Voting-based probabilistic consensuses and their applications in distributed ledgers

We review probabilistic models known as majority dynamics (also known as threshold voter models) and discuss their possible applications for achieving consensus in cryptocurrency systems. In particular, we show that using this approach in a straightforward way for practical consensus in a Byzantine setting can be problematic and requires extensive further research. We then discuss the Fast Probabilistic Consensus (FPC) protocol (Popov and Buchanan, J Parallel Distrib Comput 147:77-86, 2021), which circumvents the problems mentioned above by using external randomness.