Understanding That ‘One-in-a-Quadrillion’ Claim About the Election


By now you’ve probably heard about the Texas attorney general’s lawsuit asking the U.S. Supreme Court to postpone the scheduled Dec. 14 certification of electors to allow for investigations of “rampant lawlessness” in elections in Georgia, Michigan, Pennsylvania, and Wisconsin.

You may also have seen the claim in the lawsuit that the odds of President-elect Joe Biden winning all four of those states fairly (given certain assumptions, which we’ll talk about) was “less than one in a quadrillion to the fourth power.” You may even have seen some capable refutations of this allegation, such as here and here.

What interests me is what the outlandish “quadrillion” claim says about how the human brain processes statistics and large numbers. In short, poorly. That it was inserted into a lawsuit by the attorney general of a large state and has since been widely repeated as evidence of illegal activity says something about partisanship, yes, but it also says something about innumeracy. Math and statistics teachers of the U.S., hang your heads in shame.

First, focus on how small less than one in a quadrillion to the fourth power is. One quadrillion is one million billions. Taking that to the fourth power would make it one million million million million billion billion billion billions. More than the number of atoms in the solar system. The alleged fraction is one divided by that big number. Or actually, “less than” that. I was going to write out the zeroes but I’m afraid I’d miscount, and a math teacher mad about what I wrote in the last paragraph would reprimand me. 

This number is so big—or actually, so small, since it’s a fraction—it induces brain freeze. If Texas Attorney General Ken Paxton had said there was less than a 50% chance the election was fair, people could argue the merits. But “less than one in a quadrillion to the fourth power” is paralyzing.

The statistical aspect also seems to befuddle people. The statistical consultant who did the analysis cited in the lawsuit, an independent contractor named Charles Cicchetti, investigated the following question: What’s the chance Biden would have won the four states if a) the preferences of the 2020 electorate were just like those of the 2016 electorate and b) the voters whose votes were counted late were just like those whose votes were counted early, when Trump seemed to be ahead. You can see his analysis in the appendix of the lawsuit starting on page 20.

Now, let’s take this slowly. Cicchetti concludes that if both those things were true, there’s almost no chance that Biden would have won. That is correct, given the premise. But those two things were not true. Polls showed that Biden in 2020 had more support from voters than Hillary Clinton got in 2016. And the people who mailed in their ballots were disproportionately Democrats. In short, both assumptions on which Cicchetti “quadrillion” statistic rests are false. 

A side observation: One quadrillionth to the fourth power is actually a drastic understatement by Cicchetti of his own analysis. In a footnote he says that for one election alone, Georgia’s, the so-called Z-score was 396.3. A Z-score of just 10 equates to a probability of one in a billion quadrillion, so a Z-score of 396.3 is just ridiculous.

Again, though, that’s assuming voter preferences were the same in 2020 as in 2016—which, to repeat, they weren’t. “If my grandmother had wheels she’d be a bicycle” is true, given the premise. But my grandmother does not have wheels. Garbage in, garbage out.

©2020 Bloomberg L.P.

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