Sensitivity of Collective Outcomes Identifies Pivotal Components

13 Pages Posted: 6 Oct 2019

See all articles by Edward Lee

Edward Lee

Cornell University - Department of Physics

Daniel Martin Katz

Illinois Tech - Chicago Kent College of Law; Stanford CodeX - The Center for Legal Informatics

Michael James Bommarito

Bommarito Consulting, LLC; Licensio, LLC; Stanford Center for Legal Informatics; Michigan State College of Law

Paul Ginsparg

Cornell University - Department of Physics

Date Written: September 26, 2019

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. With this example, we construct the Fisher information matrix with respect to the distribution of majority-minority divisions and study features of the matrix that pinpoint the unique role of the median. More generally, these features identify pivotal blocs that precisely determine collective outcomes generated by a complex network of interactions. Applying our approach to data sets from political voting, finance, and Twitter, we find remarkable variety from systems dominated by a median-like component (e.g., California State Assembly) to those without any single special component (e.g., Alaskan Supreme Court). Other systems (e.g., S&P sector indices) show varying levels of heterogeneity in between these extremes. By providing insight into such sensitivity, our information-geometric approach presents a quantitative framework for considering how nominees might change a judicial bench, serve as a measure of notable temporal variation in financial indices, or help analyze the robustness of institutions to targeted perturbation.

Keywords: Complex Systems, Social Physics, Political Voting, Information Geometry, Median Voter, Robustness, Sensitivity, Finance

JEL Classification: B26, G10, K40, H10

Suggested Citation

Lee, Edward and Katz, Daniel Martin and Bommarito, Michael James and Ginsparg, Paul, Sensitivity of Collective Outcomes Identifies Pivotal Components (September 26, 2019). Available at SSRN: https://ssrn.com/abstract=3460077 or http://dx.doi.org/10.2139/ssrn.3460077

Edward Lee

Cornell University - Department of Physics ( email )

109 Clark Hall
Ithaca, NY 14853
United States

Daniel Martin Katz (Contact Author)

Illinois Tech - Chicago Kent College of Law ( email )

565 W. Adams St.
Chicago, IL 60661-3691
United States

HOME PAGE: http://www.danielmartinkatz.com/

Stanford CodeX - The Center for Legal Informatics ( email )

559 Nathan Abbott Way
Stanford, CA 94305-8610
United States

HOME PAGE: http://law.stanford.edu/directory/daniel-katz/

Michael James Bommarito

Bommarito Consulting, LLC ( email )

MI 48098
United States

HOME PAGE: http://bommaritollc.com

Licensio, LLC ( email )

Okemos, MI 48864
United States

Stanford Center for Legal Informatics ( email )

559 Nathan Abbott Way
Stanford, CA 94305-8610
United States

Michigan State College of Law ( email )

318 Law College Building
East Lansing, MI 48824-1300
United States

Paul Ginsparg

Cornell University - Department of Physics ( email )

109 Clark Hall
Ithaca, NY 14853
United States

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