Committee-based blockchains are among the most popular alternatives of proof-of-work based blockchains, such as Bitcoin. They provide strong consistency (no fork) under classical assumptions, and avoid using energy-consuming mechanisms to add new blocks in the blockchain. For each block, these blockchains use a committee that executes Byzantine-fault tolerant distributed consensus to decide the next block they will add in the blockchain. Unlike Bitcoin, where there is only one creator per block with high probability, in committee-based blockchain any block is cooperatively created. In order to incentivize committee members to participate to the creation of new blocks rewarding schemes have to be designed. In this paper, we study the fairness of rewarding in committee-based blockchains and we provide necessary and sufficient conditions on the system communication under which it is possible to have a fair reward mechanism.