Education researcher Linda Darling-Hammond and former Republican presidential hopeful Ben Carson are the most likely picks to be U.S. Secretary of Education for White House candidates Hillary Clinton and Donald Trump, respectively, according to an “Education Insiders” survey by Whiteboard Advisors released Monday. And who’s second on the list for Clinton? American Federation of Teachers President Randi Weingarten, say these insiders.

The survey of roughly 50 to 75 current and former White House and U.S. Department of Education leaders, current and former congressional staff members, state education officials, and think tank leaders also found that a slight majority of them believe that over the next two years, more states will stop participating in two consortia (PARCC and Smarter Balanced) that were originally funded by Washington and create tests aligned to the Common Core State Standards.

And these “insiders” are generally pessimistic about the extent to which both the media and presidential politics will focus on education, although there’s some belief that higher education could be an exception.

“I’m not sure if K-12 will get much attention because the recent reauthorization of ESEA [Elementary and Secondary Education Act) probably means that the next president won’t have an opportunity to influence K-12 education (at least not legislatively) unless he or she gets a second term,” according to one respondent, none of whom were quoted by name.

Let’s go back to the favorites for the next secretary of education. The survey asked respondents for the most likely picks for Clinton and Trump. Here’s what they came back with:

Darling-Hammond is the president of the Learning Policy Institute (launched last year) and a professor emeritus at the Stanford University graduate school of education. She’s got a long track record in K-12 policy work—her activities range from significantly influencing California’s shift to a new accountability system, to serving as an adviser to the Smarter Balanced testing consortium that creates exams aligned to the Common Core State Standards. She helped to start two charter schools through Stanford, but in 2010 the elementary school’s charter was not renewed, and it shut down—the high school is still operating. And she’s pushed for less testing in American schools.

Weingarten has been an outspoken advocate for Clinton. The AFT acted quickly to endorse the former secretary of state in the Democratic primary last year. By contrast, in 2008, the union waited until the general election to endorse President Barack Obama, who beat Clinton for the Democratic nomination that year.

Chris Edley is president of the Opportunity Institute and the third-most-likely education secretary under Clinton, according to the survey. A former dean of the law school at the University of California, Berkeley, Edley’s work at the institute “promotes social mobility and equity by improving outcomes from early childhood through early career.” The institute has a special focus on California.

Current Secretary of Education John B. King Jr. also got a few nods to stay on, a possibility he’s declined to address directly. And then there are the three potential candidates with direct and current links to higher education:

• Freeman A. Hrabowski III, the president of the University of Maryland, Baltimore County who’s chaired President Barack Obama’s Advisory Commission on Educational Excellence for African Americans.
• Bob Shireman, a senior fellow at the Century Foundation who focuses on for-profit college accountability and quality assurance in higher education—Shireman’s worked in both the Bill Clinton and Obama administrations.
• Donna Shalala served as the president of the University of Miami from 2001 to 2015 after serving in the Clinton administration.

The top two candidates named for Clinton—Darling-Hammond and Weingarten—obviously focus on K-12 and not higher education.

Ben Carson, Chris Christie ... and Ted Nugent

As for Trump’s potential pick to lead the Education Department, the real estate executive mentioned in March that Carson would be “very involved in education” in a Trump administration. Trump stopped short of naming Carson, a retired pediatric neurosurgeon, his education-secretary-in-waiting, but that remark might be what led the Whiteboard insiders to put Carson at the top of the heap for Trump.

Carson is a fan of home schooling. And he’s called for a reconsideration of the extent to which schools rely on local property taxes, although his exact position on the matter has been unclear.

Andreas Schleicher is the director for education and skills at the Organization of Economic Cooperation and Development, which administers PISA. He’s been critical of the extent to which recent national efforts to close achievement gaps and raise proficiency rates have actually helped U.S. students match their peers in academic achievement and readiness for life after high school. You might recall that Trump has bashed American students’ performance on international exams.

Then there’s Tony Bennett, the former Florida and Indiana superintendent. In his two jobs leading state education agencies, he was a big fan of charter schools and A-F accountability. But he left his Florida job in 2013 after the Associated Press found that while serving as the Indiana chief, before he was defeated in a re-election bid in 2012, Bennett altered the grade of an Indianapolis charter school founded by a donor to his campaign.

The others to get nods as potential education secretaries include New Jersey Gov. Chris Christie, a Republican and Trump campaign surrogate who thinks teachers’ unions deserve to get slugged; former Arkansas Gov. Mike Huckabee, perhaps most prominent in K-12 policy circles recently for doing a flip-flop on common core; Ted Nugent (yes, the rock star of “Cat Scratch Fever” and “Stranglehold” fame); and Omarosa, a contestant on “The Apprentice,” Trump’s former reality show.