If you build it, they will come – even if no one knows what it will look like, and county leaders argue about it.

The Lee County Commission approved Naples-based Kraft Construction to oversee the new Boston Red Sox spring training venue Tuesday, despite a conflict of interest issue that has been hanging over the decision.

While no design has been selected for the stadium, conflict among commissioners virtually overshadowed the decision.

Last week, Commissioner Frank Mann called into question Commissioner Tammy Hall’s ability to make an impartial decision because of her relationship with boyfriend Howard Wheeler. Wheeler works for Chris-Tel, a subcontractor for Kraft.

Mann essentially recanted his earlier statements Tuesday after Hall had been cleared by the Florida Commission on Ethics.

“I’m trying to put the sting of this issue behind us,” Mann said. “There is an argument to be made here that to refrain from voting may be the right thing to do.”

Hall made her case to the board, saying she understands the complexities of the issue despite being cleared by the state board, and claimed her family has suffered. She even offered to remove herself from the voting process.

“I do recognize the public perception in this process,” she said. “It’s distressful when family and friends are put through public debate when they are not part of the public process.”

Hall prepared to leave the dais as the vote came before the board, but she was called back to her seat by Chairman Ray Judah.

Judah said it is crucial to have Hall’s vote, as her absence might indicate some wrongdoing in the eyes of Lee County taxpayers.

“This is a transparent and open process,” he told Hall. “I don’t want people thinking you left because there’s a conflict of interest.”

The vote to approve Kraft Construction passed 4-1, with Commissioner Brian Bigelow dissenting.

The stadium, expected to resemble a “mini-Fenway” like the one in Boston, is scheduled to be completed in 2012 at an as of yet unknown cost. The location for the facility also is unknown, but it has been rumored it will be located in south Lee County, possibly Estero.

Five architectural firms were chosen to compete for the wining bid. Commissioners are expected to make a decision on the designs soon.