Inference in Opinion Dynamics under Social Pressure

TL;DR

This paper presents a new opinion dynamics model accounting for inherent and declared opinions influenced by social pressure, and analyzes the conditions under which inherent opinions can be estimated from declared opinions in social networks.

Contribution

The paper introduces a novel model of opinion dynamics with hidden and expressed opinions and provides theoretical analysis of the estimability of inherent opinions under social pressure.

Findings

Estimation of inherent opinions is possible when no large majorities exist.

Large majorities cause minorities to conform, making estimation impossible.

The model applies to social media scenarios like political opinion analysis.

Abstract

We introduce a new opinion dynamics model where a group of agents holds two kinds of opinions: inherent and declared. Each agent's inherent opinion is fixed and unobservable by the other agents. At each time step, agents broadcast their declared opinions on a social network, which are governed by the agents' inherent opinions and social pressure. In particular, we assume that agents may declare opinions that are not aligned with their inherent opinions to conform with their neighbors. This raises the natural question: Can we estimate the agents' inherent opinions from observations of declared opinions? For example, agents' inherent opinions may represent their true political alliances (Democrat or Republican), while their declared opinions may model the political inclinations of tweets on social media. In this context, we may seek to predict the election results by observing voters' tweets, which do not necessarily reflect their political support due to social pressure. We analyze this question in the special case where the underlying social network is a complete graph. We prove that, as long as the population does not include large majorities, estimation of aggregate and individual inherent opinions is possible. On the other hand, large majorities force minorities to lie over time, which makes asymptotic estimation impossible.