Computer simulations are increasingly being used to monitor and predict the movement behavior of crowds. This can enhance crowd safety at large events and transport hubs, and increase efficiency such as capacity utilization in public transport systems. However, the models used are mainly based on video observations, not an understanding of human decision making. Theories of crowd psychology can elucidate the factors underpinning collective behavior in human crowds. Yet, in contrast to psychology, computer science must rely upon mathematical formulations in order to implement algorithms and keep models manageable. Here, we address the problems and possible solutions encountered when incorporating social psychological theories of collective behavior in computer modeling. We identify that one primary issue is retaining parsimony in a model while avoiding reductionism by excluding necessary aspects of crowd psychology, such as the behavior of groups. We propose cognitive heuristics as a potential avenue to create a parsimonious model that incorporates core concepts of collective behavior derived from empirical research in crowd psychology.