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With the exponential rise in the number of devices, the Internet of Things (IoT) is geared toward edge-centric computing to offer high bandwidth, low latency, and improved connectivity. In contrast, legacy cloud-centric platforms offer deteriorated bandwidth and connectivity that affect the quality of service. Edge-centric Internet of Things-based technologies, such as fog and mist computing, offer distributed and decentralized solutions to resolve the drawbacks of cloud-centric models. However, to foster distributed edge-centric models, a decentralized consensus system is necessary to incentivize all participants to share their edge resources. This paper is motivated by the shortage of comprehensive reviews on decentralized consensus systems for edge-centric Internet of Things that elucidates myriad of consensus facets, such as data structure, scalable consensus ledgers, and transaction models. Decentralized consensus systems adopt either blockchain or blockchainless directed acyclic graph technologies, which serve as immutable public ledgers for transactions. This paper scrutinizes the pros and cons of state-of-the-art decentralized consensus systems. With an extensive literature review and categorization based on existing decentralized consensus systems, we propose a thematic taxonomy. The pivotal features and characteristics associated with existing decentralized consensus systems are analyzed via a comprehensive qualitative investigation. The commonalities and variances among these systems are analyzed using key criteria derived from the presented literature. Finally, several open research issues on decentralized consensus for edge-centric IoT are presented, which should be highlighted regarding centralization risk and deficiencies in blockchain/blockchainless solutions.