09 novembro 2016

Erros estatísticos de Nate Silver sobre Trump

Parece que o Guru das eleições não conhece muito bem de probabilidade aplicada. Ele errou feio as previsões das eleições.

Nate Silver is one of the most highly regarded statisticians of sports, politics and other domains [1]. During the 2016 presidential campaign, his early analysis of the chances of Donald Trump becoming Republican nominee stands out—he estimated only a 2% probability. Even though statistics are not about actualities but probabilities, subsequent events do not appear to be consistent with those predictions, as he later acknowledged [2-4]. He has explained the problem with the analysis as due to political factors [3], and in terms of the difficulty of analysis [4], but not why the model he used is essentially flawed. Here we point out fundamental problems with the statistical ideas he uses. Statistics begins from an assumption of independence, which is generally not valid. In this case, the assumptions lead to mathematical inconsistencies. This illustrates how statistics can lead to illogic even for sophisticated users. Indeed, perhaps it is more likely to mislead those who are sophisticated—a cautionary tale.

Silver's analysis [2] is based on a gauntlet of six "stages of doom" of nomination. He assigns each stage independently a 1 in 2 chance of being won, leading to less than 2% = (1/2)6chance of nomination. Like winning 6 coin tosses in a row.

There is an argument that makes Silver's result suspect. Some of the stages of Silver's analysis appear unique to Trump. However, each candidate faces difficulties, and every stage of the nomination is surely not guaranteed to any of them. While the specific terms that are used might not be the same, a similar analysis would hold for each one: gaining and keeping attention, withstanding scrutiny, achieving early state success, building organization, accumulating delegates, and achieving a majority for the convention. If anything, they faced greater challenges because Trump was ahead in polls.

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