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“We propose a generalizable approach for identifying pivotal components across a wide variety of systems,” says author Edward Lee, a Program Postdoctoral Fellow who studies collective behavior at the Santa Fe Institute. “These systems go beyond voting, and include social media (like Twitter), biology (like the statistics of neurons), or finance (like fluctuations of the stock market).”
In the paper, Lee and his co-authors, Daniel Katz (Illinois Tech), Michael Bommarito (Stanford CodeX), and Paul Ginsparg (Cornell University) identify a statistical signature of pivotal components that they then trace to communities on Twitter, votes in the Supreme Court and Congress, and stock indices within financial markets. They find wide diversity in how social systems depend on sensitive points, when such points exist at all.”
Using the information geometry of minimal models from statistical physics, we develop an approach to identify pivotal components in wide variety of systems. We then apply this approach to a wide variety of empirical datasets including political voting, financial markets and social systems. We find remarkable variety from systems dominated by a median-like component to those without any single special component. Other systems (e.g., S&P sector indices) show varying levels of heterogeneity in between these extremes. 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.