  Differential privacy is a widely adopted framework designed to safeguard the
sensitive information of data providers within a data set. It is based on the
application of controlled noise at the interface between the server that stores
and processes the data, and the data consumers. Local differential privacy is a
variant that allows data providers to apply the privatization mechanism
themselves on their data individually. Therefore it provides protection also in
contexts in which the server, or even the data collector, cannot be trusted.
The introduction of noise, however, inevitably affects the utility of the data,
particularly by distorting the correlations between individual data components.
This distortion can prove detrimental to tasks such as causal discovery. In
this paper, we consider various well-known locally differentially private
mechanisms and compare the trade-off between the privacy they provide, and the
accuracy of the causal structure produced by algorithms for causal learning
when applied to data obfuscated by these mechanisms. Our analysis yields
valuable insights for selecting appropriate local differentially private
protocols for causal discovery tasks. We foresee that our findings will aid
researchers and practitioners in conducting locally private causal discovery.
