On asymptotic fairness in voting with greedy sampling

Abraham Gutierrez Sanchez, Sebastian Müller, Šebek Stjepan

Research output: Contribution to journalArticlepeer-review


The basic idea of voting protocols is that nodes query a sample of other nodes and adjust their own opinion throughout several rounds based on the proportion of the sampled opinions. In the classic model, it is assumed that all nodes have the same weight. We study voting protocols for heterogeneous weights with respect to fairness. A voting protocol is fair if the influence on the eventual outcome of a given participant is linear in its weight. Previous work used sampling with replacement to construct a fair voting scheme. However, it was shown that using greedy sampling, i.e., sampling with replacement until a given number of distinct elements is chosen, turns out to be more robust and performant.
In this paper, we study fairness of voting protocols with greedy sampling and propose a voting scheme that is asymptotically fair for a broad class of weight distributions. We complement our theoretical findings with numerical results and present several open questions and conjectures.
Original languageEnglish
Pages (from-to)999-1032
Number of pages34
JournalAdvances in Applied Probability
Issue number3
Early online dateMay 2023
Publication statusPublished - 10 Sept 2023


  • Asymptotic fairness
  • consensus protocol
  • heterogeneous network
  • Sybil protection
  • voting scheme

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Information Systems
  • Discrete Mathematics and Combinatorics
  • Statistics and Probability
  • Applied Mathematics

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