One of the peculiar characteristics of modernity is our unwillingness to recognize the blindingly obvious. For example, if I'm part of a nine member board of directors at the local gun club, then my vote will significantly influence the outcome of our official governing decisions. In contrast, my vote's likelihood of deciding an election for President of the United States is negligible, particularly since I don't live in a swing state. It's obvious when I spell it out but many people balk at its implications. Whenever I tell people I'm not going to vote, they react as if I'd announced I was going out to kick puppies.
Third party voters are often excoriated for "throwing their votes away" or hindering a mainstream candidate's chances of winning. However, if the chances of my vote deciding a national election for president are negligible, then it is irrational to vote pragmatically in presidential elections. At this point the common retort is, "Sure it's negligible but it's possible!" I will concede that it's possible in the sense that it's possible to win the lottery, but I wouldn't gamble retirement money on it.
Elections in the 21st century are not about deciding how we are to be governed. They are about publicly affirming our allegiance to the governing philosophy of secular liberalism. They are about strengthening public consensus about how we are actually being governed. Conservatives, poor credulous dopes that they are, dutifully turn out to vote for the favored Republican candidates every four years and yet the United States moves ever leftward. Each further lurch to the left causes the Overton window to shift leftward as well. Twenty years ago, gay marriage was the hobby horse of one New Republic columnist named Andrew Sullivan. Today, questioning it can get you fired.
That's one possible benefit to a Jeb! vs. Hillary contest: it will forcefully demonstrate that elections are about endorsing the system rather than deciding how we will be governed.