In this paper, we consider the problem of modeling discrete social network data and learning the underlying group dynamics. The goal is to develop probabilistic profiles of large collections of data while preserving the essential temporal relationships that provide insights for various applications of interest. For example, in social network analysis, we want to analyze relationships between social agents and their behaviors over time and on various social media sites (i.e., Facebook, Twitter, Instagram, Google, etc.). In web advertising analysis, we want to analyze the relationships between customers and the types of products they buy from different shopping sites to capture customers' buying behaviors and learn the intrinsic factors that effect their buying decision process. In the study of scientific collaboration, using co-authorship networks from multiple journals on related subjects, one can analyze relationships between subjects and authors.

Cox's well-known theorem justifying the use of probability is shown not to hold in finite domains. The counterexample also suggests that Cox's assumptions are insufficient to prove the result even in infinite domains. The same counterexample is used to disprove a result of Fine on comparative conditional probability.