What kind of a claim is “Biden has an 87% chance of winning”? (on the metaphysics of probability)

If you’re spending all your time nervously checking the election forecast on FiveThirtyEight.com, your mental health may suffer. You can stop checking and do something productive to improve the world. Or you can become intrigued about what a forecast means, read Alan Hájek’s “Interpretations of Probability” in The Stanford Encyclopedia of Philosophy (Fall 2019 Edition), and write some rambling reflections. That is the Path I have chosen.

Four years ago, Nate Silver’s FiveThirtyEight gave Hilary Clinton about a 75% chance of winning the 2016 election. The fact that she lost did not invalidate this prediction–outcomes with probabilities of 25% happen often. Looking retrospectively, it seems right that Trump’s chances were small. He had to win narrowly in just the right combination of states.

Of course, we now know that he did win. In October 2016, an omniscient deity would have known that already. The deity could have known it in either of two ways: by looking into the future, or by understanding the complete present situation with one week still left to go in the election. Presumably, if you could know exactly what every American was thinking about politics, the precise distance to their nearest polling place, whose contact lists everyone was on, what Putin was up to, how heat and humidity were distributed on the face of the globe, and everything else about the situation with one week to go in the election, you would know what would happen with the vote. (I leave aside the possibility that that the universe incorporates physical randomness at the quantum level that affects things like the outcome of an election a week away.)

Applying that theory to our present circumstances, we would say that either Biden has a 100% chance of winning the 2020 election or Trump has a 100% chance. These are falsifiable claims, and a maximum of one of them will turn out to be true. Every other probability estimate will turn out to be false, because either Biden or Trump will actually win.

Yet is seems rational to say that Biden has almost a 90% chance of winning right now, and wrong to say that he has a 100% chance–and even more wrong to say that Trump has a 90% chance. A lot of data and experience go into a plausible prediction. Even if Trump will win in 2020, he doesn’t have a 90% chance right now. Another Trump victory would be a second improbable event. But again, the actual vote won’t invalidate either a 10% or a 90% estimate of Trump’s chances, because either one is compatible with him winning or losing.

A different way to make sense of this is to say: If the election were held 100 times, Biden would win almost 90% of them. But that is weird in several ways. The election cannot be held 100 times in a row, and if we repeated it at all, the repetition would affect the outcomes. If we imagine 100 identical universes that all unfold separately from now until next week, perhaps Biden would win in 90 of them. Or perhaps the future is determined by the current situation, which must the same in all of the 100 identical universes. Then they must all turn out the same way. We just don’t know which way.

Forecasters like Nate Silver use simulations with random (or pseudo-random) numbers built in. Those are meant to model the actual world. But they are not replicas of the real world, which–leaving aside quantum physics–seems to have just one future that is determined by the state of things now.

Another interpretation is that giving Biden a 90% chance today is simply an assessment of our knowledge level. It’s as much about us as it’s about the world. Biden actually has a 100% or a 0% chance, but we (unlike an omniscient deity) don’t know which of those is right. However, the tools of forecasting allow us to estimate how much knowledge we have–with precision. In fact, Nate Silver’s estimate rises and falls by the hour.

According to this subjective interpretation of probability, when Silver’s estimate moves from 85%-86%, he has not invalidated his previous prediction but has updated his assessment of the best possible level of knowledge at the present time. Once the election is over, our knowledge will become complete, and we will rightly say that the odds are 100% in favor of what actually happened.

Two problems occur to me about this interpretation. First, a prediction is not falsifiable in the usual way (and falsifiability is a hallmark of science).

Second, how much knowledge is “possible” is relative to circumstances. Anyone who could see all the current, private, survey data at the congressional-district level would have more knowledge than Nate Silver has. But he knows a whole lot more than I do. His estimates seem to be measures of how much certainty he is entitled to, based on the work he has done and money he has spent. If I say that Biden has an 87% chance because that’s what I read on FiveThirtyEight, I am really saying that I believe Nate Silver’s claim that he has an 87% level of confidence. But how could I test whether that estimate is correct? How can we know that he is right to raise or lower the estimate by a point? Certainly not by waiting to find out what happens next week.

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About Peter

Associate Dean for Research and the Lincoln Filene Professor of Citizenship and Public Affairs at Tufts University's Tisch College of Civic Life. Concerned about civic education, civic engagement, and democratic reform in the United States and elsewhere.