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On asymptotic fairness in voting with greedy sampling

Part of: Computer system organization Limit theorems Communication, information Game theory

Published online by Cambridge University Press:  10 May 2023

Abraham Gutierrez ,
Sebastian Müller Open the ORCID record for Sebastian Müller [Opens in a new window]  and
Stjepan Šebek
Abraham Gutierrez*
Affiliation:
Graz University of Technology
Sebastian Müller*
Affiliation:
Aix-Marseille Université and IOTA Foundation
Stjepan Šebek*
Affiliation:
University of Zagreb
*
*Postal address: Institute of Discrete Mathematics, Graz University of Technology, Graz, Austria. Email address: schnirelmann@gmail.com
**Postal address: Aix-Marseille Université, CNRS, Centrale Marseille, I2M, UMR 7373, 13453 Marseille, France; IOTA Foundation, 10405 Berlin, Germany. Email address: sebastian.muller@univ-amu.fr
***Postal address: Department of Applied Mathematics, Faculty of Electrical Engineering and Computing, University of Zagreb, Croatia. Email address: stjepan.sebek@fer.hr
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Abstract

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.

Keywords

Asymptotic fairnessconsensus protocolvoting schemeheterogeneous networkSybil protection

MSC classification

Primary: 60F99: None of the above, but in this section
Secondary: 94A20: Sampling theory 91A20: Multistage and repeated games 68M14: Distributed systems
Type
Original Article
Information
Advances in Applied Probability , Volume 55 , Issue 3 , September 2023 , pp. 999 - 1032
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of Applied Probability Trust

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