Voting is used widely to aggregate preferences to make a collective decision. In this paper, we focus on evaluating and designing voting rules that support both the privacy of the voting agents and a notion of fairness over such agents. We introduce a novel notion of group fairness and adopt the existing notion of local differential privacy. We evaluate the level of group fairness in several existing voting rules, showing that it is not possible to always obtain maximal economic efficiency with high fairness. Then, we present both a machine learning and a constrained optimization approach to design new voting rules that are fair while maintaining a high level of economic efficiency. Finally, we empirically examine the effect of adding noise to create local differentially private voting rules and discuss the three-way trade-off between economic efficiency, fairness, and privacy.