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.
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