Abstract The paper introduces the notion of a probabilistic mixture of a family of relational structures. This concept is of interest both from a measurement-theoretic and from a choice-theoretic point of view, since it offers a probabilistic generalization of classical deterministic measurement concepts (such as additive conjoint measurement) and, at the same time, a natural generalization for binary choice systems induced by rankings. Probabilistic mixtures with finite domains are shown to be characterizable in terms of finite systems of linear equations and inequalities and to be closely related to random-utility-like representation concepts.