OK. My mathematical skills a really rusty. (And besides, I’m old.) And it’s no fun seeing how much more I have to struggle to set up a problem than I did back in the early 60s (when I wasn’t in my mid-70s). But I think I may have managed to calculate something semi-meaningful about how likely it is that when all the dust has settled on all the battleground states, Biden will be President-Elect of the United States.
And the news is rather good.
I based my calculations on two assumptions, both of which seem reasonable enough to me:
- I assumed the the current odds on each state --as judged by the markets on Predictit.org -- were accurate assessments of probable outcomes. (I know not everybody thinks much of those collective “Wisdom of crowds” judgments, but I think they’re at least the best we’ve got for the present purposes.) And
- I assumed that the outcomes in each state were independent of each other. (Which — quite unlike predicting voting before Election Day, I think is quite reasonable, since the relevant conditions in each state — e.g. what kind of votes remain to be counted -- are more or less unique.)
I then calculated the probabilities of various ways that Biden could win.
- I multiplied the probabilities of Biden winning both AZ and NV. That comes out to .57. (The chances of both going to Trump is .06). That combination would give Biden the victory.
- The probability of Biden winning PA is .8 -– and that, all by itself, would be another way that Biden would win.
- Biden’s winning GA — and only Georgia — would assure Biden at least a tie. And the probability of Biden prevailing in GA is assessed at .68.
- The chances of Biden winning by getting both GA and NV are .52.
To avoid losing outright, Trump has to avoid all of Biden’s paths to victory. I believe that the probability of Trump avoiding all those paths would be the product of multiplying out the numbers for Trump on each path, which would be 1 minus Biden’s probability of winning on any particular path.
Multiplying all those out comes to .04.
Which means that Biden has a 96% chance of winning— given those assumptions.
(And that does not include the scenario where Biden wins ONLY GA, and they tie at 269.)
(Taken altogether — not losing, not tying — Trump has only a little over a 1 in 100 chance of winning outright.)
BTW, Predictit.org puts Biden’s chances at 87%. If my calculations are correct, that underestimates his chances by 9%, even using Predictit’s own state-by-state judgments. Smart money take note!
