Abstract
The adjustment of signed structures (symmetric positive and negative relations) under a local (myopic) sign-change dynamic is studied both analytically and through simulation. Models deriving from various theories but notably balance theory are inspected to determine the convergent properties of the dynamic process.
Notes
1This article complements a series of earlier papers (Abell and Ludwig, Citation2009; Abell, Kajawski, and Ludwig, Citation2009) regarding eventually the location of the simplest micro model which will predict the emergence of groups. Here we concentrate upon structures with symmetric relations under a local sign-change dynamic. Differing assumptions have been made in the other papers. Subsequent papers will explore structures with directed and valued relations. Balance is studied in terms of 3-cycles only as the authors take the view that larger cycles (n > 3) do not lead to stress and are not unstable. In complete structures formulation of balance in terms of 3-cycles and all longer cycles are equivalent. In incomplete structures this is not the case.
2 n = 60 is admittedly rather arbitrary, though it was chosen to move beyond a small group context, but in recognition of simulation times.