Which interactions make you unique?

In assessing re-identification risk, a key challenge lies in understanding how an individual can be identified based on specific combinations of variables. Seiler, Mase, and Owen (2023, What Makes You Unique?) recently introduced the uniqueness Shapley value to quantify the contribution of individual variables that, when revealed, lead to the identification of a specific subject. In this work, we extend their framework to explore interactions among variables in the context of subject identification. Specifically, we investigate whether the joint consideration of certain variables enhances, diminishes, or maintains their identification ability compared to the sum of their individual contributions. These non-additive effects can significantly increase re-identification risk for some subjects. To address this, we introduce the uniqueness Shapley–Owen value to measure these interactions and interpret them in terms of cooperative effects. We apply this approach to voter registration data from Alamance County, North Carolina and to the medical expenditure panel survey. Our analysis identifies individuals for whom the joint identification ability of variables is amplified, making them, ceteris paribus, more vulnerable to being identified.