Sen. Rand Paul demolished his competition in the 2014 Washington Times/CPAC presidential preference straw poll on Saturday, winning 31 percent of the vote — nearly three times the total of second-place Sen. Ted Cruz.

The poll also found a strong plurality of attendees at the Conservative Political Action Conference believe marijuana should be fully legalized, with 41 percent saying it’s time to change the law and tax it. Another 21 percent said it should be legalized only for medicinal purposes, while just 31 percent said it should remain illegal in all cases.

In the presidential poll, Mr. Cruz’s 11 percent was a big improvement for the freshman senator, who won just 4 percent in last year’s straw poll. Neurosurgeon Ben Carson was third with 9 percent and New Jersey Gov. Chris Christie was fourth with 8 percent in results that signal growing discontent with the GOP establishment in Washington.

Indeed, CPAC voters now have an unfavorable view of Republicans in Congress, with 51 percent saying they disapprove of the job the GOP is doing on Capitol Hill. Just last year the GOP had a 54 percent approval rating, and in 2012 they held a 70 percent approval rating.

But a series of tough votes over the last few months that saw Republican leaders work with President Obama to boost spending and raised the government’s debt limit have deepened a rift between the GOP’s leadership on Capitol Hill and conservative activists around the country.

That could be one reason why Rep. Paul Ryan, the Wisconsin Republican who wrote December’s budget deal that boosted spending in 2014 and 2015, saw his standing with CPAC voters cut in half — from 6 percent support in last year’s presidential straw poll to just 3 percent this year.

Sen. Marco Rubio suffered an even bigger drop, falling from 23 percent and second place in 2013 to seventh place, with 6 percent, this year.

“I like Ted Cruz, I like Rand Paul, I like Mike Lee. I like Rubio, but less now than I did a year ago because of immigration,” said David Fitzwilliam, 83.

For Mr. Paul, the victory is his second in a row, and he saw his support climb from 25 percent last year to 31 percent this year.

“He is the only true liberty candidate who focuses on civil liberties more than anybody else,” said Al Seltzinger, 36, from Baltimore. “I think the way the nation is going today with the government and the president going against the Constitution that we need someone who holds strict to the Constitution and whose voting record is pretty solid when it comes to the Constitution.”

Mr. Cruz also jumped from just 4 percent last year — when he was a newly sworn-in senator — to his 11 percent this year.

Mr. Carson, who gained prominence with a 27-minute speech challenging Mr. Obama when the two appeared at the 2013 National Prayer Breakfast, is also on the rise. In last year’s straw poll, taken just after that speech, he garnered 4 percent of the vote, but jumped to 9 percent this year.

“I love Ted Cruz, I love Rand Paul, but Ben Carson is all of the above,” said Jean Carlton, a 71-year-old CPAC attendee who said the doctor’s lack of Washington experience was a big plus.

For his part Mr. Christie, who has faced political troubles back home in New Jersey after his staffers caused a traffic jam on the George Washington Bridge to punish a town mayor, seems to be holding steady among activists. He rose from 7 percent last year to 8 percent support this year.

In his speech to the conference on Thursday, Mr. Christie argued that the GOP needs to not only pick a conservative champion, but pick a candidate who can get elected.

“We can’t govern if we can’t win,” he said.

That resonated with some CPAC straw poll voters.

“I think he has the best chance in the general election. I am less optimistic about his chances in the primary, but he seems to be more palatable to Independents and Democrats. I think electability is the main concern,” said Matthew Smith, a 19-year-old student at Yale University.

This year’s straw poll listed 25 potential candidates, which is far more than usual. The high number signals just how wide open the GOP’s presidential contest is with two years to go before the first caucuses and primaries.

On the Democratic side, meanwhile, former Secretary of State Hillary Rodham Clinton easily leads the rest of her party’s field in national and state polling.

Previous versions of The Washington Times/CPAC poll showed that the audience that gathers in Washington leans younger and more libertarian than the conservative movement throughout the country, which likely gives Mr. Paul a boost with this crowd here.

Indeed, his father, then-Rep. Ron Paul, won the straw poll twice on a similar libertarian-minded message, though he struggled to translate that support into votes when it came to primaries and caucuses.

The straw poll was conducted between Thursday and Saturday afternoon, and 2,459 votes were cast.

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