Sensitivity of collective outcomes identifies pivotal components

TL;DR

This paper introduces an information-geometric method to identify pivotal components in social systems, revealing how small changes in key elements can significantly impact collective outcomes across various domains.

Contribution

The authors develop a novel approach using information geometry to pinpoint pivotal components influencing collective properties in complex networks.

Findings

Sensitivity analysis identifies key components like the median voter in political models.

Application to datasets shows systems range from median-driven to equally influenced components.

Method can assess robustness of collective outcomes in social, economic, and biological systems.

Abstract

A social system is susceptible to perturbation when its collective properties depend sensitively on a few pivotal components. Using the information geometry of minimal models from statistical physics, we develop an approach to identify pivotal components to which coarse-grained, or aggregate, properties are sensitive. As an example, we introduce our approach on a reduced toy model with a median voter who always votes in the majority. The sensitivity of majority-minority divisions to changing voter behaviour pinpoints the unique role of the median. More generally, the sensitivity identifies pivotal components that precisely determine collective outcomes generated by a complex network of interactions. Using perturbations to target pivotal components in the models, we analyse datasets from political voting, finance and Twitter. Across these systems, we find remarkable variety, from systems dominated by a median-like component to those whose components behave more equally. In the context of political institutions such as courts or legislatures, our methodology can help describe how changes in voters map to new collective voting outcomes. For economic indices, differing system response reflects varying fiscal conditions across time. Thus, our information-geometric approach provides a principled, quantitative framework that may help assess the robustness of collective outcomes to targeted perturbation and compare social institutions, or even biological networks, with one another and across time.