If Donald Trump wins the Republican nomination, which party will win the U.S. presidential election?

I currently rate the likelihood of Trump winning the Republican nomination at 47%, so the urgency of this question is only a coin flip away.

An unweighted average of polls taken since the beginning of 2016 has HRC over Trump by 7.7%, with a standard deviation of 6.4%[1]. Hence, HRC wins 88% of the time, and Trump wins 12% of the time. And an unweighted average of polls taken since the beginning of 2016 has Bernie over Trump by 8.1% with a standard deviation of 5.9%[2]. Thus, Bernie wins 91% of the time, and Trump wins 9% of the time. Currently, I think HRC has 91% chance of winning the Democratic primary, with Bernie following at 9%. (It’s just a coincidence that the 91%/9% split shows up twice.) So that means we can carve up the probability space into four unevenly sized quadrants:

  1. HRC wins the Democratic nomination (0.91) and beats Trump (0.88) = 0.80
  2. HRC wins the Democratic nomination (0.91) but loses to Trump (0.12) = 0.11
  3. Bernie wins the Democratic nomination (0.09) and beats Trump (0.91) = 0.08
  4. Bernie wins the Democratic nomination (0.09) but loses to Trump (0.09) = 0.01

The result is that Republicans have a 9% chance of winning the election, if Trump is the nominee.

End of story, right? Probably not. My average of polls was, as I said, unweighted, and not all polls are equal. I didn’t use a weighted average because (a) the off-the-shelf weighted averages from, for example, RealClearPolitics and Pollster disagree quite sharply in some cases and (b) I don’t have a reliable weighting algorithm of my own (nor am I likely to have one any time soon). Furthermore, there are very few polls to average, so sample sizes are low. And, polls at this stage of the game have limited predictive value. Finally, the presidential contest is only indirectly (though strongly) related to individual preferences for one candidate or another. It’s possible to lose the popular vote but when the electoral college, as has happened within living memory.

So how to take all of the problems with the information we have into account without just throwing up our hands? I propose that following: The principle of insufficient reason[3] suggests that we should assign equal likelihood to states when the probability of their occurrence is unknown. Extending the principle a bit, we can say that we should assign equal likelihood to states when the probability of their occurrence is perfectly unknown, but we should assign a weighted average of equal likelihoods and likelihoods based on what evidence that we have when the probability of their occurrence is imperfectly unknown. For instance, an outcome might be unknown imperfectly to a degree of 75%. We could estimate this in this way: (0.75)(Outcome A*0.5 + Outcome B*0.5) + (0.25)(Outcome A*known probability of Outcome A + Outcome B*known probability of Outcome B). And so on. Call this discounting a forecast by the principle of insufficient reason, where we can discount by any real number between 0 and 1, inclusive.

On the basis of all of this, I estimate we should discount the polling data above by the principle of insufficient reason at a rate of 70%. On this basis the probability that a Republican will win, given that Trump is the nominee is currently (0.7)*(0.5) + (0.3)*(0.09)=0.38. Conversely, the probability that a Democrat will win, given that Trump is the nominee is currently (0.7)*(0.5) + (0.3)*(0.91)=0.62. Furthermore, I postulate that the degree of ignorance will diminish by – let’s just say – 10% points per month as we get closer to the election. So at the end of the month, I can (and will!) update the likelihood with new polling data (and anything else I can find), discounting this information by the principle of insufficient reason at a rate of 60%.

(Note: this forecast revisits and updates some material I’ve discussed in forecasting a related question or two.)

[1]Data about individual polls was taken from http://www.realclearpolitics.com/epolls/2016/president/us/general_election_trump_vs_clinton-5491.html. However, I did not use RCP’s weighting algorithm.

[2]Data about individual polls was taken from http://www.realclearpolitics.com/epolls/2016/president/2016_presidential_race.html. However, I did not use RCP’s weighting algorithm.

[3] http://mathworld.wolfram.com/PrincipleofInsufficientReason.html

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