For half a century explaining human altruism has been a major research focus for scholars in a wide variety of disciplines, yet answers are still sought. Here, paradigms like reciprocal altruism, mutualism, and group selection are set aside, to examine the effects of social selection as an under-explored model. To complement Alexander’s reputational-selection model, I introduce group punishment as another type of social selection that could have impacted substantially on the development of today’s human nature, and on our potential for behaving altruistically. Capital punishment is a decisive type of social selection, which in our past hunter–gatherer environment was aimed primarily against intimidating, selfish bullies, so it is proposed that moral sanctioning has played a major part in genetically shaping our social and political behaviours. Aggressive suppression of free-riding deviants who bully or deceive has made a cooperatively generous, egalitarian band life efficient for humans, even as it has helped our species to evolve in directions that favour altruism.