Journal on Policy and Complex Systems
CA ) examples . As in Diep et al .’ s ( 2017 ) model for two-groups conflicts , we assume that each individual in each group has an attitude s with respect to a specific conflict , as to whether or not ( and how ) to proceed in dealing with the other groups to attend to the conflict . Attitudes s range between -Mn and Mn ( the ranges may differ between groups , but here we take them to be the same for all three groups ). When individuals ’ attitudes are close to the lower bound , -Mn , they have a loose attachment to their own group ’ s stance and therefore tend to be the most open to compromise . Conversely , when attitudes s are close to the upper bound , Mn , the individuals are strongly attached to their group ’ s goals . They tend to shun concessions and instead are willing to engage in confrontation to defend their group ’ s stance . Individuals whose attitudes s are close to 0 — the midpoint of this range of attitudes — respect their group ’ s values , but they are also ready to make concessions to resolve their conflict .
Each individual interacts with every other individual inside their own group , forming a homophilic network of members . Each individual within a group acts with intensity J to persuade others to his / her stance . Each individual is also the target of others ’ efforts to sway him / her . The three groups ( networks ) form a multiplex when they interact with each other . Thus , the individuals ’ attitudes within one group are affected , indirectly by the “ average ” attitudes of the other groups , even though individuals do not necessarily communicate across groups . This is the case in the US-NK-C and BiH examples .
As group members interact with each other and consider the opposing groups ’ attitudes , their own group ’ s resulting preference average at any time t is sn ( n = 1 , 2 , 3 ). In each group n , the intensity with which an individual tries to persuade others . This intensity , which in physics terms is analogous to “ negative energy ,” is Jn * s * sn . Similarly , the inter-group intensity of interaction K , the result of an individual ’ s consideration of an opposing group ’ s stance , is also analogized to negative energy . We consider it proportional to the product between that individual ’ s preference s and the mean value of the preferences of the other groups ’ members : K12 * s * s2 + K13 * s * s3 for an individual in group 1 , where K12 and K13 represent the individual ’ s interpretation of what the average attitudes in groups 2 and 3 mean in the context of the ongoing conflict . The three-group model thus has nine parameters : 3 three intra-network couplings J ( the links among members in each group ) and six inter-network couplings K . 4
In our dynamic model , the changes in preferences are captured by assuming that the intensity of interactions involves the product of individuals ’ preferences at a current time and
3 The two-group model had four parameters ; an n-group model would have n 2 parameters , quickly escalating computational and representation impediments .
4 The links between any two groups are not necessarily symmetrical : for example , K12 may be different from K21 . In this respect , social networks composed of individuals with agency differ from physical networks , which behave according to Newton ’ s third law .
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