Probabilistic consensus via polling and majority rules

TL;DR

This paper introduces enhanced decentralized consensus algorithms based on polling and super-majority rules, which accelerate convergence and improve accuracy in distributed systems with binary opinions.

Contribution

It proposes a generalized voter model with super-majority polling, significantly speeding up consensus and reducing errors compared to traditional models.

Findings

Faster convergence to consensus with super-majority polling.

Reduced probability of incorrect consensus.

Effective in lightweight decentralized systems.

Abstract

In this paper, we consider lightweight decentralised algorithms for achieving consensus in distributed systems. Each member of a distributed group has a private value from a fixed set consisting of, say, two elements, and the goal is for all members to reach consensus on the majority value. We explore variants of the voter model applied to this problem. In the voter model, each node polls a randomly chosen group member and adopts its value. The process is repeated until consensus is reached. We generalize this so that each member polls a (deterministic or random) number of other group members and changes opinion only if a suitably defined super-majority has a different opinion. We show that this modification greatly speeds up the convergence of the algorithm, as well as substantially reducing the probability of it reaching consensus on the incorrect value.