Charles Darwin posited that social competition among conspecifics could be a powerful selective pressure. Richard Alexander (1989, 1990) proposed a model of human evolution involving a runaway process of social competition based on Darwin’s insight. Here we briefly review Alexander’s logic, and then expand upon his model by elucidating runaway, positive-feedback processes that were likely involved in the evolution of the remarkable combination of adaptations in humans. We discuss how these ideas fit with the hypothesis that increased inter-group interaction and cooperation among individuals in small fission-fusion groups opened the door to runaway social selection and cumulative culture during hominid evolution.