Consensus plays a crucial role in distributed ledger systems, impacting both scalability and decentralization. Many blockchain systems use a weighted lottery based on a scarce resource such as a stake, storage, memory, or computing power to select a committee whose members drive the consensus and are responsible for adding new information to the ledger. Therefore, ensuring a robust and fair committee selection process is essential for maintaining security, efficiency, and decentralization. There are two main approaches to randomized committee selection. In one approach, each validator candidate locally checks whether they are elected to the committee and reveals their proof during the consensus phase. In contrast, in the second approach, a sortition algorithm decides a fixed-sized committee that is globally verified. This paper focuses on the latter approach, with cryptographic sortition as a method for fair committee selection that guarantees a constant committee size. Our goal is to develop deterministic guarantees that strengthen decentralization. We introduce novel methods that provide deterministic bounds on the influence of adversaries within the committee, as evidenced by numerical experiments. This approach overcomes the limitations of existing protocols that only offer probabilistic guarantees, often providing large committees that are impractical for many quorum-based applications like atomic broadcast and randomness beacon protocols.