Diverging tendencies in multidimensional secession

Abstract

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

Emergent dynamics of extremes in a population driven by common information sources and new social media algorithms

“…(1) Few-body: Since three is typically the minimum number of degrees of freedom for which complex dynamics can arise in a system, consider N = 3 individuals (or three groups sharing a common p value) and three possible p values: 0, 0.5 and 1. Halpin-Healy 22,23 showed how such a ‘three-body’ theory in a comparable setting of conformity and dissent can provide a powerful quantitative description. Computer simulations of this N = 3 version of Fig.…”

“…Just as a liquid may then suddenly boil over without any apparent warning, extremes can appear from out of nowhere. Foundational works in economics by Arthur 21 , in physics by Halpin-Healy 22,23 , in ecology by Gavrilets 24 , in social science by Epstein, Axtell 25 and Hedstrom 26 , in political science by Lazar 4,18,19 , and in psychology by Forsyth and Lewin 27,28 and others 29–31 , suggest that addressing this challenge will therefore require the development of minimal, generative theories of the population’s out-of-equilibrium dynamics, even though any such theory will by necessity be a cartoon version of the real-world system 4,18,21–23,29–36 .

Figure 1Real-world dynamics of extremes vs. our theory. ( A – D ) Heterogeneity distribution P ( p , t ) showing the relative fraction of population having a particular p value (i.e.

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Evolutionary minority game: The roles of response time and mutation threshold

“…The minority game (mg) is one of the most studied models of such complex systems (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein). In this model, a population of N agents with limited information and capabilities repeatedly compete for a limited global resource, or to be in the minority.…”

“…A problem of wide interest in biological and socioeconomic systems is that of an evolving population in which individual agents adapt their behavior according to past experience. The Minority Game (MG) is one of the most studied models of such complex systems (see e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein). In this model, a population of N agents with limited information and capabilities repeatedly compete for a limited global resource, or to be in the minority.…”

The Dynamics of Multidimensional Secession: Fixed Points and Ideological Condensation

“…Using a coarse-grained RG prescription, which discretizes and renders deterministic the model, we analytically uncover a self-similar hierarchy of multiple branch FPs in a gapped spectrum. Additional work, concerning the intermittent extinction dynamics of individual groups, earlytime transient behaviors, as well as kinetic symmetrybreaking phenomena, will be reported elsewhere [20]. Financial support for Tim HH has been provided by NSF DMR-0083204, Condensed Matter Theory.…”