The easy answer is they think they can win. Among conservatives, Cruz is popular and influential. He led House Republicans in a politically quixotic but financially successful drive to shut down the government in opposition to Obamacare, and plays well with conservative audiences, who devour his blend of red meat and erudition. (He likes to cite philosopher John Rawls, for example). With this kind of enthusiasm for your political persona, why wouldn’t you run? And to that point, in the week following his campaign announcement, Cruz raised $31 million and generated millions of social media interactions. His odds are still slim, but like other factional candidates in the past—from Barry Goldwater to George McGovern—he might strike lightning.
The same goes for Paul. Among libertarian-minded Republicans, he’s a phenomenon. His filibusters—of John Brennan in 2013, and most recently, of the Patriot Act—have attracted huge media attention as well as hefty fundraising from supporters. Yes, he’s outside the mainstream on foreign policy for a Republican, but there’s still a chance he could succeed in a primary—at the moment, he holds fourth place in national polls of the GOP presidential race. His aspirations, in other words, make sense. And if he’s doomed to sit in the second tier? Then, with forceful views on surveillance and criminal justice, he can at least pull the field closer to his positions.
The picture is a little different for candidates like Jindal and Christie. They’re also factional—social conservatives and Northeastern moderates, respectively—but neither has a base in the GOP that isn’t already occupied by one or more candidates. Still, they’re two-term governors with conservative success under their belts. Why not run, especially when—in the case of Christie—you were a onetime star? What do you have to lose?