I'm not going to say that Representative Paul Ryan is a Culture Warrior Big Government Republican, At least not in the mold of a Rick Santorum. I don't believe he is and I don't know enough about him to say that anyway. But Paul Ryan's respect for Ayn Rand has to do with her beliefs as it relates to economics. Ayn Rand was a Objectivist/Libertarian. Didn't want government involved in the economy at all and didn't believe that government had the right to force people to do anything with their money. Which is kinda where Paul Ryan is on economics, but not quite that libertarian, but they both believe that government shouldn't be regulating the economy, but they probably differ on every key Social Issue.
You can imagine and if Ayn Rand were alive today and looking to run for office or was an elected official, she probably wouldn't be a Republican. She wouldn't fit into today's GOP. She would be seen like an outcast like how they now treat Barry Goldwater, or Ron Paul. Maybe she would be a Republican just to hold office. And live in an area, or State with a large libertarian population, where she didn't need the support of Neoconservatives in order to get elected and reelected. Representative Ryan, fits in very well with today's GOP, except that he doesn't push social issues very much if at all. Neither does Mitt Romney, which could hurt this ticket with Neoconservatives in the fall, in States like Virginia, Ohio and Florida.
But Mitt, pretty much votes the party line. Republicans like talking about Ayn Rand and telling people how much they respect her. But its only economics they talk about when it comes to Ayn Rand. They don't believe in her philosophy of Freedom of Choice essentially. That people have the right to live their own lives as they see fit. That government shouldn't interfere with how people live their own lives. Instead they believe that government should establish some type of moral code in how Americans should live. And live up to their ideals of what Americans should be and all of that. And thats just not Ayn Rand and hopefully not Paul Ryan either.
I wish even as a Liberal Democrat that people like Barry Goldwater and Ayn Rand had more influence on today's Republican Party. Then they would be a real party of ideas, that didn't believe it needed to prevent people from voting, just because they believe they wouldn't vote Republican. Which is what Voter ID is all about. But this is still Jerry Falwell and Pat Robertson's GOP, a Neoconservative Big Government party.