Dynamic monopolies with randomized starting configuration

TL;DR

This paper investigates the probability that a randomly initialized seed set forms a dynamic monopoly in systems with majority voting, providing asymptotic estimates for specific graph structures.

Contribution

It offers the first asymptotic estimates for the sampling probability of seed sets forming dynamic monopolies in randomized initial configurations.

Findings

Derived asymptotic probabilities for toroidal mesh

Analyzed random 4-regular graphs under majority rule

Provided conditions for almost sure formation of dynamic monopolies

Abstract

Properties of systems with majority voting rules have been exhaustingly studied. In this work we focus on the randomized case - where the system is initialized by randomized initial set of seeds. Our main aim is to give an asymptotic estimate for sampling probability, such that the initial set of seeds is (is not) a dynamic monopoly almost surely. After presenting some trivial examples, we present exhaustive results for toroidal mesh and random 4-regular graph under simple majority scenario.