Fox Business wanted the fourth presidential debate to show that the network respects the Republican presidential candidates, unlike more successful financial news rival CNBC, and it proved that by letting the candidates largely run the show. That tended to favor candidates eager to jump in and assert themselves, so Ohio Gov. John Kasich, Carly Fiorina, and Sen. Ted Cruz got lots of speaking time, while rule-followers like Jeb Bush and Ben Carson did not.

Because of the free-for-all quality and the focus of the debate — fiscal and monetary policy, dynamic versus zero-based scoring in federal budgeting, and the optimal way to repatriate corporate income, among other riveting topics — there was no real consensus on who won the debate. (In fact, the consensus seems to be that nobody was the clear winner.)

But while most of the eight Republicans on stage were busy trying to win the hearts and votes of the GOP primary voters, Kasich was yelling about the need to appeal to a majority of voters in the general election. Jeb Bush briefly seconded him, saying "they're doing high-fives in the Clinton campaign right now" over the Republicans candidates stridently advocating for the deportation of 11 million illegal immigrants.

Nevertheless, it was Sen. Rand Paul (Ky.) who made the most persuasive case that he could win over voters who aren't committed conservative Republicans.

Paul, who is polling at about 3 percent, spent the first half of the debate trying mightily to get voters to care about the Federal Reserve and interest rates. But he started to make his mark when he jumped in to accuse Sen. Marco Rubio of being insufficiently conservative. Paul started out with the questionably popular assertion that families shouldn't get tax credits to pay for childcare, but turned that into a more winning argument that the U.S. spends too much on the military (more than 10 times the next country on the list), adding the kicker: "Can you be conservative and be liberal on military spending?"

It was a good line, well rehearsed, and it actually won him more than a little applause from the Republican audience. Paul's best moments, however, started when he calmly made a fool of Donald Trump, patiently waiting for Trump to finish talking aimlessly about the Trans-Pacific Partnership — a trade deal Trump hates but apparently knows little about — before noting that Trump's focus on China was misguided, since China isn't part of the TPP. The Fox Business moderators were so relieved that they didn't have to point that out, they practically thanked Paul. The junior senator from Kentucky went on to point out that the TPP would probably weaken China, ending with the reasonable argument that the U.S. presidency has gathered up too much power.

Later in the debate, Paul acknowledged that, unlike many of his GOP rivals, he thinks human activity probably plays some role in climate change, even while he promised that "the first thing I would do as president is repeal the regulations that are hampering our energy that the president has put in place."

Paul's big moment was on foreign policy, however. Republicans are fond of arguing that President Obama is weak on national defense and has created a mess in the Middle East, but Paul said that his GOP colleagues are as hawkish as Hillary Clinton. That's not a new argument for Paul, but he followed it up with some potential consequences of the proposed no-fly zone that was popular on the debate stage:

Russia flies in that zone at the invitation of Iraq. I'm not saying it's a good thing, but you better know at least what we're getting into. So, when you think it's going to be a good idea to have a no-fly zone over Iraq, realize that means you are saying we are going to shoot down Russian planes. If you're ready for that, be ready to send your sons and daughters to another war in Iraq.... I am not happy about them flying over there. But I'm not naive enough to say, well, Iraq has them flying over their airspace, we're just going to announce that we're shooting them down? That is naive to the point of being something you might hear in junior high. [Rand Paul]

The knock against Rand Paul is that he's too kooky to be electable, with just a bit too much of that Ron Paul dust clinging to his garments. On Tuesday, he was the calmest, most relaxed person on stage, making the most middle-ground arguments about war and the environment. Opposing more intervention in Iraq and Syria may not be a big winner with Republicans, but it's a hit with the independents that the GOP (and Democrats) need to win the next presidential election.

Most Republicans Favor Use of Ground Troops; Most Democrats Are Opposed

The other candidates on stage did fine, or even well.

Ben Carson is gaining in the polls despite the debates — he only had to make no big mistakes Tuesday night (he only made minor ones) and ably address the accusations about his apparent inconsistencies regarding his childhood through college years. Republicans seem to be satisfied with his response about how at least he isn't a liar like Hillary Clinton — though, as The Washington Post's Chris Cillizza notes, Carson's setup question from Cavuto "would give the term 'softball' a bad name."

Carly Fiorina was intense, jumping in to advocate a hawkish foreign policy and taking a PowerPoint approach to the federal tax code. John Kasich made his presence felt, even if sometimes a little too aggressively. Donald Trump, like Carson, seemed a little out of his depth on some of the policy issues, and he actually argued on national TV that American wages are too high. Jeb Bush got a passing grade when the consensus was he needed an A+.

The two candidates that will be talked about the most as debate winners will be Marco Rubio and Ted Cruz. That's totally justifiable. Rubio was on his game and Cruz had a memorable (but meaningless, if you think about it) line about how the U.S. tax code has more words than the Bible. One of these two may very well win the Republican presidential nomination.

Rand Paul probably won't. Perhaps he was so relaxed on Tuesday night because, as Jim Newell argues at Slate, he has nothing to lose. "Rand Paul's presidential hopes mostly went out the window in mid-2014 when the Islamic State released videos of beheaded Americans," Newell says, ending "whatever post-Bush infighting existed within the Republican Party about the wisdom of rampant overseas intervention."

But if he does somehow pull off an upset and get the Republican nomination — and the Rand Paul who showed up Tuesday night sticks around — the GOP might just have its strongest general election candidate. Americans are more socially liberal than at any point since at least 1999, according to Gallup, but they remain more fiscally conservative by a sizable margin. The libertarian Cato Institute looks at that split and argues that "candidates leaning in a more libertarian direction will likely be benefited at the polls."

Paul is clearly the most libertarian candidate running for the Republican nomination, and so far that hasn't benefited him much. But it's no accident that his final words in Tuesday's debate were: "I'm the only fiscal conservative on the stage." If he can convince enough Republican voters of that, he might have staying power — or at least another berth in the next primetime debate.