Random Differential Privacy

We propose a relaxed privacy definition called {\em random differential privacy} (RDP). Differential privacy requires that adding any new observation to a database will have small effect on the output of the data-release procedure. Random differential privacy requires that adding a {\em randomly drawn new observation} to a database will have small effect on the output. We show an analog of the composition property of differentially private procedures which applies to our new definition. We show how to release an RDP histogram and we show that RDP histograms are much more accurate than histograms obtained using ordinary differential privacy. We finally show an analog of the global sensitivity framework for the release of functions under our privacy definition.