  Due to its minimal energy requirement the PoS consensus protocol has become
an attractive alternative to PoW in modern cryptocurrencies. In this protocol
the chance of being selected as a block proposer in each round is proportional
to the current stake of any node. Thus, nodes with higher stakes will achieve
more block rewards, resulting in the so-called rich-getting-richer problem. In
this paper, we introduce a new block reward mechanism called the FRD (Fair
Reward Distribution) mechanism, in which for each block produced, in addition
to a major reward given to the block proposer, a small reward is given to all
other nodes. We prove that this reward mechanism makes the PoS protocol fairer
in terms of concentration of wealth by developing on the Bagchi-Pal urn model.
