How Bayesian Analysis Cracked the Red-State, Blue-State Problem

TL;DR

This paper demonstrates how Bayesian multilevel models can effectively analyze complex geographic and demographic voting patterns in the US, addressing data sparsity and uncertainty issues.

Contribution

The authors introduce a Bayesian multilevel modeling approach to reconcile individual and state-level voting patterns, overcoming limitations of previous non-Bayesian analyses.

Findings

Bayesian inference improved handling of sparse data.

Multilevel models revealed nuanced geographic and demographic voting patterns.

Analysis can be replicated with non-Bayesian methods, but Bayesian approach offers advantages.

Abstract

In the United States as in other countries, political and economic divisions cut along geographic and demographic lines. Richer people are more likely to vote for Republican candidates while poorer voters lean Democratic; this is consistent with the positions of the two parties on economic issues. At the same time, richer states on the coasts are bastions of the Democrats, while most of the generally lower-income areas in the middle of the country strongly support Republicans. During a research project lasting several years, we reconciled these patterns by fitting a series of multilevel models to perform inference on geographic and demographic subsets of the population. We were using national survey data with relatively small samples in some states, ethnic groups and income categories; this motivated the use of Bayesian inference to partially pool between fitted models and local data. Previous, non-Bayesian analyses of income and voting had failed to connect individual and state-level patterns. Now that our analysis has been done, we believe it could be replicated using non-Bayesian methods, but Bayesian inference helped us crack the problem by directly handling the uncertainty that is inherent in working with sparse data.