – Erdös equivalent neighbor networks , a configuration with links of equal strength among all nodes .
Our model of the individuals ’ interactions within each group and between the groups yields averages of the individual preferences at any time t . Each network ( group ) has its own average value : s1 and s2 , respectively . The in-group intensity ( energy ) of advocacy of an individual from group 1 is – J1 × s × s1 while the corresponding energy of an individual in group 2 is : – J2 × s × s2 , where s1 is average of all s in group 1 and s2 is the average of all s in group 2 . To reflect the effects of mutual persuasion , the inter-group intensity of interaction ( energy ) of any individual is taken to be proportional to the product between the individual ’ s preference s and the mean value of the preferences of the other group ’ s members : K12 × s × s2 for an individual in group 1 , and – K21 × s × s1 for an individual in group 2 .
Given the individuals ’ preferences at time t , the Boltzmann probability distribution of the preferences s at time t + 1 for each group is proportional to the exponential of the intensity of interactions ( energy ):
Since persuasion is not instantaneous , we assume the interactions between the individual preferences s at time t + 1 and the collection of individuals from the two groups to be lagged , with the averages s1 and s2 evaluated at an earlier time t . ρ1 ( s , t ) and ρ2 ( s , t ) yield the fractions of all individuals who have preference s at time t , in group 1 and group 2 , respectively . We ( Diep , Kaufman , & Kaufman , 2017 ) have proposed this model and presented some of its predictions concerning the time evolution of the mean attitudes s1 and s2 . Here we concentrate on the time evolution of the distribution of attitudes .
Examples
To illustrate how this model can offer
some insight into the dynamics of social conflict , we show a couple of implementations that attempt to model two relatively recent events with a twogroup structure : “ Brexit ” and the 2016 U . S . elections . In-depth political analyses are intellectually satisfying in that they seem to link causes and effects that “ make sense ” to us . However , as in the two examples we describe , such analyses can miss the big picture . We would argue that both types of analysis are needed and that our simple model can contribute valuable input to strategists on each side .
Brexit Case
In the Brexit case , Group 1 was composed
of the British government and supporters of continued membership in the European Union ( EU ); group 2 contained individuals who wanted to exit the European Union . The case was characterized by time oscillations , with the pro-EU group and the pro-Brexit group alternating in leading in polls at different times . We chose relatively high values for J1 and J2 , with K12 < 0 and K21 > 0 to obtain similar oscillations sustained in time . In terms of the interactions between the two networks , K12 < 0 reflects that the extreme ( uncompromising ) wing of the pro-Brexit Group 2 encourages pro-EU Group 1 members to be accommodating , while the moderate ( compromising ) wing of
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