Reward Distribution in Proof-of-Stake Protocols: A Trade-Off Between Inclusion and Fairness

Proof-of-Stake (PoS) variants provide an energy-efficient alternative to Proof-of-Work (PoW). However, it is not clear whether practical PoS implementations are fair with respect to wealth, stake, and reward distribution. In this paper, we analyse the fairness of the four well-known PoS platforms Tezos, Polkadot, Cardano, and Casper through a data-driven approach. For this, we collect data on stakes and rewards for all the four platforms over several years. We then apply four measures to study the fairness along different dimensions. We calculate the Gini coefficient to explore the wealth inequality, the Nakamoto coefficient to investigate the degree of decentralization, and the expectational and robust fairness of the stake-reward proportions, i.e., if the validators receive their fair share of the rewards given their stake share. We can show that there are dynamics of high wealth inequalities and stake centralization in all the systems with Polkadot being the exception. With respect to stake-reward fairness, the platforms differ in the distributions of deviations from the fair share, i.e., in Cardano and Tezos, the differences have a lower magnitue as many small validators participate. However, by examining specific outcomes, we can show that platforms with a limited validator set such as Polkadot and Casper tend to be fairer regarding the reward payoffs, but it is not possible for smaller validators to participate. This mechanism sheds light on a trade-off that the platforms face: the more inclusive (open) the validation process is designed, the unfairer the reward distribution tends to be. Our results allow us to conclude that the way of how PoS is implemented matters greatly for its fairness.