  Automated decision systems are increasingly used to make consequential
decisions in people's lives. Due to the sensitivity of the manipulated data as
well as the resulting decisions, several ethical concerns need to be addressed
for the appropriate use of such technologies, in particular, fairness and
privacy. Unlike previous work, which focused on centralized differential
privacy (DP) or local DP (LDP) for a single sensitive attribute, in this paper,
we examine the impact of LDP in the presence of several sensitive attributes
(i.e., multi-dimensional data) on fairness. Detailed empirical analysis on
synthetic and benchmark datasets revealed very relevant observations. In
particular, (1) multi-dimensional LDP is an efficient approach to reduce
disparity, (2) the multi-dimensional approach of LDP (independent vs. combined)
matters only at low privacy guarantees, and (3) the outcome Y distribution has
an important effect on which group is more sensitive to the obfuscation. Last,
we summarize our findings in the form of recommendations to guide practitioners
in adopting effective privacy-preserving practices while maintaining fairness
and utility in ML applications.
