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 better than expected showing last night moved his mean expected delegate count from 1,191 to 1,200[a]. Quoth Nate Silver: “Based on provisional results,1 it looks as though Trump will sweep every pledged delegate in Maryland (as a result of winning every congressional district), Connecticut (as a result of winning every congressional district and getting more than 50 percent of the vote statewide), Pennsylvania (where statewide delegates are awarded winner-take-all) and Delaware (ditto), along with 11 of 19 delegates in Rhode Island (which is highly proportional). Combined with the New York results,2 that gives Trump 200 delegates since we issued the path-to-1,237 projections, five delegates ahead of his original targets”[b].

But what about variance? That’s a hard question. I estimated the standard deviation among the expert predictions to be 45[c]. (An estimate was necessary since the description of the individual predictions was pretty sketchy.) But that number is now a month out-of-date, and we don’t have (to the best of my knowledge) an updated survey from which to work (not a publicly available one anyway). I’d guestimate that the variance is narrowing since there are now far fewer delegates in play, but I don’t have any confidence in that idea, so let’s go with the status quo ante. Here’s the probability distribution:

  • 1,237+ = 0.21
  • 1,200-1236 = 0.29
  • 1187-1199 = 0.11
  • 1161-1186 = 0.19
  • 1137-1160 = 0.11
  • Less than 1137 = 0.09

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 probability that Mr. Trump will win on the first ballot is 0.99*0.21+0.85*0.29+0.68*0.11+0.50*0.19+0.25*0.11+0*0.09 = 0.65. Applying my 0.05 fudge factor[d], that gives a forecast of 0.70.

I suppose that this passes the laugh test, but I’m highly unsure about it – especially given my cluelessness regarding variance here. GIGO, I suppose. Another approach would have been to look at the estimated delegate outcomes in each of the remaining states and then look at how far Mr. Trump has been from his expected outcomes in states that have already had primaries, using the latter to estimate variance. That’s more work than I have time for, sadly. It’s also problematic since in many of the earlier primaries Mr Trump had more than 1-and-a-half opponents, as he will in the remaining primaries. So I guess I’m sticking with my guns until I can think of something better to do.

[a] http://projects.fivethirtyeight.com/election-2016/delegate-targets/republicans/

[b] http://fivethirtyeight.com/features/its-trumps-nomination-to-lose/

[c] http://fivethirtyeight.com/features/will-donald-trump-clinch-the-republican-nomination-before-the-convention/

[d] https://www.gjopen.com/comments/comments/210642

 

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