Adam Hollier’s primary defeat erodes Black political power in Detroit.

Soon after Representative Brenda Lawrence stunned her longtime colleagues with the news that she would not seek re-election in the fall, Warren Evans saw a potential downside of her retirement for Black Democratic politics in Detroit.

The nation’s largest majority-Black city risked being without Black representation in Congress for the first time in decades.

Mr. Evans, the county executive in Wayne County, which includes Detroit and is heavily Democratic, was worried that too many Black candidates would jump into the race and split the vote in a newly redrawn district. So he gathered community and labor leaders together to form a coalition that could settle on one candidate to back.

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In Michigan and Arizona, election officials are fighting conspiracy theories as they count the votes.

DETROIT — As voters in two top battleground states cast ballots in statewide primaries on Tuesday, election officials were still feeling the hangover from the 2020 presidential election.

In Michigan, officials beefed up security at the Huntington Place convention center in downtown Detroit, where two years ago — when it was known as the TCF Center — the police pushed back hordes of people trying to stop poll workers from counting absentee ballots that they falsely believed to be fraudulent. This year, prominent election deniers who have clung to those falsehoods have organized to become the poll workers counting votes and have forced officials to respond to a string of specious claims and concerns about safety.

In Arizona, Republican legislators who have long been involved in questioning Joe Biden’s victory there were calling for people to stake out ballot drop boxes to ensure that no one was illegally stuffing with them ballots, according to voting rights groups and a local news report. The fear stems from a debunked conspiracy theory popularized by a recent film. Another theory circulating online — this one involving a fast-drying pen that elections officials asked voters to use to fill out ballots — prompted the Maricopa County attorney to send a letter telling one Republican candidate to stop urging people to steal the pens.

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Gov. Abbott of Texas, who blasted Biden, did not blame Trump for similar migrant deaths on his watch.

When 10 migrant men died in San Antonio in 2017 after riding for hours in a sweltering tractor-trailer without food or water, Gov. Greg Abbott of Texas called the deaths a “heartbreaking tragedy” and took note of state legislation he signed to combat what he described as a human trafficking epidemic in his state.

Two years later, when an S.U.V. filled with undocumented migrants crashed in South Texas after being chased by the police, killing six people, Mr. Abbott released no official statement.

Mr. Abbott did not appear to comment on Twitter about either episode — nor did he attribute the deaths to the policies of the president at the time, Donald J. Trump.

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Jim Obergefell and L.G.B.T.Q. groups warn that abortion ruling could impact other rights.

Advocates for L.G.B.T.Q. rights on Friday sounded the alarm over Justice Clarence Thomas’s concurring opinion overturning Roe v. Wade, calling it a potential assault on the legal doctrine protecting a wide array of Americans’ civil rights.

In his opinion, Justice Thomas argued that the court should reconsider and overturn cases guaranteeing the rights to same-sex marriage, same-sex consensual relations and contraception, saying the foundational legal theory on which they are based lacks constitutional grounding.

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Nevada Senator Hopes History Repeats as She Faces a Hard-Right Rival

LAS VEGAS — In 2010, Senator Harry Reid of Nevada beat back a deep-red wave and dire national predictions for his political career when he pulled out a re-election victory against a Tea Party-endorsed candidate. He was a Democratic powerhouse with name recognition, pugilistic instincts and a state political machine long in the making behind him.

Twelve years later, Senator Catherine Cortez Masto, who replaced him in Congress, finds herself in a re-election battle in November against the Trump wing of the Republican Party. But Ms. Cortez Masto is not as well known as her Senate predecessor and mentor, the so-called Reid Machine is not as strong as it had been during his tenure and Democrats are facing an even tougher national political landscape.

“When you take that all together — this is why Nevada’s Senate contest is one of the most competitive races in the country,” said Mike Noble, a pollster who works in the state.

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G.O.P. primary victories in Nevada set the stage for Trump-centered battles in the fall.

Republican voters in Nevada on Tuesday elevated conservative candidates who have ardently embraced Donald J. Trump’s false claims of election fraud, turning a key swing state into a contest this fall between embattled Democrats and Republicans who insist President Biden stole the 2020 election.

The victories in the Nevada primaries for Mr. Trump capped a series of elections on Tuesday that saw one South Carolina Republican lawmaker who had crossed Mr. Trump go down in defeat, another survive her Trump-backed challenge and a Hispanic Republican grab a South Texas House seat vacated by a Democrat.

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For Beto O’Rourke, Talk of Gun Control Has Become Both a Political Risk and Reward

DALLAS — When Beto O’Rourke interrupted a news conference in Uvalde to criticize Gov. Greg Abbott, Jason Smith bristled.

Mr. Smith, a Fort Worth lawyer and Democrat, worried that Mr. O’Rourke’s approach was too confrontational in that moment, a day after an 18-year-old gunman stormed into Robb Elementary School. But in the days that followed, as details emerged that the police waited in a school hallway for more than an hour as children called 911 for help and Mr. Abbott acknowledged being “misled” about the response to the massacre, Mr. Smith changed his mind.

“I was really glad he did it,” he said of Mr. O’Rourke.

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Deadliest U.S. School Shooting in Decade Shakes Rural Texas Town

UVALDE, Texas — The gunman who killed 19 children and two teachers in a rural Texas elementary school on Tuesday entered the building despite being confronted by an armed school security officer, then wounded two responding police officers and engaged in a standoff inside the school for over an hour, state police officials said.

While gaps remained in the timeline of events, details emerged on Wednesday of a protracted scene of carnage at Robb Elementary School in Uvalde. What began around 11:30 a.m., with the first report of an armed man approaching the school, ended as specialized officers breached a pair of adjoining classrooms and killed the gunman barricaded inside just after 1 p.m., state police officials said.

It was not known how many were killed in the first minutes of the massacre, which was the deadliest in an American school since 20 children and six educators were shot to death at Sandy Hook Elementary School in Newtown, Conn., in 2012. But officials said that the officers had successfully contained the gunman, identified as Salvador Ramos, until more specially trained officers could arrive.

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In Texas, a Proxy Fight Over Democrats’ Stance on Immigration

LAREDO, Texas — Just a month after President Biden took office, pledging to roll back Trump-era policies in an attempt to take a more humane approach to immigration, Representative Henry Cuellar, a Democrat from South Texas, began to sound an alarm.

He warned that the number of migrants seeking to enter the country would rise, and soon released photos of children sleeping under tinfoil blankets at a crowded migrant processing facility in his district at the edge of the U.S.-Mexico border.

Now Mr. Cuellar, 68, has become one of the administration’s most consistent critics on immigration, appearing on Fox News and at times echoing Republicans, saying immigrants are pouring into the United States because they believe “that the border is open.”

His criticism has been met with fierce resistance from Jessica Cisneros, 28, a progressive immigration lawyer who is trying to unseat him in a Democratic runoff on Tuesday.

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The G.O.P. Establishment Scores a Rare Victory in Ousting Madison Cawthorn

HENDERSONVILLE, N.C. — In his campaign headquarters the morning after his electoral victory, Chuck Edwards showed no interest in dissecting one of the biggest political upsets so far in this year’s Republican primary season.

Mr. Edwards, 61, a three-term state senator and business owner, thwarted Representative Madison Cawthorn’s turbulent re-election bid in North Carolina, beating him in Tuesday’s primary in a rare defeat of a Trump-backed Republican incumbent.

“I’m excited for the opportunity to unify the Republican Party, put the primary behind us and focus our attention towards the real issues,” Mr. Edwards said on Wednesday, seated at a sleek mahogany conference table at his campaign office in downtown Hendersonville.

What went unspoken was that many voters saw him as the establishment candidate who benefited from the boost of old-guard Republicans at home and in Washington. Mr. Cawthorn, 26, had alienated two powerful Republicans with a litany of political and personal errors and scandals: Representative Kevin McCarthy of California, the House minority leader, and Senator Thom Tillis of North Carolina.

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Madison Cawthorn loses his re-election bid after a deluge of scandals

Chuck Edwards, a three-term state senator and business owner, has edged out Representative Madison Cawthorn in the Republican primary for a House seat representing North Carolina’s 11th District.

Luke Ball, a representative for Mr. Cawthorn, said late Tuesday that the congressman had called Mr. Edwards to concede. Mr. Edwards’s narrow triumph was called by The Associated Press.

The outcome served as a rebuke of Mr. Cawthorn, a right-wing firebrand and the youngest freshman in Congress, who was once seen as a rising star of the Republican Party.

It is also a significant victory for the old guard Republicans in North Carolina and Washington who in recent months had been feuding with Mr. Cawthorn over his personal and political errors and foibles.

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In Madison Cawthorn’s District, Strong Opinions of Him, For and Against

The right-wing firebrand is counting on Republican primary voters to look past his bad press. Opponents are counting on them to lose patience with him.

HENDERSONVILLE, N.C. — When Representative Madison Cawthorn’s name comes up in this city of 14,000, where he was born and raised and it is not difficult to bump into someone who knew him from his home-schooling days, there tends to be a visceral reaction.

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In Ohio Senate Race, Democrats Pin Their Hopes on the Suburbs

J.D. Vance, the Republican nominee, enters the general election as the favorite. For Representative Tim Ryan, the Democrat, Ohio’s sprawling metro areas offer a possible path to victory.

LORAIN, Ohio — J.D. Vance’s convincing victory Tuesday in the Republican Senate primary in this red-tinged state may have put an exclamation point on the power of former President Donald J. Trump’s imprimatur among conservative activist voters.

But Mr. Vance, the shape-shifting author and venture capitalist — once a Never-Trump antagonist, then an acolyte of the former president — has one possible battlefield left for the general election: the suburbs.

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Vance Wins Republican Senate Primary in Ohio After Nod From Trump

J.D. Vance, the author of “Hillbilly Elegy,” won a G.O.P. race that saw nearly $80 million in television advertising.

CINCINNATI — J.D. Vance, the best-selling author whose “Hillbilly Elegy” about life in Appalachia illuminated a slice of the country that felt left behind, decisively won the Ohio Senate primary on Tuesday after a late endorsement by Donald J. Trump helped him surge past his rivals in a crowded field.

Casting himself as a fighter against the nation’s elites, Mr. Vance ran as a Trump-style pugilist and outsider who railed against the threats of drugs, Democrats and illegal immigration, while thoroughly backpedaling from his past criticisms of the former president.

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In Ohio Senate Primary, Republicans Feel Strain Of Party’s Identity Crisis

CLEVELAND — The homestretch of Ohio’s contentious Republican Senate primary has revealed a party united in its conviction that American values, indeed the nation’s way of life, are under attack, but divided on whether to embrace a strict isolationism to address its mounting misgivings about global interconnectedness and American leadership abroad.

That divide has played out in policy differences — some subtle, others glaring — in the candidates’ approach to the economy, immigration and foreign policy. The strains reflect the broader splits in a party undergoing something of an identity crisis, with ideological conservatives, the old Republican establishment of big business, and the Trump-inspired newer rank and file all pulling in different directions.

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