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Boosted by independent voters, Sen. Rand Paul (R-Kentucky) has the best odds of beating likely Democratic presidential frontrunner Hillary Clinton in three key swing states, according to new Quinnipiac University polls released Wednesday.

The polls of voters in Iowa, Colorado, and Virginia paint Clinton as less of a sure thing than is the perception. Paul comes close in two of the three, and former Florida Gov. Jeb Bush ties her in Virginia. But Paul is the most likely candidate to attract independent voters, the younger and more atypical voters who choose Republicans.

Here’s a breakdown of the Clinton vs. Paul results:

  • Colorado: Clinton 43, Paul 41
  • Iowa: Clinton 45, Paul 37
  • Virginia: Clinton 44, Paul 42

In all of the three states, Clinton suffers more with independent voters than national polls have shown. In Colorado and Virginia, two states President Barack Obama carried in both 2008 and 2012 where she appears most vulnerable, Clinton actually loses the independent vote to Paul. In Virginia, she loses the independent vote by 5 points.

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Paul’s libertarian-leaning views have long made him popular with younger and more independent-minded voters, and broadening the grassroots base he’ll inherit from his father, former U.S. Rep. Ron Paul, will be key to a successful run. Fusion’s Massive Millennial Poll last month found Paul tied for second among young Republican voters, behind Bush and tied with New Jersey Gov. Chris Christie.

On the other hand, independent voters appear a bit more sour on Bush, though he does tie Clinton in the Virginia poll.

Here’s a breakdown of the Clinton vs. Bush results:

  • Colorado: Clinton 44, Bush 36
  • Iowa: Clinton 45, Bush 35
  • Virginia: Clinton 42, Bush 42

But the poll provides a clear signal that he might have trouble attracting the kind of independent voters he’ll need to win a general election. More than 35 percent of voters in each state said they’d be less likely to vote for him because both his father, George H.W. Bush, and brother, George W. Bush, have served as president. Majorities in each state, however, said it won’t make a difference in how they vote.

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Bush will attempt to begin to draw a distinction between himself and his family during a speech in Chicago on Wednesday, in which he is set to declare that he is his “own man.”

“I also have been lucky to have a father and a brother who both have shaped America’s foreign policy from the Oval Office,” Bush said, according to speech excerpts. “I recognize that as a result, my views will often be held up in comparison to theirs’ – sometimes in contrast to theirs.

“I love my father and my brother. I admire their service to the nation and the difficult decisions they had to make. But I am my own man – and my views are shaped by my own thinking and own experiences.”

Brett LoGiurato is the senior national political correspondent at Fusion, where he covers all things 2016. He'll give you everything you need to know about politics, with a healthy side of puns.