The 2020 presidential contest ended four weeks ago Tuesday, but for President Trump and his allies, the fight continues. The president, as you’re no doubt well aware, continues to insist that it was he, and not President-elect Joe Biden, who won the election. There is no evidence that this is true in any sense; Trump lost the electoral college by the same margin with which he won it four years ago, even as he lost the popular vote by a much wider margin.

Through some combination of dishonesty and delusion, though, Trump maintains that he won by a wide margin. To bolster his case, he has elevated various scattershot theories aimed loosely at suggesting that something — anything! — sketchy may have occurred. Those theories ebb and evolve depending on how ludicrous they are shown to be, meaning that the collection of falsehoods itself changes over time.

Given the ongoing effort to elevate various claims, we thought it worthwhile to catalogue some of the more common assertions. Each of the claims in bold below is false, as the text that follows demonstrates. Feel free to use this as a one-stop rebuttal to Trump’s claims; if other assertions warrant future inclusion, we’ll add them.

1.8 million ballots were mailed out in Pennsylvania, but 2.5 million were returned. This claim conflates ballots sent in the primary (1.8 million) with the number returned (2.6 million) in the general. More than 3 million ballots were requested for the general election.

Biden’s leads in key states are a function of the suspicious addition of large numbers of ballots. It is true that large batches of votes shifted the lead in several states. The important distinction, though, is that this is not evidence of anything suspicious or nefarious occurring.

Take Wisconsin, for example. The sudden surge in votes that has prompted consternation from Trump and his allies was the reporting of results from Milwaukee County, where more than 1 in 8 votes statewide were cast. Those votes went heavily for Biden, just as they had gone heavily for Hillary Clinton in 2016.

If votes were being added illicitly, either a number of counties — and county administrators — would have had to be in on the fix or one county would see a wide deviation from its results in 2016. There’s no evidence that this happened.

It’s inconceivable that Biden received 80 million votes. It isn’t. Never have there been more people living in the United States and, by extension, more citizens of voting age. As we reported last week, although Biden’s vote total is higher than that of any candidate in history, as a percentage of the population that is eligible to vote, it’s somewhere among the top-10 performances in history.

That doesn’t answer the question of how Biden did so well. The answer to that question, though, is also simple: He was running against Trump. Trump has been the most polarizing president in history, with a majority of Americans disapproving of his job performance and with fervent opposition from most Democrats and many independents. Polling showed that many of them were motivated to vote not by Biden but by Trump. Trump likes to tout how energetic his supporters were — but to ignore the energy of his opponents.

It can’t be the case that Biden received more votes from Black voters than Barack Obama did. Again, it can, for the same reasons as above.

We should note first that this assertion isn’t proved. If we apply exit poll data to the vote totals in 2008, 2012 and 2020 — a fraught endeavor, given margins of error — we see that Biden received an estimated 17.7 million Black votes while Obama received 16.2 million in 2008 and fewer in 2012. But, again, there are millions more Black Americans in the United States than there were 12 years ago. From 2008 to 2017, Census Bureau data indicate that the number of African Americans in the United States increased by more than 11 percent, or 4.3 million.

What’s interesting about this claim is that Trump supporters broadly try to have it both ways: touting Trump’s faring better with Black voters than past Republican nominees did, which is probably true, while also disparaging the idea that more African Americans voted for Biden.

More people were reported to have voted in Detroit than live there. The city has data on the presidential election. There were more than 500,000 eligible voters and about 250,000 actual votes cast, a relatively low level of turnout, compared with other places.

That so many of these claims center on Black voters and heavily Black areas is probably not a coincidence, leveraging long-standing skepticism among Republicans of Black and Democratic cities.

It is suspicious that Trump lost while so many other Republican candidates were successful. There is only one office for which every American votes at the same time: president. That mutes the effects of partisan polarization at a state or local level: Red states may vote for Republicans and blue ones for Democrats, but everyone votes on the chief executive. In other words, we should expect that there are different partisan effects for nonpresidential races than for presidential ones.

Again, though, we have to note the way in which Trump is unique. No president in the history of modern polling has been as polarizing, and most Americans (and voters) had strong opinions about his presidency. That seems to have meant that many voters objected to Trump specifically while not objecting to Republicans generally. Much of the ground the GOP gained in 2020 was also being clawed back from the Democratic overperformance in 2018 — itself a function of Trump’s unpopularity but without the boost to Republicans that Trump’s presence on the ballot offered this year.

Voting machines shifted the results of the election in Biden’s favor. There’s literally no evidence of this that doesn’t start from the assumption that some fraud must have occurred. It’s a useful deus ex machina, leveraging uncertainty about technology and a black-box process to explain things such as the 80 million Biden votes that Trump and his allies find suspicious in the first place.

Republicans were prevented from watching votes being tallied, allowing fraud to occur. Here we're deviating from claims of fraud to more esoteric claims that maybe something bad happened. But even this isn't true.

As votes were counted, including in Pennsylvania, the Trump campaign had advocates observing. The campaign has tried to imply that it didn’t, arguing either that the observers were too far from the counting to be effective or that observers were turned away, which occurred in some places as volunteers showed up to try to root out suspected fraud. Courts have repeatedly ruled against the campaign on this issue.

Even if one accepts the campaign’s complaints at face value, though, this isn’t proof that any fraud occurred.

There are hundreds of sworn affidavits proving that fraud occurred. There are not. There are, instead, hundreds of sworn affidavits in which Trump supporters articulate things they saw, usually while serving as untrained volunteers observing the vote-counting process. As we’ve reported repeatedly, those statements rarely even allege fraudulent activity. Most instead document suspicious-seeming things, allegations that the city of Detroit aptly described as being “grounded in an extraordinary failure to understand how elections function.”

Just because someone is willing to swear under oath that they saw something happen doesn’t mean that what they saw happen was what they believed it to be.

Statistical or historic analysis shows that something strange happened with the voting in various states. Analyzing vote totals can be a good way to determine whether something suspicious occurred in an election. But it’s also quite easy to use numbers to whip up uncertainty about unsurprising things. Those batches of votes in key states that are attributable to large counties reporting their results for example, can be whipped up into complex conspiracy theories involving scatter plots and complicated mathematical equations. If you’re lucky, that sciencey appearance might even hoodwink a U.S. senator — even if the purported anomalies are easily explained by the existence of cities.

By themselves, in other words, such analyses don't prove fraud but, instead, might suggest it.

Less reliable are comparisons between this election and elections past. An article on a far-right website, for example, wondered about Biden’s losing “key bellwether” counties and being the first successful candidate in 60 years to lose both Florida and Ohio. Those counties are bellwethers, though, as a function of a few decades of recent elections. Even that trend involving Florida and Ohio lasted only 14 elections, a small sample size. It’s also cherry-picked: Trump was the first candidate since 1976 to lose both Nevada and Colorado. So what?

When considering historic analogies for presidential contests, it’s worth reviewing this XKCD cartoon from 2012.

Georgia needs to match signatures to ballots for its recount to be valid. One thing that we’ve seen in recent weeks (as in the preceding example) is that the arguments Trump and his allies use evolve into forms that comport with the available evidence. The proof they claim exists is always just out of reach or otherwise unattainable. Trump, for example, claims that the Wisconsin recounts — which expanded Biden’s lead slightly — were meant to uncover fraudulent votes, evidence for which would be provided this week. Given that the counting was conducted by counties in the state, that seems unlikely.

In Georgia, where both an audit and a recount have been conducted, the goal posts lie elsewhere. Trump and his team insist that the actual verification process should mandate that mail-in ballots again be confirmed against voter signatures. The problem with this, obvious to any casual observer of American elections, is that doing so would offer no information about the votes themselves, because vote choices are necessarily separated from the voter. This is the essence of the secret ballot: No one knows for whom you voted. So even if you did find, say, 1,000 suspect signatures, you’d have no idea for whom those people voted.

One observation that applies both to this claim and the effort in general is this: The goal isn’t to answer questions, it’s to raise them.