A Formulation of the Trilemma in Proof of Work Blockchain

The blockchain trilemma, introduced in 2017 on a blog post authored by Vitalik Buterin, one of Ethereum’s co-founders, asserts that achieving decentralization, scalability, and security simultaneously within a blockchain is unattainable. While this concept has garnered empirical support through extensive analyses of blockchain performance, it remains unproven theoretically. In this study, we establish a formula representing the trilemma within a Proof of Work blockchain and validate it through theoretical and experimental analyses. Additionally, we explore the correlation between a formula term denoting decentralization and established decentralization indices, finding a strong correlation with the Herfindahl-Hirschman Index. Moreover, our analysis reveals that strategies to enhance trilemma properties within the trilemma’s constraints can be classified into two distinct categories. The first strategy is to reduce the block header or transaction size. The second strategy is to optimize the propagation time per byte between nodes.