Decentralization in Open Quorum Systems: Limitative Results for Ripple and Stellar

Authors Andrea Bracciali , Davide Grossi , Ronald de Haan

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Andrea Bracciali
  • Department of Computer Science, University of Stirling, UK
Davide Grossi
  • Bernoulli Institute for Maths, CS and AI, University of Groningen, The Netherlands
  • Amsterdam Center for Law and Economics, University of Amsterdam, The Netherlands
  • Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands
Ronald de Haan
  • Institute for Logic, Language and Computation, University of Amsterdam, The Netherlands


We are indebted to the anonymous reviewers of Tokenomics 2020 for several punctual and helpful suggestions on an earlier version of the paper.

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Andrea Bracciali, Davide Grossi, and Ronald de Haan. Decentralization in Open Quorum Systems: Limitative Results for Ripple and Stellar. In 2nd International Conference on Blockchain Economics, Security and Protocols (Tokenomics 2020). Open Access Series in Informatics (OASIcs), Volume 82, pp. 5:1-5:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Decentralisation is one of the promises introduced by blockchain technologies: fair and secure interaction amongst peers with no dominant positions, single points of failure or censorship. Decentralisation, however, appears difficult to be formally defined, possibly a continuum property of systems that can be more or less decentralised, or can tend to decentralisation in their lifetime. In this paper we focus on decentralisation in quorum-based approaches to open (permissionless) consensus as illustrated in influential protocols such as the Ripple and Stellar protocols. Drawing from game theory and computational complexity, we establish limiting results concerning the decentralisation vs. safety trade-off in Ripple and Stellar, and we propose a novel methodology to formalise and quantitatively analyse decentralisation in this type of blockchains.

Subject Classification

ACM Subject Classification
  • Security and privacy → Distributed systems security
  • Blockchain
  • decentralization
  • game theory
  • computational complexity


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