  How can individuals exchange information to learn from each other despite
their privacy needs and security concerns? For example, consider individuals
deliberating a contentious topic and being concerned about divulging their
private experiences. Preserving individual privacy and enabling efficient
social learning are both important desiderata but seem fundamentally at odds
with each other and very hard to reconcile. We do so by controlling information
leakage using rigorous statistical guarantees that are based on differential
privacy (DP). Our agents use log-linear rules to update their beliefs after
communicating with their neighbors. Adding DP randomization noise to beliefs
provides communicating agents with plausible deniability with regard to their
private information and their network neighborhoods. We consider two learning
environments one for distributed maximum-likelihood estimation given a finite
number of private signals and another for online learning from an infinite,
intermittent signal stream. Noisy information aggregation in the finite case
leads to interesting tradeoffs between rejecting low-quality states and making
sure all high-quality states are accepted in the algorithm output. Our results
flesh out the nature of the trade-offs in both cases between the quality of the
group decision outcomes, learning accuracy, communication cost, and the level
of privacy protections that the agents are afforded.
