Social Choice and Catastrophe

Abstract

This paper surveys results in general theory based on dynamical models, and emphasizes role of structural stability. In this context it is natural to consider a preference field H for society, combining economic fields, associated with preferred changes wrought by agents in economic market place, together with fields of preferred changes in polity. A condition called half-openness of H is sufficient to guarantee existence of a local direction gradient,d, for society, and thus of a social choice. The condition is equivalent to a dual property that dual co-cones of H have non-empty intersection. This result is analogous to Chichilnisky's necessary and sufficient condition for market equilibrium.We then consider models of belief aggregation similar to Condorcet's Jury theorem and mention Penn's Theorem on existence of a belief equilibrium. The half open property may fail for general dynamical processes and this feature is linked to creation of belief cascades at of Some comments are addressed to notion of punctuated equilibrium in evolutionary models in biology and language. Finally, Thom's notion of a structurally stable chreod is introduced. Even when a belief or preference field is locally chaotic because of a failure of half openness, it is possible to define a generalized social correspondence called heart. The heart is lower hemi-continuous and is characterized by a possible rapid expansion at a critical value of parameters. It is suggest that events in heart obey a power law distribution which is generally associated with the edge of chaos.