On asymptotic fairness in voting with greedy sampling

TL;DR

This paper investigates the fairness of voting protocols with heterogeneous weights using greedy sampling, proposing an asymptotically fair scheme and supporting it with theoretical analysis and numerical results.

Contribution

It introduces a voting protocol with greedy sampling that achieves asymptotic fairness for diverse weight distributions, advancing fairness in weighted voting systems.

Findings

The proposed scheme is asymptotically fair for broad weight distributions.

Greedy sampling improves robustness and performance over traditional sampling methods.

Numerical results support theoretical claims and highlight open questions.

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.