Will the Republican candidate for president win the party’s nomination on the first ballot, at the party’s convention in July? (update)

Mr. Trump’s surprisingly good showing in the New York primary requires some changes to my forecast. It’s not that I didn’t expect him to win; it’s that I didn’t expect him to win by such a significant margin. 90 out of 95 delegates? Reach for the smelling salts. Living oracle Nate Silver tells us that Trump’s expected (mean) outcome is now 1,191 delegates[1]. Let’s assume that the standard deviation is still 45 delegates. The result is the following probability distribution:

  • 1,237+ = 0.16
  • 1,200-1236 = 0.26
  • 1187-1199 = 0.11
  • 1161-1186 = 0.20
  • 1137-1160 = 0.13
  • Less than 1137 = 0.14

Nothing’s happened to change my mind since last time about the likely outcomes, which are

  • 1,237+ –> 0.99 (If Mr. Trump goes over 1,236, he’s almost sure to win on the first ballot)
  • 1,200-1236 –> 0.85 (If Mr. Trump is over 1,200, he’s very likely to win on the first ballot)
  • 1187-1199 –> 0.68 (If Mr. Trump is within 50 delegates, he’s about a 2-to-1 favorite)
  • 1161-1186 –> 0.50 (If Mr. Trump is in the upper 1,100s his chances to securing enough delegates are about even-money)
  • 1137-1160 –> 0.25 (If Mr. Trump is this far away from 1,237 he’ll look weak and wounded, and delegates will be much less likely to to be wooed)

So the new forecast is that there’s a 0.58 [= (0.16*0.99)+(0.26*0.85)+(0.11*0.68)+(0.20*0.50)+(0.13*0.25)] chance that Mr. Trump will win the nomination on the first ballot. That’s a pretty sharp uptick in his chances, and frankly I’m a little concerned that my model responded so decidedly because of a difference of about 20 delegates. The culprit might well be the half-assed way that I estimated variance; further study is in order. But I’ll continue to update this business as primary results role in.

[1] http://fivethirtyeight.com/live-blog/new-york-primary-presidential-election-2016/


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