Policy and Complex Systems
Figure 6 . Time evolution of fractions of democrats and republican supporters . In this scenario the attitude s = −3 in both groups votes for the democrats .
Republicans are : J2 > J1 ; they influence Republicans more than Republicans influence them : K12 > K21 . The results below were obtained for : J1 = 0.25 , J2 = 0.3 , K12 = 0.1 , K21 = 0.02 . In Figure 4 we show the time evolution of the non-compromising attitude s = 3 and of the compromising attitude s = −3 .
We consider a couple of scenarios . In the first scenario ( Figure 5 ), those in Group 1 whose preferences s range from 3 to −2 are likely to vote for the Republican candidate . Similarly , in Group 2 those with preferences s ranging from 3 to −2 vote for the Democratic candidate . In both groups , those whose preference s = −3 either do not vote ( they are not sufficiently engaged ) or they vote for a third candidate . In this scenario , the Republican candidate wins the elections .
In the second scenario ( Figure 6 ) those in both groups with preference s = −3 , whom we could view as independents groups , vote for the Democratic candidate . As a result , the democrats win the election .
Conclusions
We have proposed a parsimonious
model for generating anticipatory scenarios , to be used by parties in two-group social conflict to devise strategies . We have shown how distributions of attitudes inside each group and their time evolutions can be derived , to gain insight into possible group choices . We have illustrated with two examples — 2016 “ Brexit ” referendum and US elections — how such a model can be used to analyze real two-group conflicts . It has the potential to be enriched with several realistic features to describe other conflicts .
In the model ’ s current form , for illustrative purposes , we have selected the values of the intra-group interactions J and the inter-group interactions K to match the example narratives regarding these conflicts . We intend to explore ways to determine these coupling constants endogenously . For example , the cohesion couplings J may increase when the two-group dynamics moves towards conflict , i . e . the mean attitude s of group members approaches the value 3 , representing dominant intransigence . Similarly , Js may decrease when the dynamics evolve away from conflict toward a settlement , i . e . the mean attitude s of group members tends to a conciliatory s value of −3 . The model will then become nonlinear , and consequently may exhibit chaotic dynamics .
Currently our model is symmetric around 0 with respect to the range s to – s of individual attitudes from belligerence
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