  A deterministic privacy metric using non-stochastic information theory is
developed. Particularly, minimax information is used to construct a measure of
information leakage, which is inversely proportional to the measure of privacy.
Anyone can submit a query to a trusted agent with access to a non-stochastic
uncertain private dataset. Optimal deterministic privacy-preserving policies
for responding to the submitted query are computed by maximizing the measure of
privacy subject to a constraint on the worst-case quality of the response
(i.e., the worst-case difference between the response by the agent and the
output of the query computed on the private dataset). The optimal
privacy-preserving policy is proved to be a piecewise constant function in the
form of a quantization operator applied on the output of the submitted query.
The measure of privacy is also used to analyze the performance of $k$-anonymity
methodology (a popular deterministic mechanism for privacy-preserving release
of datasets using suppression and generalization techniques), proving that it
is in fact not privacy-preserving.
