CARSON CITY, Nev. — In Iowa, the Republicans who showed up to caucus sites filled out blank pieces of paper with the names of their chosen candidate. The Nevada caucuses are different: A paper ballot will be provided when the doors close tonight. And that ballot includes six candidates who have already left the presidential race.

The effect of seeing those names, like most details of these caucuses, is a mystery. In New Hampshire, around 1 percent of Republican voters cast ballots for a candidate who had quit the race already. Another 1 percent wrote in the name of someone else — mostly, surprisingly, Sen. Bernie Sanders (I-Vt.). While people familiar with internal polls doubt that either Sen. Ted Cruz (R-Tex.) or Sen. Marco Rubio (R-Fla.) can defeat Donald Trump here, opponents of Cruz hold out some hope that a few libertarian-minded voters will show up and spoil their ballots by backing Paul.