The political identity crisis has been heightened by the nomination of Donald Trump as its standard-bearer and has driven Madsen toward the Libertarian Party and its candidate, former New Mexico Gov. Gary Johnson.
Earlier this year, Madsen hosted Johnson during a visit to the Utah Legislature, and the senator introduced him to the Republican and Democratic caucuses. In April, Madsen gave the keynote at the state Libertarian Party convention.
"I've been kind of an oddball legislator," Madsen told the gathering. "I don't fit. And it's been 12 years [in office] of kind of a square peg in a round hole."
In May, Madsen flew to Orlando, Fla., to speak at the Libertarian Party's national convention.
This week, during the Republican National Convention, Madsen said he is grasping for a sense of what the modern Republican Party stands for.
"A lot of people have taken the 'conservative' moniker and I wonder what they're conserving anymore, because the status quo is truly the bureaucratic administrative state, you know, the police state, the surveillance state," he said. "And it seems like so many people who call themselves conservative are more interested in conserving that than constitutional principles and the Bill of Rights."
Madsen, who is retiring from the Legislature this year, is an outspoken proponent of legalizing medical marijuana as is Johnson and said he was disappointed that a proposal to add language supporting medical cannabis to the GOP platform was soundly defeated.
But he views it as a larger trend toward the party of compromising on the concept of limited government.
"The whole thing is entirely owned by the [Senate Majority Leader] Mitch McConnells and the leadership in the Republican Party that, over time, has really selected lame candidates," Madsen said. "The so-called Democrat-light candidate, where we're halfway as good as them but we don't stand for a distinct set of principles. I don't know what this [party] stands for. … I don't know what's going on here."