Precise control and maintenance of the size of cell populations is fundamental for organismal development and homeostasis. The three cell types that comprise the mammalian blastocyststage embryo are generated in precise proportions and over a short time, suggesting a size control mechanism ensures a reproducible outcome. Guided by experimental observations, we developed a minimal mathematical model that shows growth factor signaling is sufficient to guarantee this robustness. The model anticipates, without additional parameter fitting, the response of the embryo to perturbations in its lineage composition. We experimentally added lineage-restricted cells to the epiblast both in vivo and in silico, which resulted in a shift of the fate of progenitors away from the supernumerary cell type, while eliminating cells using laser ablation biased the specification of progenitors towards the targeted cell type. Finally, we show that FGF4 couples cell fate decisions to lineage composition through changes in local concentration of the growth factor. Our results provide a basis for the regulative abilities of the mammalian embryo and reveal how, in a self-organizing system, individual cell fate decisions are coordinated at the population level to robustly generate tissues in the right proportions.