If a Statistical Model Predicts That Common Events Should Occur Only Once in 10,000 Elections, Maybe It's the Wrong Model

Political scientists forecast elections, not primarily to satisfy public interest, but to validate statistical models used for estimating quantities of scholarly interest. Although scholars have learned a great deal from these models, they can be embarrassingly overconfident: Events that should occur once in 10,000 elections occur almost every other election cycle, and even those that should occur once in 5 quintillion elections are sometimes observed. We show that these problems miss parts of the predictive distribution of central importance to political science, such as by underestimating how often popular incumbents lose their seats. We then build the first generative statistical model of all US federal legislative elections, covering both the U.S. House (1946–2024) and Senate (1954–2024), and validate it with extensive out-of-sample tests. It turns out that the same set of structural parameters forecast accurately in both houses of congress, potentially implying a single data-generation process for all national legislative elections in the postwar era. This model suggests the possibility of more reliable estimation of quantities of scholarly interest, in addition to accurate forecasts.