Vol. 13, No. 5, 2020

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Disagreement networks

Florin Catrina and Brian Zilli

Vol. 13 (2020), No. 5, 803–822
Abstract

We first describe an observation based on an analysis of data regarding the outcomes of decisions in cases considered by the United States Supreme Court. Based on this observation, we propose a simple model aiming toward producing an objective notion of an ideology index. As an initial step in justifying this concept we produce explicit formulas for the highest-energy eigenvectors of reversible Markov chains with rank-2 transition matrices.

Keywords
reversible Markov chain, highest-energy eigenvector, ideal point
Mathematical Subject Classification
Primary: 05C50, 60J20
Secondary: 91F10
Milestones
Received: 29 September 2019
Revised: 18 June 2020
Accepted: 8 September 2020
Published: 5 December 2020

Communicated by Jonathon Peterson
Authors
Florin Catrina
Department of Mathematics and Computer Science
St John’s University
Queens, NY
United States
Brian Zilli
Department of Mathematics
Iowa State University
Ames, IA
United States