Key events10m ago‘Fiercely independent’ South Carolina votes on Lindsey Graham’s Senate successor25m agoWisconsin and Minnesota primaries sees progressives clash with Democratic establishment‘Fiercely independent’ South Carolina votes on Lindsey Graham’s Senate successorGeorge ChidiIn the race to replace the late US senator Lindsey Graham, 10 candidates have been barnstorming South Carolina diners, church halls and recreation centers, compressing a normal year of campaigning into about a fortnight.The Republican party is staging a special primary election in the state on Tuesday to choose Graham’s replacement. His sister, Darline, who has been serving as interim senator following his sudden death last month, is on the ballot.If no candidate wins an overall majority of votes, the top two will advance to a runoff on 25 August. Polling suggests that this is the most likely outcome.“You know, South Carolina politics is very local,” said Eaddy Roe Willard, a longtime Republican activist in South Carolina’s Richmond county. “Something one of our former chairmen used to say about presidential candidates: we don’t decide whether or not we’re gonna vote for you until we’ve had a chance to shake your hand at least three times.”On Friday Russell Fry, a Republican representative, pressed the flesh at Savage Craft Ale Works in West Columbia. On Monday morning, Darline Graham shook hands at Lizard’s Thicket breakfast restaurant, 2 miles away. Mark Sanford, the former South Carolina governor, and US representative Ralph Norman were also just a few miles down the road in Aiken on Friday, Willard said.After Lindsey Graham’s death on 11 July, Henry McMaster, South Carolina’s governor, appointed Darline Graham to fill the vacancy in the US Senate.Lindsey Graham had already won the Republican primary election for his seat, so the Republican party must hold a special election to replace him on the ballot in November’s general election. The timeline is brutal by American political standards, holding an election within a few weeks of the vacancy.The winner will face Annie Andrews, the Democratic nominee and a pediatrician, in November.Wisconsin and Minnesota primaries sees progressives clash with Democratic establishmentHello and welcome to the US politics live blog.Democratic primaries for governor in Wisconsin and US senator in Minnesota will once again see left-wing candidates face off against more traditional ones.The party’s ideological rift, that has already been seen in contests across the States this year, shifts to the upper Midwest later today.In Wisconsin, state representative Francesca Hong, a self-described democratic socialist, is front-runner for the party’s nomination for governor in a swing state where winning the governor’s mansion is central to Democrats’ hopes for 2028 and beyond.In Minnesota, Peggy Flanagan is running for the nomination for an open Senate seat against centrist Democratic representative Angie Craig. Meanwhile, seven Minnesota Republicans are vying to face off against likely Democratic gubernatorial nominee senator Amy Klobuchar in November.The primaries come a week after Abdul El-Sayed narrowly defeated Haley Stevens in Michigan’s divisive and costly US Senate primary.El-Sayed’s victory has energized progressives, while stoking fears among Democratic party leaders that the shift to the left, particularly in battleground states like Michigan and Wisconsin, will make it more difficult to win in the November midterms.The left vs center theme is on display in Democratic primaries in multiple states voting on Tuesday, with other significant races also taking place in the likes of Alabama and South Carolina.In other developments: