Political science deals with phenomena where data are expensive to collect, samples are non-representative, and predictions are scrutinized by millions. Bayesian methods have become indispensable in the field because they excel at precisely the challenges political scientists face: combining sparse data with structural knowledge, handling multilevel data structures, and producing probabilistic forecasts that honestly communicate uncertainty.
Multilevel Regression and Poststratification (MRP)
MRP — often pronounced "Mister P" — is perhaps the most influential Bayesian method in modern political science. It addresses a fundamental problem: national polls rarely have enough respondents in each state, district, or demographic subgroup to produce reliable local estimates. MRP solves this by fitting a multilevel regression model to individual survey responses, then poststratifying by weighting the predictions according to the known population distribution of demographic and geographic cells.
α^state_s ~ N(γ · Zₛ, σ²_state) [state effects with predictors]
Poststratification θ̂_state = Σ_j N_j · π̂_j / Σ_j N_j [population-weighted prediction]
MRP has been used to estimate state-level support for same-sex marriage, gun control, immigration policy, and candidate preference, often outperforming simple disaggregation of large national polls. The Bayesian hierarchical structure is essential: it provides the partial pooling that makes small-area estimation possible.
Election Forecasting
Bayesian election forecasting models combine polling data, economic fundamentals, historical patterns, and structural features into probabilistic predictions. The models developed by groups at The Economist, FiveThirtyEight, and academic researchers share a common Bayesian architecture: a prior on election-day vote share informed by fundamentals, updated by polling data through a dynamic model that accounts for time-varying poll quality, house effects, and correlated errors across states.
A key insight of modern election forecasting is that polling errors are correlated across states — if polls underestimate a candidate in Pennsylvania, they likely do so in Michigan and Wisconsin as well. Bayesian models capture this through correlated random effects or factor structures, producing more realistic uncertainty in the overall outcome. Ignoring these correlations led to overconfident predictions of the 2016 U.S. presidential election by many forecasters.
Ideal Point Estimation
Ideal point models place legislators and proposals on a latent ideological dimension using roll-call voting data. The Bayesian IRT (item response theory) model treats each vote as a function of the legislator's ideal point and the bill's parameters, estimating both from the observed voting matrix. MCMC-based models like IDEAL and the ordinate package produce posterior distributions of ideal points, quantifying the uncertainty in ideological placement that maximum-likelihood alternatives ignore.
"The goal of election forecasting is not to predict who will win, but to honestly characterize what we know and do not know. A forecast that says 70% is doing its job perfectly when it is wrong 30% of the time." — Andrew Gelman, Columbia University
Causal Inference and Policy Evaluation
Bayesian methods support causal inference in political science through posterior distributions of treatment effects, Bayesian synthetic control methods, and Bayesian structural equation models. The Bayesian framework is particularly valuable for policy evaluation with small samples — the number of U.S. states is 50, the number of democracies in a comparative study may be 30 — where frequentist asymptotic guarantees fail but Bayesian inference with informative priors remains valid.
Text as Data
Bayesian topic models, particularly latent Dirichlet allocation and its extensions, analyze large corpora of political text — legislative speeches, party manifestos, judicial opinions, social media — to discover latent themes and track their evolution. Structural topic models allow the prevalence and content of topics to vary with metadata like party affiliation, time period, or institutional context, revealing how political discourse shifts across groups and eras.