The law also states, "An ordinance, resolution, rule, regulation, contract, or appointment may not be approved at a closed meeting."
Appointing leaders is not among the reasons listed within the law for which a public body may close a meeting to the public.
"I think it's very clear that secret ballots are not permitted under the Open Meetings Act," said Jeff Hunt, a Salt Lake City attorney who specializes in First Amendment issues.
Hunt, who has represented several local media outlets including The Salt Lake Tribune on unrelated First Amendment cases, said he doesn't think secret ballots are "consistent with the letter and spirit of the Open Meetings Act."
Roberts, who was chosen as chairwoman for the fifth time, said the board has often voted by secret ballot in the past. She said no one has expressed concern about the practice to the board during her tenure.
She said voting by secret ballot can help members vote more freely without fear of hurting fellow board members.
Roberts earned 10 votes while her opponent Tami Pyfer earned five. For the vice chairman spot, David Crandall earned 10 votes and his opponent, also Tami Pyfer, earned five.
Plus, Roberts said, the state Senate and House vote for their leaders secretly as well.
Senate President Wayne Niederhauser, R-Sandy, confirmed that the Senate majority caucus votes for its leaders in a closed meeting. But it appears that vote is legal because the Open and Public Meetings Act states political parties, political groups and political caucuses are not considered public bodies.
"These are people we've worked with and will work with," he said, "and I think that it's important to avoid feelings and potential animosity."
He said he can see arguments both in favor and against allowing a true public body to also vote for its leaders by secret ballot, but he empathizes with the argument that "silent votes" be allowed.
Hunt, however, said having to make uncomfortable decisions publicly "kind of goes along with the territory" of being an elected official.
"You have to be prepared to make those decisions in view of the public," Hunt said. "That's just part of the public trust that you exercise and while it may be uncomfortable for certain members and maybe it would be easier to do it in a secret session, expediency and comfort are not the prime values served by the Open Meetings Act. Transparency and accountability are."
Hunt said the board would not necessarily have to redo its vote unless someone legally challenged it, getting a court to void the action.
Roberts said, barring such a legal challenge, it would be up to the board to decide whether to redo its vote or alter its bylaws to make the vote public in the future.
The board's own bylaws require the board to vote for its leaders by ballot, saying, "Each member will check the personal choice for Chair and Vice Chair."
The bylaws are silent on whether members must identify themselves on the ballots.
"If the board were made aware that might be a problem, then they as a body could decide whether to address it and change the process," Roberts said.