  Decisions about sharing personal information are not trivial, since there are
many legitimate and important purposes for such data collection, but often the
collected data can reveal sensitive information about individuals.
Privacy-preserving technologies, such as differential privacy (DP), can be
employed to protect the privacy of individuals and, furthermore, provide
mathematically sound guarantees on the maximum privacy risk. However, they can
only support informed privacy decisions, if individuals understand the provided
privacy guarantees. This article proposes a novel approach for communicating
privacy guarantees to support individuals in their privacy decisions when
sharing data. For this, we adopt risk communication formats from the medical
domain in conjunction with a model for privacy guarantees of DP to create
quantitative privacy risk notifications. We conducted a crowd-sourced study
with 343 participants to evaluate how well our notifications conveyed the
privacy risk information and how confident participants were about their own
understanding of the privacy risk. Our findings suggest that these new
notifications can communicate the objective information similarly well to
currently used qualitative notifications, but left individuals less confident
in their understanding. We also discovered that several of our notifications
and the currently used qualitative notification disadvantage individuals with
low numeracy: these individuals appear overconfident compared to their actual
understanding of the associated privacy risks and are, therefore, less likely
to seek the needed additional information before an informed decision. The
promising results allow for multiple directions in future research, for
example, adding visual aids or tailoring privacy risk communication to
characteristics of the individuals.
