Opinion | Trump Is Wrong. There’s No Evidence of Election Fraud in Philadelphia.

Joe Biden’s lead in the presidential election results in Pennsylvania has now surpassed 81,000 votes, far exceeding Donald Trump’s 44,000-vote victory margin there four years ago. Yet the Trump campaign continues to claim in court huge but incalculable levels of fraud, particularly in Philadelphia.

As with cases filed elsewhere around the country, Mr. Trump will not succeed. Even a cursory examination of the data refutes any notion of substantial voting fraud.

As a threshold matter, it is important to understand how eerily similar the 2020 results in Philadelphia were to 2016. As of Tuesday evening, 743,966 votes for president had been counted in Philadelphia — an increase of 34,348 votes from 2016. This 4.8 percent increase in turnout is less than half of the 11.6 percent increase in turnout seen in the state as a whole.

Not only was the increase in the number of ballots cast in Philadelphia from 2016 to 2020 relatively modest, but Mr. Trump won more votes and a greater percentage of the votes there than he did in 2016. He received 18 percent of the two-party vote this year, up from 15.7 percent in 2016, gaining 24,122 votes. In contrast, Mr. Biden received two percentage points less of the two-party vote in the city than Hillary Clinton did in 2016. If any fraud was attempted in Philadelphia, it failed miserably.

Mr. Biden also did worse in Philadelphia in comparison with 2016 than in most other counties in the state. Mr. Biden outpaced Mrs. Clinton in 57 of Pennsylvania’s 67 counties. Though he got one percentage point more of the two-party vote than she did statewide, he underperformed her by 2.3 points in Philadelphia County — the biggest percentage-point decline in any county in the state. Philadelphia stands out as the county where Mr. Biden did particularly poorly, not suspiciously well.

Just because Mr. Biden did worse than Mrs. Clinton and underperformed expectations this year does not disprove possible fraud, of course. Central to the “bad things are happening in Philadelphia” claim by Mr. Trump is the notion that a suspicious number of absentee ballots came in for Mr. Biden in Philadelphia. Absentee ballot fraud — either from dead people voting or election officials stuffing ballot boxes — is central to the Trump campaign’s claim of a stolen election. Again, the available evidence suggests nothing irregular.

Mr. Biden received a higher percentage of the vote by mail than he did in the Election Day vote throughout the state. Philadelphia, which is much more Democratic than the rest of the state — 76 percent of the county’s voters are registered as Democrats, compared to 47 percent statewide — lies just where we would expect it to be, given the partisanship of the county.

Skeptics of this analysis are likely to say that it is irrelevant, because the margins were so close that even a small number of manufactured ballots could make a difference. To this, we offer two rebuttals.

The first is that Mr. Biden’s lead in the state, over 81,000 votes, is not close, and continues to grow. Second, for Mr. Biden’s lead to be the result of “stuffed” absentee ballots in Philadelphia would require that over 20 percent of mail ballots there to have been fraudulent. Such a large number of questionable ballots would have tripped off alarm bells for the Democratic and Republican officials who were overseeing the count.

Statistical evidence such as this should not be necessary to cast doubt on the fraud claims being made in court by Mr. Trump’s campaign. The arguments simply are implausible on their face, in Pennsylvania and elsewhere. The allegations suggest a conspiracy or a remarkable coincidence of Republican and Democratic election officials in multiple states looking past or covering up hundreds of thousands of illegal votes.

That’s not all that is implausible. The purported fraud appears to have affected only the top of the ballot and not the down-ballot races. Republican congressional candidates were surprisingly successful in those same states where allegations of illegality in the presidential race have been made.

All of this may seem like beating a dead horse or trying to kill a fly with a bazooka, given the Trump campaign’s repeated losses in court. (On Tuesday, the Pennsylvania Supreme Court rejected the campaign’s contention that observers in Philadelphia were kept too far away to properly watch the vote counting.) But the president’s dangerous claims of fraud are taking root in the public consciousness, causing significant doubt, especially among Republicans. Sixty-one percent expressed no confidence in a recent survey that the election was held fairly.

One does not need to place witnesses on the stand to have them recant their claims or to embarrass the lawyers who cannot support these allegations. The evidence available in the public record demonstrates on its own that the claim of widespread fraud is itself a fraud.

The more compelling conclusion is the one reached last week by the election and security experts in the Department of Homeland Security, which declared that the 2020 election was “the most secure in American history.”

Nathaniel Persily, a law professor at Stanford, and Charles Stewart III, a professor of political science at M.I.T., are founders of the Stanford-M. I. T. Healthy Elections Project.

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