Diversity and Popularity in Organizations and Communities

This paper examines social groupings whose structure depends only on the distribution of ability to attract attention. When people‘s attention is a scarce resource, those individuals who are rated highest by a large number of other individuals will have to ration their attention, resulting in constraints on the social structure of the group. The incidence of popular individuals by that definition reflects the extent to which individuals agree on who their highest-rated colleague is. We propose three basic distributions or ways to generate the matrix of perceived ability so as to yield popularity profiles that can be parametrically adjusted to match observations. We demonstrate that each of these assumption sets leads to a slightly different correlation between the value of the assumption‘s parameter and the set of observable popularity patterns. Since popularity, in real life, often determines such things as power, centrality, over-utilization and perhaps reduced accessibility, having more realistic ways of representing it is important for modeling and understanding virtual organizations and communities.