Consensus and leader election are fundamental problems in distributed systems. Consensus is the problem in which all processes in a distributed computation must agree on some value. Average consensus is a popular form of consensus, where the agreed upon value is the average of the initial values of all the processes. In a typical solution for consensus, each process learns the value of others' to determine the final decision. However, this is undesirable if processes want to keep their values secret from others. With this motivation, we present a solution to privacy-preserving average consensus, where no process can learn the initial value of any other process. Additionally, we augment our approach to provide outlier resistance, where extreme values are not included in the average calculation. Privacy is fully preserved at every stage, including preventing any process from learning the identities of processes that hold outlier values. To our knowledge, this is the first privacy-preserving average consensus algorithm featuring outlier resistance. In the context of leader election, each process votes for the one that it wants to be the leader. The goal is to ensure that the leader is elected in such a way that each vote remains secret and the sum of votes remain secret during the election. Only the final vote tally is available to all processes. This ensures that processes that vote early are not able to influence the votes of other processes. We augment our approach with shallow ranked voting by allowing processes to not only vote for a single process, but to designate a secondary process to vote towards in the event that their primary vote's candidate does not win the election.