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Political scientists forecast elections, not primarily to satisfy public interest, but to validate statistical models used for estimating quantities of scholarly interest. These models usually include linear functions of carefully chosen covariates (to account for systematic variation) and normal error terms, sometimes with random effects (to account for surprises). Although we 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 year, and even those which should occur once in a trillion-trillion elections are sometimes observed. We develop a generative statistical model of US district-level congressional elections and validate it with extensive out-of-sample tests. We use this model to compute the first correctly calibrated probabilities of incumbent losses, one of the most important quantities for evaluating a democracy. We find that even when marginals vanish, incumbency advantage grows, and other dramatic changes occur, the risk of an out-party incumbent losing a midterm election contest has been high and essentially constant since the 1950s. We then develop a broader theory of American democracy consistent with the results from our generative model.