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

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

Abstract:

Election surprises are hardly surprising. Unexpected challengers, deaths, retirements, scandals, campaign strategies, real world events, and heresthetical maneuvers all conspire to confuse the best models. Quantitative researchers usually model district-level elections with linear functions of measured covariates, to account for systematic variation, and normal error terms, to account for surprises. However, although these models  work well in many situations they can be embarrassingly overconfident: Events that commonly used models indicate should occur once in 10,000 elections occur almost every year, and even those which the model indicates should occur once in a trillion-trillion elections are sometimes observed.  We develop a new general purpose statistical model of district-level legislative elections, validated with extensive out-of-sample (and distribution-free) tests. As an illustration, we use this model to generate the first ever correctly calibrated probabilities of incumbent losses in US Congressional elections, one of the most important quantities for evaluating the functioning of a representative democracy.  Analyses lead to an optimistic conclusion about American democracy: Even when marginals vanish, incumbency advantage grows, and dramatic changes occur, the risk of an incumbent losing an election has been high and essentially constant from the 1950s until the present day.
Last updated on 07/18/2022