Georgia on my mind

Posted in Books, Kids, Statistics, Travel with tags , , , , , , , , on May 12, 2021 by xi'an

The riddle of this week was inspired by the latest presidential elections when one State after another flipped the winner from Trump to Biden. Incl. Georgia.

On election night, the results of the 80 percent who voted on Election Day are reported out. Over the next several days, the remaining 20 percent of the votes are then tallied. What is the probability that the candidate who had fewer votes tallied on election night ultimately wins the race?

Assuming many votes, perfect balance between both candidates (p=½), and homogeneity between early and late ballots, the question boils down to the probability of a sum of two normals, X+Y, ending up being of the opposite sign from X, when the variances of X and Y are α and 1-α. Which writes as the expectation

$2 \mathbb{E}_\alpha[\Phi(-X/\sqrt{1-\alpha})]$

equal to

$\frac{2}{2\pi}\left(\frac{\pi}{2} + \arctan\{\sqrt{\alpha/(1-\alpha)|}\}\right)$

which returns a probability of about 0.14 when α=0.8. When looking at the actual data for Georgia, out of 5 million voters, at some point 235,000 ballots remained to be counted with Trump on the lead. This means an α about 0.05 and implies a probability of 7% (not accounting for the fact that the remaining mail-in-ballots were more favourable to Biden.)

and it only gets worse [verbatim]

Posted in Kids, Travel with tags , , , , , , , , , , , , , , , , , , , , , , , , , on October 4, 2020 by xi'an

“A basic principle of the law — and of everyday fairness — is that we apply rules with consistency, and not based on what’s convenient or advantageous in the moment. The rule of law, the legitimacy of our courts, the fundamental workings of our democracy all depend on that basic principle.” Barack Obama [on Ruth Bader Ginsburg’s replacement], 18 September

“I don’t know that [Ruth Bader Ginsberg] said that, or if that was written out by Adam Schiff, and Schumer and Pelosi,” DT, 21 September

“I don’t wear a mask like [Joe Biden]. Every time you see him, he’s got a mask. He could be speaking 200 feet away from them and he shows up with the biggest mask I’ve ever seen.”, 29 September

“With time it goes away. And you’ll develop like a herd mentality [sic]. It’s going to be herd developed, and that’s going to happen. That will all happen.” DT, 16 September

“If you take the blue states out, we’re at a level that I don’t think anyone in the world would be at,” DT, 17 September

“It will start getting cooler, just you watch.” DT, 14 September

“I don’t think science knows, actually.” DT, 14 September

“Because of the new and unprecedented massive amount of unsolicited ballots which will be sent to ‘voters,’ or wherever, this year, the Nov 3rd Election result may NEVER BE ACCURATELY DETERMINED, which is what some want.” DT, 17 September

“There is NO WAY (ZERO!) that Mail-In Ballots will be anything less than substantially fraudulent.” “DT, 26 May

“I can tell you there’s [no race problem] with me. Because I have great respect for all races, everybody.” DT, 15 September

“America is fundamentally good, and has much to offer the world, because our founders recognized the existence of God-given unalienable rights and designed a durable system to protect them” M. Pompeo, July 2020