Apokedro: A Decentralization Index for Daos and Beyond

Abstract

Decentralization is a core principle of blockchain technology and Decentralized Autonomous Organizations (DAOs), enhancing security and resilience by distributing control across a network. Traditional metrics like the Gini coefficient and Nakamoto coefficient often fall short in capturing the complex dynamics of decentralization. This paper introduces the Apokedro decentralization index, a metric that evaluates decentralization by considering the probabilities of all possible subsets of nodes that could collectively centralize control. These concepts from game theory, such as the Nash equilibrium, and the Apokedro index, when incorporated, provide a nuanced assessment of centralization risks. Key contributions include the mathematical formulation of the index, an efficient computational algorithm utilizing pruning techniques, and benchmarking experiments that compare the index performance against traditional metrics across various statistical distributions. The Apokedro index offers a comprehensive tool for measuring decentralization in blockchain networks and DAOs.