ABSTRACT
Allocation processes—the division of some commodity among multiple agents—are fundamental to social interactions in various arenas. This chapter determines the consequences of this fact on an analytically tractable process of allocation subject to random external perturbations. This is a complex system: under majority rule the process is chaotic, while under weighted majority rule the system self-organizes to produce a path-dependent majority owner/dictator/monopolist. The chapter explains the sense in which the absence of equilibria in allocation processes indicates that they are complex systems. It considers a natural modification of the allocation process. For many allocation processes, however, this is not the most realistic probabilistic model. So complex allocation processes can include the venerable economics phenomenon of increasing returns and demonstrate the path-dependent consequences. The chapter examines the entropy measure of complexity for iterated discrete choice systems to the economics setting of continuous allocation processes. It also considers allocation processes driven away from an initial equal allocation by Gaussian fluctuations.
