  Privacy-preserving data analysis has become more prevalent in recent years.
In this study, we propose a distributed group differentially private Majority
Vote mechanism, for the sign selection problem in a distributed setup. To
achieve this, we apply the iterative peeling to the stability function and use
the exponential mechanism to recover the signs. For enhanced applicability, we
study the private sign selection for mean estimation and linear regression
problems, in distributed systems. Our method recovers the support and signs
with the optimal signal-to-noise ratio as in the non-private scenario, which is
better than contemporary works of private variable selections. Moreover, the
sign selection consistency is justified by theoretical guarantees. Simulation
studies are conducted to demonstrate the effectiveness of the proposed method.
