Nonlinear thermodynamics and social science modeling: fad cycles, cultural development and identificational slips

American Journal of Economics and Sociology, The, Oct, 1995 by Elias L. Khalil

Given this strict usage of term, the so-called 'equilibrium' of particular institutions understood as "standards" (like driving on one side of the road, units of measure, money, and language) is not about uniqueness. Any alternative standard, insofar as it is widely used, would suffice to accomplish the lowering of transaction costs. Stated differently, what matters in a "standard" is not its unique attribute but rather its wide-spread use necessitated by network externality. Thus, there is a difference between the concept "equilibrium," on one hand, and the term "standard," on the other.

In this light, group membership, as studied by Roth, resembles the notion "standard" rather than the concept "equilibrium." While group membership could be stable, it lacks uniqueness. A capricious act or chance event could start a certain taste in dress or attendance of a particular church. But once a practice is capable of attracting a threshold of adherents, it engenders its own self-feeding and self-sustaining mechanisms to entice more people to adopt and continue the practice. This is similar to the use of a standard of measure in a certain locality, like the thumb for an inch or the arm for a yard. It usually has an accidental origin. But once a threshold of practitioners is reached, the convention becomes stable without implying it is unique. There are diverse solutions, what economists call "multiple equilibria," to the problem of network externality. The "multiple equilibria" notion, which should not be confused with the strict concept "equilibrium," denotes positions which are stable but not unique.

Examples of multiple equilibria include standards, many of them trivial, on how to write addresses, format letters, use idioms, indicate time, and turn screws. Such standards explain the stability, but not uniqueness, of a certain layout of the typewriter's keyboard (David, 1985) and even the spontaneous rise of order in the use of sidewalks on a university campus. Concerning this last, one day we might find the students walking on the right-hand side, while on another day we might find them walking on the left-hand side. The switch of sides is usually abrupt, as in the case of the spread of diseases which Roth models adequately. The switch of sides might rise because of a sudden, accidental unison influx of students from a nearby parking lot, the interruption of traffic by a bicyclist, the occurrence of an automobile accident, the appearance of a puddle of water on one side of the sidewalk, or any exogenous event.

The same kind of dynamics seems to operate with regard to the change of fads. Some peculiar events, like a new movie star consuming commodity X, could destabilize a certain taste and initiate another. Along the same rationale, Roth (1992, 227-29) follows the erratic change of fortunes of revivalist church communities in nineteenth century Vermont. The stable growth of such revivalist churches was stopped by the erratic "accidents" of a suicide in one case and a rape in another. Insofar as church membership was sensitive to such "accidents," church membership could be adequately described with the same tools used to discuss the multiple equilibria of standards or pedestrian traffic. Namely, standards and sudden cyclical jumps in church membership are properly subject to nonlinear dynamics that Roth borrows from the study of the ferromagnetic phenomenon (225-26).