Abstract
A compelling problem in a population is to estimate the number of people the average person knows. A consequential related problem is to estimate the size of important subpopulations. A random sample of a population is asked whether they know anyone in a given subpopulation of size e, thus yielding an estimate of the probability that this occurs in the population. Using an equal likelihood probability model, this leads to a lower bound estimate for c, the average number of people a person in the population knows. When the number of people a person knows has a binomial distribution over the population this value is an estimate for c itself. Here we test this method on data from Mexico City, where a large random sample of people was asked whether they knew anyone in each of several different subpopulations in Mexico City of known and unknown sizes. We develop procedures for obtaining various bounds and estimates for c and determine some of the respondents' attributes on which variation in probability of knowing someone in a subpopulation and variation in personal network size seem to depend. We apply these to the estimation of e for rape victims in Mexico City and the estimation of c from data on AIDS victims in the United States.
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