This paper proposes a conceptual framework for the analysis of reward sharing schemes in
mining pools, such as those associated with Bitcoin. The framework is centered around the
reported shares in a pool instead of agents and introduces two new fairness criteria:
absolute and relative redistribution. These criteria impose that the addition of a share to a
round affects all previous shares of the round in the same way, either in absolute amount or
in relative ratio. We characterize two large classes of reward sharing schemes …