  As members of a network share more information with each other and network
providers, sensitive data leakage raises privacy concerns. To address this need
for a class of problems, we introduce a novel mechanism that privatizes vectors
belonging to the unit simplex. Such vectors can be seen in many applications,
such as privatizing a decision-making policy in a Markov decision process. We
use differential privacy as the underlying mathematical framework for these
developments. The introduced mechanism is a probabilistic mapping that maps a
vector within the unit simplex to the same domain according to a Dirichlet
distribution. We find the mechanism well-suited for inputs within the unit
simplex because it always returns a privatized output that is also in the unit
simplex. Therefore, no further projection back onto the unit simplex is
required. We verify the privacy guarantees of the mechanism for two cases,
namely, identity queries and average queries. In the former case, we derive
expressions for the differential privacy level of privatizing a single vector
within the unit simplex. In the latter case, we study the mechanism for
privatizing the average of a collection of vectors, each of which is in the
unit simplex. We establish a trade-off between the strength of privacy and the
variance of the mechanism output, and we introduce a parameter to balance the
trade-off between them. Numerical results illustrate these developments.
