  Differential privacy (DP) and local differential privacy (LPD) are frameworks
to protect sensitive information in data collections. They are both based on
obfuscation. In DP the noise is added to the result of queries on the dataset,
whereas in LPD the noise is added directly on the individual records, before
being collected. The main advantage of LPD with respect to DP is that it does
not need to assume a trusted third party. The main disadvantage is that the
trade-off between privacy and utility is usually worse than in DP, and
typically to retrieve reasonably good statistics from the locally sanitized
data it is necessary to have a huge collection of them. In this paper, we focus
on the problem of estimating counting queries from collections of noisy
answers, and we propose a variant of LDP based on the addition of geometric
noise. Our main result is that the geometric noise has a better statistical
utility than other LPD mechanisms from the literature.
