Cox, 49, said he wants to keep taxes low to help the economy and considers education a priority, but that doesn't necessarily mean more spending.
"Obviously, additional taxes is not something I would like to see, and if I can figure out how to save more money as far as government spending, I would like to. The more money we can leave in the private sector, the better," Cox said. "I care about public schools, but I'm not necessarily somebody who's just going to throw money at public schools."
Cox has lived in the district for 24 years, is a licensed architect and promotes renewable energy. He is a graduate of what is now Salt Lake Community College.
He has been a GOP state delegate several times and served as chairman of House District 32. He was an early supporter of Cherilyn Eagar's campaign for U.S. Senate and backed Jason Chaffetz's campaign for the U.S. House. He is aligned with the tea party and 912 movements.
His election will mark a conservative shift as he takes over the seat from Bigelow, who was generally viewed as a moderate Republican.
Winder beat Cox 12-8 on the first ballot, with other votes going to several other candidates in the mix. But Cox was the second choice of more delegates and prevailed in the second round of balloting.
Technically, Cox's name must still be forwarded to the Utah Republican Party, which will make the recommendation to Herbert, who will formally appoint the replacement.