Cox was appointed as a city councilor of Fairview, Utah, and elected mayor the next year. In 2008, he was elected as a Sanpete County commissioner. Cox was elected to the Utah House of Representatives in 2012 and became the first member to call for the impeachment of John Swallow, the attorney general of Utah, over violations of laws governing campaign finance. Cox and Lieutenant Governor Bell served as co-chairs of Governor Herbert's Rural Partnership Board. In October 2013, Herbert selected Cox to succeed Bell as lieutenant governor, following Bell's resignation. His nomination was approved unanimously by the Utah Senate's Government Operations Confirmation Committee on October 15. The next day, he was confirmed unanimously by the full Utah Senate and sworn in. As lieutenant governor, Cox's office produced a report on Swallow's financial interests, demonstrating that Swallow had failed to properly disclose all of his income and business interests. Swallow resigned before the release of the report. On May 14, 2019, Cox announced his intent to seek the Republican nomination for Governor of Utah in 2020. Cox won the Republican primary election with 36.4% of the vote, while Jon Huntsman Jr. received 34.6%.
Political positions
In October 2015, Cox endorsed Marco Rubio for the Republican Party nomination in the 2016 presidential primary. After Rubio withdrew, Cox endorsed Ted Cruz in March 2016. Of Donald Trump, the front-runner, Cox said: "We care a lot about decorum. We care about our neighbors. We are a good, kind people. He does not represent neither goodness nor kindness." He said he would not support Trump if he wins the Republican nomination: "I think he's disingenuous. I think he's dangerous. I think he represents the worst of what our great country stands for.... I won't vote for Hillary, but I won't vote for Trump, either." On June 13, 2016, Cox spoke at a vigil in Salt Lake City honoring those who died in the Orlando nightclub shooting the day before. He surprised many when he apologized for mistreating schoolmates and his lack of support for the gay, lesbian, bisexual, and transgender community. He aimed part of his speech at the "straight community":
Personal life
Cox is the oldest of eight children and grew up on a farm in Fairview. He and his wife, Abby, have four children, and reside on their family farm in Fairview. Cox's father, Eddie, serves on the Utah Transportation Commission and was also a Sanpete County commissioner. Cox plays bass guitar in a garage band. His brother-in-law, Travis Osmond, the son of Merrill Osmond, taught him how to play the bass. State Representative Mike McKell is also a brother-in-law. Cox's fourth cousin, Jon Cox, succeeded him in the Utah House of Representatives.