Diverging Tendencies in Multidimensional Secession

We review mean-field and fluctuation-dominated behaviors exhibited by the Seceder Model, which moves an evolving population to various critical states of self-organized segregation, delicately balancing opposed sociological pressures of conformity & dissent, and giving rise to rich ideological condensation phenomena. The secession exponent and finite societal Seceder limits are examined. This paper discusses recent research [1] on the Seceder Model [2], an intriguing far-from-equilibrium stochastic model of opinion dynamics in which the competing tendencies of conformity and dissent cause an evolving population to fragment, disperse, and coalesce, forming distinct groups characterized by free and frequent interchange of individuals. We imagine a population that is ultimately economic, sociological, or political in character, with interactions based upon shared investment strategies, cultural opinions, or electoral inclinations. This is in sharp contrast to many well-known examples of inanimate cluster formation found in Nature (e.g., in the astrophysical context-Saturnian rings, globular clusters, Virgo galactic supercluster, etc.), where the underlying forces are physical in origin; here, the interactions are based upon signaling, opinion, and information exchange. The Seceder Model bears close spiritual kinship to a number of distinguished evolutionary minority games, among them the Zhang & Challet variant [3] of Arthur's El Farol Bar problem [4], as well as its stochastic generalization by Johnson and coworkers [5], where it was discovered that the introduction of chance brought the population to a state of self-organized segregation in which two groups adopted diametrically opposed strategies. Further work by Hod & Nakar [6] revealed a dynamical phase transition in this setting, between 2-group segregation and single-group clustering, driven by the economic cost-benefit ratio implicit in the model. Relevant, too, is the work of Hauert and collaborators [7, 8], who studied 3-group dynamics amidst cooperation, defection, and abstention in a noncompulsory public goods game, mischievously dubbed by popular science pundits [9] as the " Physics of Loners " ! In its initial rendering, they considered a well-mixed formulation in which participants could interact readily with any other member of the population. Afterwards, they introduced spatial structure, finding peculiar traveling wave phenomena within the model; see Hauert's web page. Finally, in a paper titled " Meet, Discuss, and Segregate! " Weisbuch et al. [10] consider a model of opinion dynamics in which a population of interacting agents adjust continuous positions via random binary interactions subject to threshold constraints. High thresholds (large inertial barriers) produce a societal convergence of opinion to a …