Researchers often face the problem of needing to protect the privacy of subjects while also needing to integrate data that contains personal information from diverse data sources in order to conduct their research. The advent of computational social science and the enormous amount of data about people that is being collected makes protecting the privacy of research subjects evermore important. However, strict privacy procedures can make joining diverse sources of data that contain information about specific individual behaviors difficult. In this paper we present a procedure to keep information about specific individuals from being "leaked" or shared in either direction between two sources of data. To achieve this goal, we randomly assign individuals to anonymous groups before combining the anonymized information between the two sources of data. We refer to this method as the Yahtzee procedure, and show that it performs as expected theoretically when we apply it to data from Facebook and public voter records.