Response Functions to Critical Shocks in Social Sciences: An Empirical and Numerical Study

TL;DR

This paper introduces a novel approach in social sciences using critical exogenous shocks, called Dirac shocks, to test structural predictions and analyze social cohesion, supported by empirical examples and numerical simulations.

Contribution

It adapts observational strategies from natural sciences to social sciences, enabling structural prediction testing through the analysis of responses to critical shocks.

Findings

Critical shocks reveal social 'cracks' and predict future system evolution.

Response to shocks depends on social cohesion and can foreshadow bifurcations.

Numerical simulations show slow relaxation and high variability in consensus models.

Abstract

We show that, provided one focuses on properly selected episodes, one can apply to the social sciences the same observational strategy that has proved successful in natural sciences such as astrophysics or geodynamics. For instance, in order to probe the cohesion of a policy, one can, in different countries, study the reactions to some huge and sudden exogenous shocks, which we call Dirac shocks. This approach naturally leads to the notion of structural (as opposed or complementary to temporal) forecast. Although structural predictions are by far the most common way to test theories in the natural sciences, they have been much less used in the social sciences. The Dirac shock approach opens the way to testing structural predictions in the social sciences. The examples reported here suggest that critical events are able to reveal pre-existing ``cracks'' because they probe the social cohesion which is an indicator and predictor of future evolution of the system, and in some cases foreshadows a bifurcation. We complement our empirical work with numerical simulations of the response function (``damage spreading'') to Dirac shocks in the Sznajd model of consensus build-up. We quantify the slow relaxation of the difference between perturbed and unperturbed systems, the conditions under which the consensus is modified by the shock and the large variability from one realization to another.