mardi 28 mars 2017

A Look Back at the 2016 US Presidential Election

Can the Qc125 model be used to project US elections? The simple answer for now is yes.

Obviously, this model will never be as advanced and detailed as Nate Silver's FiveThirtyEight model, but I was curious as to whether the Qc125 model could be transferred from Quebec FPTP system to the american Electoral College system. At the base level, it is remarkably easy - since 48 of the 50 states are winner-take-all (Maine and Nebraska are slightly different).

So I decided to test my "beta US model" by using the 2016 presidential election data. I say "beta" model, because I haven't yet put in the hours to find the ideal state correlation algorithm. This, for sure, is going to be the most challenging part of this (or any) model.

Obviously, we do know the outcome of the election, so the model should be able to give fairly good numbers when fed with precise data. So I used the state by state results and added a margin of error varying randomly up to 4% for each of the Democratic and Republican parties. (Libertarians and Greens are also in the model, but neither of them came close to winning a single Electoral College vote).

Here are the results from 10 000 simulations:

The simulator gives a slight Electoral College edge to the Republicans with an average of 276,4 votes to 261,6 for the Democrats. Considering Trump won 306 EC seats, you could wonder why the simulator results are so much tighter than the actual results. The answer is simple: this is an average number of EC votes. Trump won all of Pennsylvania 20 EC seats with an 0,7% popular vote edge. Running 10k simulations, Trump is only going to win PA in about 52%-53% of all simulations. The winner take all nature of the EC makes a big difference here.

As for the popular vote, the model nails it on the nose - which shouldn't be a surprise since I plugged in the actual election results. If the model had output different numbers, it would clearly mean the model is garbage!

What about the odds of outright winning the election? I remember FiveThirtyEight gave Trump about 30% odds of winning, which was more prudent and ultimately closer than other sites. Here, out of 10k simulations, the Republican ticket wins only 58,5% of simulations - which is testament to how close Trump's victory actually was. The Democrats won 41,1% of simulations and there was 0,5% probability of an EC tie (Watch the fifth season of Veep to know more about this outcome!)

Here is the distribution of EC seats with respect to the popular vote of all 10k simulations:

Here are the EC outcome probabilities. Note that the final outcome is indicated on the graph (306R - 232D).

And here is the popular vote distribution:

I feel like I am going to enjoy this over the coming years. Obviously, I am going to have to put in many hours to correctly correlate state results. Fortunately, I have plenty of time before the 2020 election.

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