We define an implicit preference over an attribute as one that is expressed more strongly the more that attribute is mixed with others. Thus a hiring manager with a pro-male implicit preference might choose female candidates over otherwise identical men, but switch to favoring men when they differ in additional attributes. We prove a representation theorem for a dataset of inequalities between comparative utilities, u(x,z), which allows us to identify implicit preferences both from cycles in binary choice, and from comparison-dependent evaluations. We show that implicit preferences can have diverse psychological foundations: rule-driven decision-making, signaling, and implicit knowledge. We apply the theory to two recent experimental datasets, finding evidence of implicit selfishness, implicit risk aversion, and implicit racial bias.