BOYISH looks and wide eyes betray his lineage. Jason Carter is running for governor of Georgia, a post his grandfather Jimmy held before he was president. The Carter name is both a boon and a burden. It is unlikely that Jason would have cruised to the Democratic nomination without it. However, the 39th president has a mixed reputation even in his home state. Liberals applaud his Nobel peace prize and his charity work. Conservatives, who are more numerous in Georgia, remember the malaise of the late 1970s, the botched Iranian hostage crisis and the ridiculous episode of the “killer rabbit”.

The younger Mr Carter insists that he is his own man. Christian conservatives, who form a big chunk of the Georgian electorate, tend to be pro-Israel; so whereas Jimmy Carter talks of Israeli “apartheid”, Jason stresses his support for the Jewish state. He distances himself from his grandfather’s love of green regulations and hostility to oil pipelines. Unlike his grandpa, he is pro-death penalty and no foe of the gun lobby. The elder Mr Carter obligingly plays a “minimal” role in his campaign.

Will this be enough for Jason to win in a state that is far more Republican than it was in Jimmy’s day? It could be close: the RealClearPolitics poll of polls puts Mr Carter’s Republican opponent, Nathan Deal, two percentage points ahead. Mr Carter has raised $1m more than Mr Deal so far this year, which is striking, since Mr Deal is the incumbent governor. Mr Deal’s supporters dismiss Mr Carter as a “liberal trial lawyer” and a “limousine liberal” (he has accepted donations from Steven Spielberg and George Soros). But the race may turn on issues of more substance.

Mr Deal can boast that unemployment has fallen from 10.1% when he took office in 2011 to 7.8% now. But it is worse than it was in April (6.9%) and better than only one other state, Mississippi. Average hourly wages have increased 3.7% in Georgia under Mr Deal, less than the national average of 4.6%. The governor has offered tax breaks for new factories and cut a few regulations, but this has yet to bear fruit.

The governor has taken a firm stand on health care, albeit mostly to say “no”. His last significant act as a congressman (his previous job) was to vote against Obamacare. As governor, he spurned federal money to expand Medicaid, the public health programme for the hard-up, reasoning that Georgia would eventually get stuck with much of the bill. Mr Carter has not talked much about health care—the word “Obamacare” is toxic in Georgia—but he says he would expand Medicaid. That should help him with blacks, who are 30% of the population and solidly Democratic, but who don’t always vote.

Mr Carter knows he needs a good turnout among blacks. “I’d tell you how important it is to get out and vote, but y’all already know,” he told a sea of pink, green and yellow hats at Atlanta’s Jackson Memorial Baptist church on August 10th. Ben Jealous, a former head of the NAACP, a civil-rights group, has crunched some numbers. If 60% of Georgia’s unregistered black voters get registered and then turn out at levels seen in previous elections, that would be 290,000 extra votes—30,000 more than the average margin of victory in Georgia’s recent governor’s races.

Mr Carter talks more about education, but his ideas sound somewhat half-baked. He wants a new, separate education budget—Georgia spends less on education than 39 out of the 50 states. Mr Carter says a top-to-bottom review of government spending would uncover needed cash. But when pushed, he cannot pinpoint the wasteful expenditure he would cut. “Everyone knows it’s there,” he says, which is not much of an answer.

By contrast, Mr Deal is happy to keep schools much as they are. Besides rewarding the best teachers with more pay, he intends only to tinker with the formula for funding schools. At a festival in Norcross on August 29th he thanked Vietnamese parents, through an interpreter, for educating their children so assiduously. “We appreciate your respect for family and for religion,” he said. A star-struck manicurist in the crowd said he would vote for Mr Deal because “he really cares about the Vietnamese community”. But he will have to try hard to win more minority votes: he received hardly any four years ago.

Mr Deal faces allegations that his aides smothered an investigation into the finances of his 2010 campaign. Charles Bullock of the University of Georgia predicts that he will win anyway, but that Mr Carter’s “brand power” will help the Democrats in future elections. Mr Carter has time on his side. His grandfather did not become governor until his second attempt.