Clicks, comments, transactions, and physical movements are being increasingly recorded and analyzed by Big Data processors who use this information to trace the sentiment and activities of markets and voters. While the benefits of Big Data have received considerable attention, it is the potential social costs of practices associated with Big Data that are of interest to us in this paper. Prior research has investigated the impact of Big Data on individual privacy rights, however, there is also growing recognition of its capacity to be mobilized for surveillance purposes. Our paper delineates the underlying issues of privacy and surveillance and presents them as in tension with one another. We postulate that efforts at controlling Big Data may create a trade-off of risks rather than an overall improvement in data protection. We explore this idea in relation to the principles of the European Union’s General Data Protection Regulation (GDPR) as it arguably embodies the new ‘gold standard’ of cyber-laws. We posit that safeguards advocated by the law, anonymization and pseudonymization, while representing effective counter measures to privacy concerns, also incentivize the use, collection, and trade of behavioral and other forms of de-identified data. We consider the legal status of these ownerless forms of data, arguing that data protection techniques such as anonymization and pseudonymization raise significant concerns over the ownership of behavioral data and its potential use in the large-scale modification of activities and choices made both on and offline.