WP049: Diversity and Popularity in Organizations and Communities

Little is known about the structure of communities and organizations where constraints on interaction are virtually negligible. In an on-line community or a virtual organization, we expect that interactions will primarily be driven by the perceived preferences of individuals for one another, rather than by physical, spatial and institutional constraints. Consequently, social structure will depend on the distribution of ability to attract other people's requests for interaction. Huberman and Hogg (1995) demonstrated a mathematical relationship between variance in how these abilities are distributed and traditional measures of network size and clustering. We wish to extend the Huberman/Hogg model to include a limit on the number of interaction requests to which a popular person can respond - the familiar "Bounded Rationality" of March and Simon (1958).

The effects of bounded rationality are most acutely felt by individuals who are highly sought by others, i.e. the most popular ones. However, under the original Huberman & Hogg model, the most popular person in a group is rated "best" (and thus sought most often) by only a very small proportion of the population. This is contrary to our real life experience in many domains, where
"popular" or "competent" people are often judged to be desirable by a sizable proportion of the group or organization.

In this paper, 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. The three alternative sets of assumptions, which may be applied individually or jointly, are:

• Ratings have two components: a universal one which is shared by all evaluators, and a specific one which is independently assigned by each member of the group.
• There is a limited number of independent traits or skills on which people are rated. All ratings are linear combinations of this limited number of traits.
• Popularity is based on percentile rank in the population, not on absolute rating.

We demonstrate that each of these assumption sets leads to a slightly different correlation between the value of the assumption's parameter and the resultant value for popularity of the most popular individuals. The parameters also affect the count of "most popular" people, the ratings of individuals other than the most popular, and other such observables. We can thus adjust for simultaneous observations by variously combining these assumptions. The parameter values used to match observed popularity patterns are natural inputs to future models, which may, for example, correlate network features to factors such as network size and ability variance. 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.