Election, Trump and statistics

A sentiment that I often heard after the US presidential election, was that Trump’s victory was a complete surprise. Even the night before nobody expected it. Everyone looked at FiveThirtyEight, saw the following charts and thought: “Hillary has so much better chances, surely she will win”.

Wait, what? What exactly do these number say? They say that Trump has roughly 1-in-3 chance of winning. Things that have these chances of happening, happen all the time. I you knew, that you have 1-in-3 chance of breaking your leg if you go snowboarding this weekend, wouldn’t you rather stay at home?

Humans are notoriously bad at judging probabilities, statistics and numbers in general. And worst of all, we are not aware of this weakness. I’m now reading a wonderful book Thinking, Fast and Slow by Daniel Kahneman, and it is filled by examples of various fallacies of our intuition. One of the most striking, at least to me, is the conjunction fallacy. Here’s an original question from a study that lead to its discovery:

Linda is thirty-one years old, single, outspoken, and very bright. She majored in philosophy. As a student, she was deeply concerned with issues of discrimination and social justice, and also participated in antinuclear demonstrations. Which alternative is more probable? a) Linda is a bank teller. b) Linda is a bank teller and is active in the feminist movement.

This question with different variations was given to various audiences, and generally 85% of people participating in the study, chose answer b). It’s hard to imagine a philosophy student, probably a hippy, working as a bank teller. An additional detail of her being active in the feminist movement makes the story more plausible.

Plausible, but not probable! The set of bank tellers fully contains the set of feminist bank tellers. If Linda is a feminist bank teller, she is necessarily a bank teller.

The story of the election is somewhat similar. Most of democrats and liberals in general were used to the idea of Hillary winning the election. They had a mental picture of her as the next president, winning maybe not by a landslide, but by some comfortable margin. They maintained this picture throughout the election year, since she was always slightly leading in the polls. On the other hand, it was very difficult to imagine what will happen if Trump wins. How will his presidency look like? This picture is much less coherent.

And thus, even though the forecasts predicted 30% chance of Trump winning, in most minds this probability was replace by plausibility. Unfortunately, the universe doesn’t give a damn about what we think. Something that has high enough probability may well happen.