I have some brief thoughts about the outcome of the US election from an entirely data science perspective. It’s hard to remain objective and have a scientific hat on when it comes to political events, but I never intended this blog to be a place to discuss political opinion. Instead, I want to look at this election outcome as an opportunity to talk about probabilistic forecasts.

FiveThirtyEight tracked many polls over time to forecast the probability of the two candidates. These fluctuated quite a bit, but in the end their final forecast was an over 70% probability of a Clinton win.

So was their model *wrong*?

Funnily enough it was Nate Silver himself who, in his book, talked about how we evaluate a probabilistic forecast, his example being the weather. In the case of the weather, this is the question:

Someone makes a forecast that tomorrow it will rain with a probability of 30%. It rains tomorrow. Was the forecast correct?

The key idea here is that in instances like this the standard notion of “accurate” doesn’t hold. You simply can’t evaluate the model based on a single data point, unless its prediction was a 100% probability. That’s because the model isn’t designed to make a single prediction. In the case of the weather, forecasts are made multiple times a day, so very quickly you have a whole set of “predictions” and true outcomes.

From that you now **can** evaluate the model.

When they say the probability of rain is 30% it doesn’t just mean that it’s unlikely to rain. It also means that out of all the times they predict 30% it will end up raining 30% of the time; to evaluate it therefore requires multiple similar predictions. For example, after a hundred 30% predictions, if it only rained on two occasions it’s obvious the model was too pessimistic (assuming you treat rain as a negative outcome).

Then what about an event as rare as a general election?

That’s a harder question and one where there are disagreements.

Clinton lost the electoral vote but appears to have won the popular vote – an outcome FiveThirtyEight estimated to be around 10% likely. It was explicitly covered by the forecast, which simply said that it’s a rare event, but still not an implausible one. Again, it is hard to quantify whether that 10% was correct or not.

Ultimately in cases like this there are too many variables to be able to make a definitive prediction. It is more worthwhile to think of it as a statement of the probability distribution of all possible outcomes rather than a means to actually predict who will be President. Of course this probability distribution can be wrong, it’s just not apparent how to evaluate this.

I must admit I don’t know that much about the technical details of such an evaluation.

However, I am interested in finding out, so I will go away and do some research and report back later this month in a future blog article.

Footnote: This is the 9^{th} entry in my 30 day blog challenge.

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