exert

exert: [VERB] If someone or something exerts influence, authority, or pressure, they use it in a strong or determined way, especially in order to produce a particular effect.

We are also greatly influenced by consumption norms within the relevant group. A light eater eats much more in a group of heavy eaters. A heavy eater will show more restraint in a light-eating group. The group average thus exerts a significant influence. - pp. 64, Nudge