In many species, newly immigrated or newly dominant males are known to attack and kill dependent infants they have not sired. One of the female counter-strategies against this adaptive male infanticide in group-living taxa is polyandrous mating. A mathematical model demonstrates the existence of a basic conflict of interest between the dominant male and the female. We model the intensity of this conflict, and the pressure to evolve counter-strategies, in relation to (i) the risk of takeover of top dominance by males from inside the group rather than outside and (ii) variation in the relative strength of the dominant male and, thus, expected length of future tenure. The model predicts that dominant males prefer single-male groups, or failing that, prefer multi-male groups with takeovers by outside males. Females, in contrast, generally prefer to live in multi-male groups with takeovers by inside males, but prefer single-male groups if dominant males are extremely powerful. Empirical data suggest that females can control adult group composition, but cannot control either the source of takeovers or relative male strength. The main conclusion is that intersexual conflict in the form of infanticide may over time affect the social system in which a species lives.