Looking for stability in proof-of-stake based consensus mechanisms

The Proof-of-Stake (PoS) consensus algorithm has been criticized in the literature and in several cryptocurrency communities, due to the so-called compounding effect: who is richer has more coins to stake, therefore a higher probability of being selected as a block validator and obtaining the corresponding rewards, thus becoming even richer. In this paper, we present a PoS simulator written in the Julia language that allows one to test several variants of PoS-based consensus algorithms, tweak their parameters, and observe how the distribution of cryptocurrency coins among users evolves over time. Such a tool can be used to investigate which combinations of parameter values allow to obtain a “fair” and stable consensus algorithm, in which, over the long term, no one gets richer or poorer by the mere act of validating blocks. Based on this investigation, we also introduce a new PoS-based consensus mechanism that allows the system to keep the wealth distribution stable even after a large number of epochs.