Committee-based blockchain consensus protocols combine permissionless consensus and classical state machine replication protocols to process transactions efficiently. Due to corruptions by the adversary, reconfiguration mechanisms have to be deployed to update committee members. How to select enough fraction of honest nodes is a key issue that needs to be addressed.In this chapter, we propose a fair selection protocol for reconfiguring a committee in a permissionless blockchain. Our fair selection protocol consists of two main phases: the mining process and the confirmation of the new nodes list. We analyze the impact of the network latency and give a rigorous proof of the mining process. Furthermore, we point out that in the process of confirming the new nodes list, “node censorship” by a malicious leader could lead to an increase in the proportion of new nodes controlled by an adversary. We propose a threshold-vote rule to defend against the node censorship attack and prove the security of the entire protocol, including safety and liveness properties. Our fair selection protocol could be implemented in committee-based permissionless blockchains according to different demands with proper parameters.