The Internet of Things (IoT) is commonly deployed with devices of limited power and computation capability. A centralized IoT architecture provides a simplified management for IoT system but brings redundancy by the unnecessary data traffic with a data center. A decentralized IoT reduces the cost on data traffic and is resilient to the single-point-of-failure. The blockchain technique has attracted a large amount of research, which is redeemed as a perspective of decentralized IoT system infrastructure. It also brings new privacy challenges for that the blockchain is a public ledger of all digital events executed and shared among all participants. The decentralized IoT system relies on the leader election deeply to implement the decentralized communications among the distributed nodes. The conventional leader election must have a centralized authority, contrasting to the decentralization. As an alternative, self-tallying type schemes have been proposed in the literature for decentralized systems. These schemes suffer from adaptive and abortive issues. Also, some additional factors should be considered, such as the availability of candidate nodes. If the candidate node is unavailable after the voting phase due to being offline or ongoing tasks, the next available candidate should be elected. To accommodate such a need, in this paper, we propose a new leader election paradigm called voluntary-tallying leader election, which achieves the core requirements such as ballet secrecy, voter privacy and the additional feature of voluntary-tallying. We formalize the system and security models for this new election paradigm and present a secure and practical construction.