Former President Donald Trump, like a tone-deaf musician, used the anniversary of the Jan. 6 Capitol riot last week to once again allege, without evidence, that the 2020 election was rigged. “Look at the numbers,” he told his followers, “they speak for themselves.”

He’s right, they do: They conclusively show his fraud allegations are bogus. For proof, let’s take a deep dive into Pennsylvania’s results.

Trump won the Keystone State in 2016 by less than a point and lost it in 2020 by a bit more than a point. As a result of that, supposed misdeeds in the state have loomed large in the MAGA crowd’s fraud narrative. Trump and others have alleged Democrats directly stuffed ballot boxes during the counting in Democratic-controlled cities, such as Philadelphia, or did so indirectly through fraudulently cast mail-in ballots.

Millions of people, mainly Republicans, believe these claims, even though there is no specific evidence to support them. They watched Democrats mercilessly assail Trump for years and have become used to rallying around him in response. Media declarations that the election was legitimate don’t stick. Worse, they tend not to support their defense of the election with clear evidence, making it a “he said, she said” argument. The sides talk past one another without engaging the facts.

That’s why it’s worth looking at Pennsylvania in detail. The state is one of the few that did not allow no-excuse mail voting in 2016 but then changed the law to permit it for 2020. Democrats also controlled the counting mechanism in Philadelphia and Pittsburgh in both years. That makes it the perfect place to test whether fraud occurred.

If Democrats stuffed the ballot boxes in large urban areas in 2020, there would be an unexplained increase in turnout in those areas. The same would be true for areas with higher rates of mail voting if the new practice gave rise to voter fraud.

But that didn’t happen in either case. How do I know? First, I compared the total number of votes cast for president in each county in 2016 and 2020, calculating how much they went up or declined. I then looked at the number of citizens of voting age for each county. This number, calculated each year by the Census Bureau, tells us how many people are theoretically eligible to vote. Together, these data points can tell us what percentage of eligible voters actually cast ballots in 2016 and 2020. If Trump’s fraud theories were true, that share would have increased at a greater rate in counties where the ballot boxes were allegedly stuffed or in those with a larger share of mailed ballots.

Here’s what actually happened: Philadelphia had the second-lowest increase of any of Pennsylvania’s 67 counties, with the share of eligible voters who cast a ballot going up by a mere 2.2 percent. Allegheny County, which contains Pittsburgh, rose by 7.4 percent. That’s smaller than the median rise in turnout for all counties of 8.4 percent. Other big Democratic-controlled counties, such as Erie, Delaware and Dauphin, also had smaller turnout increases than the average county.

There’s no indication that fraudulent mail-balloting raised turnout either. The share of total votes cast by mail varied widely by county. Almost half of Philadelphia’s ballots were cast by mail, whereas in rural Fulton County, only 15.2 percent were cast by mail, the lowest in the state. And contrary to Trump’s fraud theory, counties that had larger shares of mailed ballots did not always have larger changes in eligible voter turnout.

In fact, three counties with some of the lowest rates of mail balloting — Potter, Jefferson and Bedford — were among the top 10 in terms of an increase in turnout among eligible voters. Meanwhile, two big mail-voting counties — Centre and Philadelphia — were in the bottom 10 for turnout increase.

So where are all those extra, fraudulent ballots the whole “rigged election” theory hinges on?

The kicker for the fraud theory comes when you plot the increase in turnout for eligible voters for each county on a chart; if you’ve taken a statistics class, the result might look familiar. That’s because it’s an almost perfect normal distribution, or a “bell curve.” And it is exactly what you would expect if turnout increases were to occur randomly without anyone putting their thumb on the scale to affect it.

Trump recently said he wanted a debate on his voter fraud theory, arguing it would be a TV ratings bonanza. I accept his challenge, but I doubt he’ll follow up. Trump doesn’t like to lose, and he’ll be beaten like a drum if he ever has to defend his allegations against real evidence.

Henry Olsen is a Washington Post columnist and a senior fellow at the Ethics and Public Policy Center.

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