Negative Representation and Instability in Democratic Elections

TL;DR

This paper explores how negative representation and electoral instability arise in democratic elections, showing that increased polarization and low turnout can cause phase transitions leading to unstable election outcomes, with empirical evidence from US elections.

Contribution

It introduces the concepts of negative representation and electoral instability, proving their connection, and models how polarization and turnout influence election stability.

Findings

Unstable elections necessarily involve negatively represented opinions.

Electoral instability can be triggered by increased polarization and low voter turnout.

US presidential elections in the 1970s experienced a phase transition to instability.

Abstract

The challenge of understanding the collective behaviors of social systems can benefit from methods and concepts from physics [1-6], not because humans are similar to electrons, but because certain large-scale behaviors can be understood without an understanding of the small-scale details [7], in much the same way that sound waves can be understood without an understanding of atoms. Democratic elections are one such behavior. Over the past few decades, physicists have explored scaling patterns in voting and the dynamics of political opinion formation, e.g. [8-13]. Here, we define the concepts of negative representation, in which a shift in electorate opinions produces a shift in the election outcome in the opposite direction, and electoral instability, in which an arbitrarily small change in electorate opinions can dramatically swing the election outcome, and prove that unstable elections necessarily contain negatively represented opinions. Furthermore, in the presence of low voter turnout, increasing polarization of the electorate can drive elections through a transition from a stable to an unstable regime, analogous to the phase transition by which some materials become ferromagnetic below their critical temperatures. Empirical data suggest that United States presidential elections underwent such a phase transition in the 1970s and have since become increasingly unstable.