Abstract
Trust is needed to build solid relationships, create reliable institutions, and develop cohesion, especially in times of crisis. On one hand, the level of trust in organizations and between individuals within the society is declining; on the other hand, in a fast-paced and complex world like the one we live in today, the launch of new ideas and practices and their application is increasing at an unprecedented speed. In addition, technology connects us all on a global scale, where competition and cooperation are no longer restricted to particular geographical areas; rather, interactions between key players become of greater and greater importance. Moreover, pairwise interactions cannot capture alone the impact of group pressure, advertising, and word-of-mouth when it comes to the adoption of new ideas. In this work, we propose a framework to study the interplay between the level of trust, global influence, and higher-order interactions. We model the diffusion of ideas by combining a mean-field differential equation with simplicial complexes. We investigate the resulting dynamics and focus on specific times of interest for the political, social, and business world: the almost-all adoption and the majority adoption time (aat and mat respectively). We show that the aat can be anticipated by increasing the order of the system (higher pressure from bigger groups). We also show that the aat increases (later adoptions) as the level of distrust increases. When distrust is high, the order does not have a large impact on the aat , it can only make a difference when the level of distrust is low. However, we also show that the global influence, expressed through the advertisement coefficient, can help reduce the adoption time even when distrust is high. In addition, we created tables of reference that put in relation the level of distrust, global influence, and order of the system. We also point out that a version of the model in which the advertisement coefficient is zero can capture circumstances in which total adoption is not reached. Furthermore, the model opens the way to applications to real data, for example, allowing one to study the advantage of measures apt to increase global influence or levels of trust among individuals.