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.

Highlights

  • When collective outcomes are highly sensitive to the behaviour of few individual components, these components are pivotal

  • We study the sensitivity of q(k) in the context of a reduced toy model that captures the essence of a median voter

  • Despite A.K. and S.O.’s prominent role in the narrative of Supreme Court voting, we find that other justices come to the foreground when we consider the sensitivity of the Court to behavioural change

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Summary

Introduction

When collective outcomes are highly sensitive to the behaviour of few individual components, these components are pivotal. A classic example is the swing, or median, voter, prominent in political science and economics: if voters can be deterministically ranked according to preference, the median will always vote in the majority and is predictive of the outcome [1,2,3]. In contrast with an idealized notion of a median, we consider a ‘pivotal’ voter, one that could change collective outcomes even when accounting for such complexity We develop this generalized notion and use it to identify components that are especially indicative of collective changes in political voting, financial indices and social media on Twitter

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