Algorithms are regularly used for mining data, offering unexplored patterns and deep non-causal analyses in what we term the “classifying society”. In the classifying society individuals are no longer targetable as individuals but are instead selectively addressed for the way in which some clusters of data that they (one or more of their devices) share with a given model fit in to the analytical model itself. This way the classifying society might bypass data protection as we know it. Thus, we argue for a change of paradigm: to consider and regulate anonymities—not only identities—in data protection. This requires a combined regulatory approach that blends together (1) the reinterpretation of existing legal rules in light of the central role of privacy in the classifying society; (2) the promotion of disruptive technologies for disruptive new business models enabling more market control by data subjects over their own data; and, eventually, (3) new rules aiming, among other things, to provide to data generated by individuals some form of property protection similar to that enjoyed by the generation of data and models by businesses (e.g. trade secrets). The blend would be completed by (4) the timely insertion of ethical principles in the very generation of the algorithms sustaining the classifying society.