Is Biden's chance of winning 90% or 97%? That's the question I asked myself at noon on Thursday, November 5th, as the election hung in the balance and votes trickled in.
This post is intended to help you interpret election betting markets. But why would you want to do that?
We look at betting markets because, to bastardize Winston Churchill, they are the worst system for estimating probabilities except for all the rest. Prominent examples of "the rest" include projections provided by celebrity data scientist Nate Silver (now incurring the wrath of Twitter), and the well publicized model provided by the Economist publication. Those models rated Trump as a 9/1 or 19/1 outsider, roughly, whereas the markets rated Trump at 2/1.
Were they serious? Would the Economist risk nineteen years of subscription revenue to gain one? The departure from markets is so pronounced as to be a joke before the election, never mind afterwards, and it touches on a bigger philosophical problem. A model for probabilities should take advantage of all relevant information in the world, within reason, and some of that information just happens to take the form of betting markets themselves (as compared with polls, for example).
The best professional gamblers know this. They calibrate a combination of their own homework and the market. This is a crucial step. No modesty, no accuracy. In a past life I worked with a professional handicapper. I've never, ever assigned 19/1 against, post calibration, when the market says 2/1. That would represent utter incompetence and lead to certain ruin, if taken literally in the construction of an optimal portfolio of bets.
The election markets thought the race would be tight - despite the polls indicating otherwise. Markets represent competitive prediction and, subject to local laws, nobody is blocked from making the predictions more accurate (nobody in the U.K., for example) at any time. Celebrity models, as we might disparagingly refer to them, don't have this property for a mix of pragmatic and personal reasons. Someone like myself might suggest to the Economist, a week prior to the election, that they were missing something important but that won't find its way into the model.
That applies not only to outsiders but also, presumably, those who are directly on the modeling team. They require permission to improve the model. "Blocking" data science such as this is the norm, but it clearly introduces a single point of intellectual failure. The likelihood of a gentle suggestion along the lines of "95% is way too high and here's why ..." being "approved" and therefore influencing the outcome is quite small. It physically can't be included without a re-write of the generative model underneath.
Markets don't have that problem.
Markets react. They move as quickly as the first person to realize something is out of whack, not the last. Unfortunately, the highly defensive custodians of models aren't usually so quick. For example, a person in charge of the Economist's model flatly rejected the notion that events in the last few days (combined with similar failure last time around) justify a serious rethink. Instead, he responded to me in a patronizing tone and suggested that his model did better than the markets because it had Biden winning all along!
This is a spurious argument, of course, since any narrow victory by Biden could be used to justify any model ridiculously over-estimating Biden's pre-election day probability of victory. The Intermediate Value Theorem demands that a vast number of utterly terrible models will be right at least once - but it also politely requests we not abuse it in this fashion.
And then there is the incomparable Nate Silver, responding to critics of his 2020 performance:
If they’re coming after FiveThirtyEight, then the answer is f--k you, we did a good job.
The Reverend Bayes turns in his grave, watching Silver's lack of Bayesian updating. Thanks Nate for highlighting why markets are nimbler than ... whatever it is that you are doing and don't feel comfortable sharing with the rest of us. I'll be your first client when you take up bookmaking. In contrast the Huffington post had the decency to publish a mea culpa after missing badly last time around, and that was both heart-felt and informative.
But don't laugh too hard at the fall from grace of the celebrity pundits. If your own business depends critically on predictive modeling, you are likely subject to the whims of authoritarian data science too. It is unlikely that you have set up an apparatus that allows for seamless, ongoing improvement in predictive capability that is not subject to ego and territoriality. Most likely, your models are also subject to blocking, groupthink and the paucity of human pyramids as organizing principles for prediction. I hope that if you've made it to this site, you poke around and examine a different paradigm.
I'm not suggesting that election betting markets, or other competitive prediction mechanisms, are perfect. Far from it. Some simple tools can help with scrutinizing them. This post provides the reader with a number - the implied correlation between state by state election markets - that might help them interpret, or assess the reasonableness of, current odds offered on Trump and Biden.
The point is that the election markets don't provide one answer right now. They provide two conflicting answers. The straight up markets for Biden and Trump winning suggest Trump has a ten percent chance of winning. However, if one looks at the probabilities that punters assign to candidates winning individual states, it is hard not to reach the conclusion that Biden's chance of winning the election is much higher than 90%, and Trump's chances correspondingly less than 10%.
The electoral college scenarios don't admit a trivial multiplication linking state to overall probabilities, because we are not, at the time of writing, in a position where Trump must win all remaining states. However it is easy, as I show in the notebook provided with this article, to run a quick simulation. As an illustration, I will read the following odds from the Betfair exchange. These are quoted in a convention that may be foreign to the American reader, but you can interpret them simply as the inverse of Biden's probability of winning.
|State||Biden inverse probability||Votes|
If you disagree with any of these numbers you can change them in the notebook. I'm not looking to express opinions here, just provide you with simple tooling to interpret what markets are saying about the election. I literally cannot type fast enough to keep these numbers up-to-date while writing this article, but you can change them any time you like and re-run the notebook.