Consumers frequently exchange their private personal data with companies in return for goods and services, such as access to search results or social networks. The authors provide a normative criterion to help assess whether companies compensate consumers adequately for their private data in these exchanges. Across a series of 11 experiments, they find that individuals place a higher price on their private data when they sell them for money than when they barter them for goods. In an application of the compatibility principle in cognitive psychology, the authors also find in two additional experiments that this effect occurs because money is a more compatible medium for valuing private data than goods are, which increases the weight of the data in monetary valuations, raising the prices that participants demand for their private data in money compared with goods. This discrepancy in valuations constitutes a violation of procedure invariance and amounts to an intransitivity of participants’ preferences for privacy. The findings raise the question of whether companies are compensating consumers adequately for their data and whether the ubiquitous markets for privacy function efficiently. Accordingly, the authors point to a possible consumer welfare argument for antitrust regulation of technology companies.