MoietyProperties.doc 21 References

Contributions to complexity theory in relation to social organization are given by original proofs in graph theory that show the structural conditions that maximize the probability of finding shortest-step solutions to problem-solving from start to goal in a network through a set of random paths. The proofs link findings in simulation models, such as James March's (1991) discovery of advantages to exploratory (random) behaviors over selection for exploitation in human problem solving, to features of “dual” social organization that enhance these advantages. Examples are the moiety systems frequently found in pre-state kinship-based societies, structured competition, and certain collaborative disciplines in business organization. Comparable applications are found in the problem of how ants’ random traversal of the spatial maze of their environment to find food sources structure a cooperative solution to the minimum search problem through the structure of their pheromone marking of paths, which limits the interaction space to one that resembles a spatially localized moiety-like structure of traversal. Hence we show, in the general case, the conditions under which certain very general classes of mazes (as appropriately structured start-to-target graphs) allow shortest paths to be found by aggregating certain types of random individual behavior. The "collective intelligence" of these aggregate solutions to problem solving, then, reside as much in the structure of the maze or graph as in the ability to record information collectively. The argument supports the importance of co-evolution between speciesactants and species-environments. 1 We thank Norman Johnson, Joel Gunn and an anonymous referee for helpful critiques and commentary. This research was supported by NSF grant #BCS-9978282, “Longitudinal Network Studies and Predictive Cohesion Theory,” to D. R. White, 1999-2001, with consultant Frank Harary. * Professor of Anthropology, University of California, Irvine. ** Professor of Computer Science, New Mexico State University, Las Cruces