Society has come to rely heavily on standard census and survey methods for determining the number of individuals who may be classified as belonging to some definable subpopulation. However there are many subpopulations that cannot be enumerated by direct count, such as the number of women who have been raped, the number of alcohol or drug abusers, the number of runaway children, or the number people who are particularly susceptible to certain diseases. The increasing frequency with which hard-to- count situations are being encountered has greatly heightened interest in finding probabilistic methods for estimating the size of such sets, and the present project offers an original and promising approach to the problem. The research team consists of an anthropologist, a physicist, and a mathematician who have successfully collaborated for many years--most recently in developing a form of social network analysis in which relatively small-scale personal acquaintanceship data are projected into minimum and maximum boundaries according to a mathematical model of network size. Activities over the next two years will focus on improving the theoretical basis for the model, testing and refining it through reanalysis of existing data, and performing further fieldwork aimed at exploring the effects of different techniques of data collection. The anticipated results should considerably increase our knowledge of social network phenomena, and perhaps open the way for developing a family of models capable of predicting the size of different kinds of hard-to- count populations.
