How Bayesian analysis cracked the red-state, blue-state problem. (English) Zbl 1332.62426

Gelman, Andrew

Stat. Sci. 29, No. 1, 26-35 (2014).

Summary: 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.

MSC:

62P25	Applications of statistics to social sciences
62F15	Bayesian inference
62D05	Sampling theory, sample surveys
91F10	History, political science
91B12	Voting theory
91D20	Mathematical geography and demography
62-07	Data analysis (statistics) (MSC2010)

Keywords:

multilevel regression and poststratification (MRP); political science; sample surveys; sparse data; voting

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