In computing, informatics and other scientific disciplines, combinations of two or more systems have been shown to perform better than individual systems. Although combinations of multiple systems can be better than each individual system, it is not known when and how this is the case. In this paper, we focus on visual cognition systems. In particular, we conduct an experiment consisting of twenty trials, each focused on a pair of visual cognition systems. The data set is then analyzed using combinatorial fusion. Our results demonstrate that on average, combination of two visual cognition systems can perform better than individual systems only if the individual systems have high performance ratio and cognitive diversity. These results provide a necessary condition as to when two visual cognition systems should be combined to achieve better outcomes.