Eliminating Majority Illusions

TL;DR

This paper investigates the topological factors in social networks that cause majority illusions, demonstrating the problem's computational complexity and proposing fixed-parameter tractable algorithms for specific network structures.

Contribution

It provides a systematic study of the algorithmic complexity of eliminating opinion illusions and offers FPT algorithms for certain network topologies, along with hardness results.

Findings

The problem is NP-hard even for planar, bounded-diameter networks.

FPT algorithms are developed for star-like and tree-like networks.

A PTAS is provided for planar graphs.

Abstract

An opinion illusion refers to a phenomenon in social networks where agents may witness distributions of opinions among their neighbours that do not accurately reflect the true distribution of opinions in the population as a whole. A specific case of this occurs when there are only two possible choices, such as whether to receive the COVID-19 vaccine or vote on EU membership, which is commonly referred to as a majority illusion. In this work, we study the topological properties of social networks that lead to opinion illusions and focus on minimizing the number of agents that need to be influenced to eliminate these illusions. To do so, we propose an initial, but systematic study of the algorithmic behaviour of this problem. We show that the problem is NP-hard even for underlying topologies that are rather restrictive, being planar and of bounded diameter. We then look for exact algorithms that scale well as the input grows (FPT). We argue the in-existence of such algorithms even when the number of vertices that must be influenced is bounded, or when the social network is arranged in a ``path-like'' fashion (has bounded pathwidth). On the positive side, we present an FPT algorithm for networks with ``star-like'' structure (bounded vertex cover number). Finally, we construct an FPT algorithm for ``tree-like'' networks (bounded treewidth) when the number of vertices that must be influenced is bounded. This algorithm is then used to provide a PTAS for planar graphs.