Sen. Rand Paul, R-Ky. walks from the stage after speaking during the Conservative Political Action Conference in February. Carolyn Kaster/AP hide caption

Sen. Rand Paul, R-Ky. walks from the stage after speaking during the Conservative Political Action Conference in February.

Rand Paul is not like other potential presidential candidates.

The Kentucky senator, who announced his candidacy for the White House on Tuesday morning, doesn't fit neatly into the molds of either party.

Socially liberal on issues of crime and punishment especially when it comes to drug sentencing against a federal ban on same-sex marriage, and no foreign policy hawk, he's not your prototypical Republican.

As a fiscal conservative and an opponent of abortion rights, though, he's certainly no Democrat either.

"It's time for a new way, a new set of ideas and a new leader," Paul says in a Web video, with a heavy metal soundtrack, previewing his presidential campaign.

Paul fits more with libertarians. And, though he is the scion of the last carrier of the torch of "liberty," he's also not quite his father's libertarian.

Paul's father, the former Rep. Ron, ran for president three times before retiring. The elder Paul, 79, was always regarded as something of a gadfly, an outspoken fresh voice in the Republican primary with a passionate following of young libertarians.

Though Paul did not win a single state in 2008 or 2012, when measured by Election Day voting percentage, he routinely finished in the top three. In fact, he finished a solid second behind Romney in the critical early state of New Hampshire.

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Can Libertarian Rand Paul Win A Republican Primary?