The Dynamics of Multidimensional Secession: Fixed Points and Ideological Condensation

We explore a generalized, stochastic seceder model of societal dynamics with variable size polling groups and higher-dimensional opinion vectors, revealing its essential modes of self-organized segregation. Renormalizing to a discrete, deterministic version, we pin down the upper critical size of the sampling group and analytically uncover a self-similar hierarchy of dynamically stable, multiple-branch fixed points. In $d\ge 3$, the evolving, coarsening population suffers collapse to a 2D ideological plane.