Reaching Majority Agreement in a Disconnected Network

TL;DR

This paper explores the conditions for achieving majority agreement in disconnected networks, identifying when it is possible or impossible, with specific insights into the ternary case.

Contribution

It provides new theoretical conditions for majority agreement in disconnected networks, including a unique analysis of the ternary case.

Findings

Conditions for guaranteed majority agreement

Impossible cases identified under certain network disconnectivity

Special results for ternary network configurations

Abstract

We investigate the problem of reaching majority agreement in a disconnected network. We obtain conditions under which such an agreement is certainly possible/impossible, and observe that these coincide in the ternary case.