Firms and platforms now routinely use online consumer data to offer customized prices, products, or advertising. This surge in data-driven market segmentation has sparked renewed academic and regulatory interest in the welfare implications of price discrimination. As demonstrated by [Bergemann et al., 2015], market segmentations can lead to a wide range of welfare outcomes and, in particular, be designed so as to maximize total consumer surplus. Yet, despite policymakers' concerns about the potential adverse effects of market segmentation on poorer consumers [The White House Council of Economic Advisers, 2015], little theoretical progress has been made regarding the heterogeneous welfare effects that market segmentation might have across consumers. This concern is all the more relevant given that segmentations that maximize consumers' surplus tend to primarily benefit consumers with a high willingness to pay, who are more likely to be richer [Condorelli, 2013, Dworczak et al., 2021].

Rewards such as prizes, labels, certifications, grants, market authorizations, positions or promotions are often allocated conditionally on a measured characteristic (or aggregate)---a score---resulting in an assortative matching of scores and rewards. In many contexts, it is natural to think of scores and rewards as complements in the designer's preferences, which rationalizes assortativity. This is the case, for example, when allocating productive resources, such as grants, to agents of heterogeneous productivity. Screening on scores, however, gives agents strong incentives to invest in the underlying characteristic, and also, possibly, to manipulate its measure. For instance, environmental certification may lead firms to engage in emissions abatement and greenwashing.