Blockchain empowers a decentralized economy by enabling distributed trust in a peer-to-peer network. Decentralization is a core property of blockchain that not only ensures system security but also enables the democratization of systems and processes through the promise of a distributed peer-to-peer network. However, surprisingly, a widely accepted definition or measurement of decentralization is still lacking. We explore an SoK on blockchain decentralization focusing on measurement, quantification, and methodology. First, we establish a taxonomy for analyzing blockchain decentralization in the five facets of consensus, network, governance, wealth, and transaction by qualitative analysis of existing research. Second, we propose an index that measures and quantifies the decentralization level of blockchain across different facets by transforming Shannon entropy. We verify the explainability of the index via comparative static simulations. We also define and discuss alternative indices, including the Gini Coefficient, Nakamoto Coefficient, and Herfindahl-Hirschman Index (HHI). We provide open-source Python code for calculating the decentralization index by comparing various alternatives on GitHub. Third, by applying our proposed index to empirical research on top DeFi applications, we demonstrate how the three scientific methods of descriptive, predictive, and causal inferences are useful in studying blockchain decentralization. Finally, we identify future research directions: 1) to explore the interactions between different facets of blockchain decentralization, 2) to design blockchain mechanisms that achieve sustainable decentralization, and 3) to study the interplay of decentralization levels and the ends of security, privacy, and efficiency. We also raise challenges in addressing the controversies in blockchain decentralization.

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