1. A computer-implemented method comprising: constructing an influence model for each campaign in a set of two or more campaigns, wherein constructing each influence model comprises: sending an advertising treatment of a respective campaign over a network to each entity in the respective campaign's treatment group of entities; selecting the respective campaign's control group of entities, wherein the respective campaign's control group excludes entities of the respective campaign's treatment group and the respective campaign's advertising treatment is not sent to the entities of the respective campaign's control group; selecting treatment group converters from each respective treatment group of entities, each treatment group converter having met a conversion criterion of its respective campaign after exposure to the respective campaign's advertising treatment; and selecting control group converters from each respective control group of entities, each control group converter having met the conversion criterion of the its respective campaign without exposure to the respective campaign's advertising treatment; and comparing features of media consumption histories of the respective campaign's treatment group converters to features of media consumption histories of the respective campaign's control group converters; receiving, by an influence system, a notification that an opportunity to expose a specified entity to advertising content is available, the specified entity not included in any of the treatment groups; applying the constructed influence model for each campaign to features of the specified entity's media consumption history; selecting a campaign from the set of two or more campaigns based on a result of applying each constructed influence model to features of the specified entity; and sending advertising content of the selected campaign to the specified entity responsive to selecting the campaign.