  In this paper I study how to regulate firms' access to consumer data when the
latter is used for price discrimination and the regulator faces non-Bayesian
uncertainty about the correlation structure between data and willingness to
pay, and hence about the way the monopolist will use the consumers' information
to segment the market. I fully characterize all policies that are worst-case
optimal when the regulator maximizes consumer surplus: the regulator allows the
monopolist to access data if the monopolist cannot use the database to identify
a small group of consumers. Furthermore, from the set of policies that achieve
the largest worst-case consumer surplus, I identify the ones that are
undominated; i.e., there is no alternative policy that never yields lower
consumer surplus, and sometimes strictly higher consumer surplus.
