Mayoral hopefuls, from left to right, Christine Quinn, Bill Thompson, John Liu, Tom Allon and Bill De Blasio, discuss city education policies.

When the five leading mayoral candidates were asked on Monday how they would select the next schools chancellor at a forum on city education policy, the presumed longshot had the most specific answer.

Newspaper publisher Tom Allon, who recently switched his party affiliation from Democrat to Republican, was the only candidate to name names — and his shortlist contained an eclectic mix of people.

He started with Eric Nadelstern, a former Department of Education deputy who is bullish on school closures and other Bloomberg administration policies, then moved to Hunter College President Jennifer Raab before naming Linda Darling-Hammond, a Stanford University education professor who has been critical of policies favored by the Bloomberg administration. To round out his list, he named John White, who became Louisiana’s school superintendent not long after leaving the city Department of Education in 2011.

Allon’s list elicited laugher and whoops of surprise from the audience, as well as a disapproving remark from Comptroller John Liu, who was sitting beside Allon on the stage.  The forum was hosted by Manhattan Media, the company that Allon owns, with help from GothamSchools. (View the entire event.)

The one thing all of people on Allon’s list have in common is that they have experience working with schools and educators, which Mayor Bloomberg’s three chancellors have not had. Bloomberg’s first and longest-serving chancellor, Joel Klein, drew criticism because he had come from the corporate world, and most of the candidates were eager to say they would not make the same decision. Liu, Public Advocate Bill de Blasio, and former comptroller Bill Thompson all promised to choose an educator to lead the schools.

City Council Speaker Christine Quinn was the only outlier. She said she did not think the next schools chancellor should necessarily have an education background.Quinn cited Raab, one of Allon’s suggestions, as a prime example of someone who could lead an educational institution without prior experience in education.

“Raab has done an amazing job in my opinion at Hunter. She had no educational experience before getting to that job,” Quinn said. “So if we said, ‘Only an educator,’ Jennifer would never have become president of that school. I think you need somebody with education experience, education know-how, but I don’t want to rule anybody out who may have had different types of experience … I don’t want to limit us.”

The likely candidates were unanimous in not wanting to limit their chancellor search to people outside of the current Department of Education, who would be most likely to bring a new approach to the department.

Thompson made the strongest case against hiring internally for the job.

“The policies that have been put forward by the Department of Education have not helped our children, and I think we’d have to look outside to find our next chancellor,” he said. But, he added, “I wouldn’t go as far as to say that I would exclude everybody.”

Public Advocate Bill de Blasio said that, whether or not his pick came from within the Department of Education, he would want to create a “serious, public screening” process around selecting the chancellor. Bloomberg’s three chancellor picks were each a surprise because he never named publicly the candidates he was considering.

“No one said mayoral control meant mayoral inability to communicate,” de Blasio said. “We need a chancellor who is presented to the public, not just pushed down our throats.”

Liu, who spoke after Allon, said he too has “a shortlist” but would not reveal it yet. Like de Blasio, he emphasized the role the public could potentially play in picking the next chancellor.

“I would also engage the public more in terms of what the schools need, what communities need, what families need,” Liu said.

He also cautioned against writing off current department officials too quickly. “There are a lot of people at the DOE with experience levels that we could draw from,” he said.