Whenever someone says `we have a problem here, and we need to spend public money to fix it` the first question asked is `how big is this problem -- how many people are affected by it?` The current research will improve a new method -- called the `network scale-up` -- for estimating the size of hard-to-count populations like the homeless and victims of various kinds of crime. The network scale-up method involves asking people how many people they know in various populations whose size is well known. One difficulty with the network scale-up method is that people often over-report their knowledge about members of small populations and under-report their knowledge about members of large populations. Under-reporting may occur because people are unaware that someone they know is, in fact, a member of a specific population, while over-reporting may occur when people are forced to choose a specific number for their knowledge of a population, and guess. In this project, we will use focus groups and a network survey to provide a qualitative understanding of the dimensions of these effects. The network survey will produce information about the probability that people know certain kinds of things about each other. For example, people often know the occupations of each of their acquaintances, but are less likely to know that their acquaintances have a twin sibling. The probabilities derived from this research will enhance the accuracy of the network scale-up method for estimating the size of populations whose size is not known. We will then conduct national, representative surveys to incorporate and test refinements of the method.