Please note: The Washington Post is providing this important election information free to all readers. Get election results and other major news delivered to your inbox by signing up for breaking news email alerts.

Republicans have made claims of election irregularities in six states where President-elect Joe Biden leads in the vote count, alleging in lawsuits and public statements that election officials did not follow proper procedures while counting ballots in Tuesday’s election.

So far, they have gone 0 for 6.

Since Election Day, President Trump has repeatedly claimed that a broad conspiracy of misdeeds — apparently committed in both Republican and Democratic states — had cost him the election.

“WATCH FOR MASSIVE BALLOT COUNTING ABUSE,” Trump tweeted Tuesday, the latest in a series of missives in which he has made misleading claims about the vote. Trump’s campaign has encouraged donors to contribute to a legal-defense fund so he can fight the cases in court.

But in the lawsuits themselves, even Trump’s campaign and allies do not allege widespread fraud or an election-changing conspiracy.

Instead, GOP groups for the most part have focused on smaller-bore complaints in an effort to delay the counting of ballots or claims that would affect a small fraction of votes, at best.

And, even then, they have largely lost in court.

The reason: Judges have said the Republicans did not provide evidence to back up their assertions — just speculation, rumors or hearsay. Or in one case, hearsay written on a sticky note.

The result has been a flurry of filings that Trump has cited as a reason to avoid conceding defeat — but, so far, have done nothing to prevent the defeat itself.

Pennsylvania

As absentee ballots helped Biden overtake Trump in Pennsylvania last week, Republicans sought to stop Philadelphia officials from counting them. Their argument: GOP observers had been barred from the rooms where the votes were being counted.

The problem: That wasn’t true.

Republican observers were there, after all. Trump had “a nonzero number of people in the room,” one of his attorneys conceded in federal court Thursday evening.

“I’m sorry, then what’s your problem?” asked U.S. District Judge Paul S. Diamond, who denied the request to halt the count.

The Trump campaign repeated this claim Monday in another federal lawsuit, adding that standards for verifying mail ballots were applied unevenly across the state in a way that disadvantaged Republicans. The suit seeks to block certification of election results in the state on an emergency basis.

Trump’s team saw a few small victories in the state, though none seems likely to come close to affecting the race’s outcome. The campaign won an order to move observers closer to the counting machines in Philadelphia.

And it succeeded in getting Supreme Court Justice Samuel A. Alito Jr. to issue an order that election officials must separate ballots that arrived after Election Day but before Friday evening — a step that counties have already taken. Under an earlier ruling by the state Supreme Court, election officials may tally those ballots, which are a tiny fraction of the overall vote, but state officials have ordered them to be kept segregated in case of further legal challenges.

Elsewhere in Pennsylvania, Republicans sued to stop local election officials from releasing the names of voters whose absentee ballots had been rejected for errors such as a lack of signature. Local counties release the names so voters can fix the flaws in their ballots.

These suits have not succeeded, either.

In Northampton County, Pa., for instance, a judge wrote that the local GOP needed to prove why it would be injured if voters had a chance to correct their ballots. “As a result, its request for an injunction must fail,” wrote Judge Michael J. Koury Jr.

On Saturday, Trump’s lawyer Rudolph W. Giuliani said that the campaign was preparing to file another lawsuit Monday, alleging wrongdoing on a grand scale in Pennsylvania. “Many cases are going to be filed — some big, some small. This is going to be eventually a big case,” Giuliani said.

Michigan

In Michigan, Biden trailed on election night — but then, as in other Midwestern states, surged back to overtake Trump as thousands of absentee ballots were counted. In three lawsuits, Republicans have alleged that there was impropriety in those ballot counts.

They lost, both times. And for the same reason: Republicans could not provide evidence of wrongdoing.

In one case, Republicans said GOP election observers in Detroit were being excluded when city officials fixed, or “cured,” ballots that their machines couldn’t read. In these cases — which might be caused by a stray mark or a coffee stain — officials can make a duplicate ballot, with the same votes, and run that one instead.

Republicans said they had “information and belief” that this curing process had been done repeatedly without a GOP official there to observe it. They asked a judge to delay certifying Detroit’s results. The judge said no. He said the GOP’s evidence of misconduct was “mere speculation.”

“The City of Detroit should not be harmed when there is no evidence to support accusations of voter fraud,” Judge Timothy M. Kenny wrote.

In another suit, Trump’s presidential campaign asked a judge to stop all processing of absentee ballots in Michigan.

In that case, a Republican election observer said she’d been given a sticky note by an unnamed poll worker, alleging that late-arriving ballots were being counted improperly. But she couldn’t provide the poll worker’s name or any other proof.

A judge rejected that, saying that the GOP’s evidence was inadmissible as hearsay. The judge also said that — because Trump’s campaign had waited until late afternoon on Wednesday to file — its suit was moot.

“By the time this action was filed, the votes had largely been counted, and the counting is now complete,” Judge Cynthia Diane Stephens wrote Friday.

Meanwhile, Republican National Committee Chairwoman Ronna McDaniel raised another series of claims during a news conference Friday in Bloomfield Hills, Mich., alleging that election workers in Detroit were told to backdate certain ballots. Detroit officials denied the accusation.

McDaniel acknowledged that her allegations had not been fully vetted and said the information had been shared with federal prosecutors. A Justice Department official said the information McDaniel provided has been referred to the FBI. It was unclear what, if any, action the agency planned to take. An FBI spokeswoman in Detroit referred a reporter to the U.S. attorney’s office, which declined to comment.

The allegation about backdating was part of a suit filed Monday in which two GOP poll challengers asked a judge to block the city of Detroit from certifying its election results.

Their complaint cited an account from another woman, who said she was a city ballot-counting employee and claimed she was told enter incorrect data into a voter-tracking system.

That allegation is focused on absentee ballots, which the state required to arrive by 8 p.m. on Election Day. The city employee, Jessy Jacob, said that after Election Day, supervisors told her to enter data into a computer system to show that some absentee ballots had arrived before the deadline. Jacob said she felt that was improper, implying that the ballots might have been backdated after missing the deadline.

Michigan Secretary of State Jocelyn Benson has said there is no evidence of wrongdoing: the ballots had indeed arrived before the deadline, but a clerk had forgotten to save their arrival date in a computer file, she said.

“What she calls ‘backdating’ is simply dating. The actual date of receipt of the ballot was stamped on the envelope. We followed a proper process by putting that date into the system,” said David Fink, a private attorney representing the city of Detroit in the lawsuit. “The fact that it was done after the ballot was received has absolutely no significance.”

In her news conference last week, McDaniel also asserted that 2,000 Republican ballots in Rochester Hills, Mich., had been “given to Democrats . . . due to a clerical error.”

Tina Barton, the GOP city clerk of Rochester Hills, said in a video posted on Twitter that McDaniel was referring to an “isolated mistake that was quickly rectified” and called her allegation “categorically false.”

“As a Republican, I am disturbed that this is intentionally being mischaracterized to undermine the election process,” she said in the video.

In an interview, she said that there was a technical issue that temporarily created duplicate results when mail ballots were scanned, but it was immediately fixed.

Barton said that she learned of the RNC chairwoman’s claim only when a reporter called her for comment.

“I have spent 15 years building my reputation of being a good election official — not only a good one, but a great one — and to have someone make a statement that we committed fraud of some kind, that 2,000 ballots were found, I couldn’t stand by and not respond,” she said.

Georgia

In Georgia, Trump’s campaign filed a lawsuit the day after the election, focused narrowly on absentee ballots in Chatham County, home to Savannah. The campaign asked that any absentee ballots arriving after polls closed on Tuesday be set aside.

For most voters, Georgia requires ballots to arrive before the end of Election Day, though there’s an exception for military voters and overseas voters.

The Trump campaign cited an affidavit from a poll worker who said he thought he might have seen late-arriving ballots improperly mingled with ones cast on time. Even if that was true, it was not an election-changing problem: The allegation dealt with a small number of ballots in a single county.

Georgia Democrats filed two affidavits from other poll workers who said they observed no such intermingling. A Georgia judge dismissed Trump’s suit in one day, writing that there was “no evidence” the county elections board had failed to comply with the law.

Arizona

In Arizona, the Trump campaign and the Republican National Committee filed suit in state court Saturday alleging that poll workers pushed or told some voters to push a button on a tabulating machine to cast their ballot, even after machine tabulators had detected an “overvote” — that is, the machine detected the possibility that the person had voted for two candidates.

Under state rules, they said, voters are supposed to be allowed to cancel such ballots and try again because sometimes stray ink marks or smudges can cause the tabulator to improperly assess an “overvote.” The campaign asked a judge to order a manual review of such ballots and to bar the certification of the Arizona vote until it is complete.

Trump supporters spent much of the week alleging that the tabulators were thrown off by the use of Sharpie pens and therefore disqualified large numbers of votes. State officials have insisted Sharpie pens are in fact the best writing instrument to use with the machines because of their fast-dry ink, and they do not cause problems.

Arizona Secretary of State Katie Hobbs (D) said the new suit was a “repackaging” of previous claims and merely an attempt to delay the count. And a top Maricopa County election official said just 180 votes for president are at issue — a tally that “is not going to make one iota of a difference,” said Roopali Desai, a lawyer for Hobbs, in a hearing Monday.

Nevada

In Nevada, two days after the election, a group of Trump allies claimed that thousands of people had voted illegally in Clark County, home to Las Vegas.

“That is unacceptable, and it’s giving legal people a sense that the system is corrupt,” said Richard Grenell, Trump’s former acting director of national intelligence.

Neither the Trump campaign nor the GOP were named plaintiffs in the federal lawsuit that was eventually filed by Republicans, which presented no evidence that thousands of people had voted improperly.

By then, the allegation had been whittled down drastically. Instead of 10,000 cases, Trump’s allies presented one: a woman named Jill Stokke, who said she was denied the right to vote in person because her mail ballot had been stolen and filled out by someone else.

But, in fact, Stokke’s story was more complicated. Election officials said they had indeed received a mail ballot from her — but the signature matched her own. They had offered her a chance to cancel that mail ballot and vote again if she would sign an affidavit saying the mail ballot had been stolen. She did not.

The Trump allies wanted U.S. District Judge Andrew Gordon to order a ban on the use of a machine for verifying signatures, a move that would have slowed down an already slow count. He did not. Instead, Gordon told the plaintiffs to return to court if they found more evidence to back their claims.

Beyond that lawsuit, GOP officials also alleged that more than 3,000 people voted in Nevada despite not living in the state.

Lawyers for the Trump campaign sent a letter Thursday to U.S. Attorney General William P. Barr alleging “criminal voter fraud in the State of Nevada” and claiming to have identified 3,062 people who voted improperly. They enclosed a list of addresses of voters who they said had moved out of state, information they said came from cross-checking voter data with the National Change of Address database.

At a news conference Sunday before a crowd of cheering supporters in Las Vegas, Trump campaign officials went further, claiming that as many as 9,000 nonresidents wrongly voted and that the Clark County elections system was riddled with other fraud, without offering credible evidence.

Groans and gasps could be heard from the crowd as campaign officials accused Democratic officials in Clark County of disenfranchising Republican voters. “Stop the steal,” the crowd chanted.

Local election officials have stressed that Nevada law allows some people to vote while living out of state: students, military personnel and military spouses.

“You don’t have to live here in order to be eligible to vote here,” Joe Gloria, the Clark County registrar of voters, told reporters last week.

The addresses of Amy Rose and her husband, an Air Force service member, are on the Trump campaign’s list of out-of-state voters. Rose and her husband currently live in Davis, Calif., where she works for a veterans support organization and her husband is pursuing a doctorate, doing Air Force-funded research in aerospace engineering.

“It’s really appalling to be used as pawns” to undermine confidence in the election results, Rose said. “We both take our duties as citizens seriously. It was quite shocking to see our integrity challenged without any basis in fact.”

In a statement, the Nevada GOP said it has “no intention of invalidating any legal voter.”

A Justice Department official said the department was “looking into” the allegations but declined to provide more detail.

Wisconsin

The Trump campaign said Monday that it is continuing with plans to seek a recount of the results in Wisconsin, where unofficial tallies show Biden leading Trump by about 20,500 votes, a .6 percent margin of victory. State allows a candidate to request a recount if the margin of a race is under 1 percent but the campaign must pay unless it is under .25 percent.

Under Wisconsin law, a recount petition in a presidential election cannot be filed until all counties complete a canvas of local results. The state’s 72 counties have until Nov. 17 to finish the process. Once the last county completes the process, the campaign would have until 5 p.m. on the following business day to ask for the recount. As a result, the Trump campaign cannot file its petition until next week.

In a statement last week, Trump campaign manager Bill Stepien cited “irregularities” in the Wisconsin vote but the campaign has cited no specifics and provided no specific examples of possible problems in the state. Multiple Republicans have said a recount is unlikely to change the results in the state. Former governor Scott Walker (R), a Trump supporter, called the margin a “high hurdle” for Trump to overcome.

If the Trump campaign pursues a recount, it could come at a significant price. When Green Party candidate Jill Stein sought a recount of the Wisconsin results in 2016, she was required to wire nearly $3.5 million to the state to pay for the effort before it began.

Michelle Ye Hee Lee, Matt Zapotosky, Aaron Schaffer and Andrew Tran in Washington, Tom Hamburger in Detroit and Hannah Knowles in Phoenix contributed to this report.