In order to predict the features of non-raiding human warfare in small-scale, socially stratified societies, we study a coalitionary model of war that assumes that individuals participate voluntarily because their decisions serve to maximize fitness. Individual males join the coalition if war results in a net economic and thus fitness benefit. Within the model, viable offensive war ensues if the attacking coalition of males can overpower the defending coalition. We assume that the two groups will eventually fuse after a victory, with ranks arranged according to the fighting abilities of all males and that the new group will adopt the winning group's skew in fitness payoffs. We ask whether asymmetries in skew, group size and the amount of resources controlled by a group affect the likelihood of successful war. The model shows, other things being equal, that (i) egalitarian groups are more likely to defeat their more despotic enemies, even when these are stronger, (ii) defection to enemy groups will be rare, unless the attacked group is far more despotic than the attacking one, and (iii) genocidal war is likely under a variety of conditions, in particular when the group under attack is more egalitarian. This simple optimality model accords with several empirically observed correlations in human warfare. Its success underlines the important role of egalitarianism in warfare.