Beyond the Median Voter: A Model of How the Ideological Dimension Shapes Party Polarization

TL;DR

This paper presents a mathematical model showing how the dimensionality of ideological space influences party polarization, explaining paradoxes in voter and party behavior and revealing a phase transition akin to ferromagnetism.

Contribution

It introduces a multidimensional ideological model that explains party polarization dynamics and the impact of ideological complexity on political behavior.

Findings

Lower ideological dimensions increase party polarization.

Issue polarization among voters has a secondary effect.

The model predicts a phase transition in party positioning.

Abstract

Defying the median voter theorem, party polarization has spread globally, especially in the United States. As concerns grow over its risks to democracy, political science has probed its causes, revealing two paradoxes: while polarization between U.S. political parties has undeniably increased since the 1970s, the corresponding rise in issue polarization among voters remains contested; moreover, the growing number of politically relevant issues would be expected to counteract party polarization rather than reinforce it. To examine these findings theoretically, we analyze a mathematical model of bipartisan elections where voters and parties interact in a multidimensional ideological space. We derive equations that determine the critical threshold of expected voter support needed for a party to find it strategically advantageous to position itself at the center or outside of it. This threshold fundamentally increases with the decrease of the effective dimension of the ideological space, while issue polarization among voters plays a secondary role. Thus, the model points to both paradoxes being explainable if ideological dimensionality is causally linked to polarization. The model reveals a Curie point: below this threshold, parties polarize as in a ferromagnetic phase, with voters acting like aligned spins; above it, they shift toward the center, akin to a paramagnetic phase.