John Kasich needs New Hampshire’s undeclared voters to surge to the Republican primary. Bernie Sanders would like to see those same voters pick the Democratic race.

Recent history shows either scenario is plausible.

But ongoing upheaval in the ranks of New Hampshire’s undeclared (or “independent”) voters makes it hard to know what (if any) direction they're moving over the long term.

In fact, independents have shown themselves more than willing to swing heavily toward either party’s primary in recent decades.

In the last two cycles with competitive primaries on both sides, undeclareds swung like a pendulum from the Republicans (in 2000) to the Democrats (in 2008).

In 2000, 62 percent of independent voters drew a Republican ballot, sending John McCain to victory over George W. Bush. That trend meant that, the Democrat most attractive to independents, Bill Bradley, saw his hopes of an insurgent win over Al Gore torpedoed.

The 2008 cycle was the mirror opposite of 2000. That year, 62 percent of undeclared voters were drawn to the Democratic contest between Barack Obama and Hillary Clinton, leaving just 38 percent voting Republican.

This massive swing between parties undermines the theory that New Hampshire’s undeclared voters, on the whole, are secret partisans – essentially Democrats or Republicans in everything but registration. It also adds complexity to one of the most vexing questions of this cycle: what will undeclared voters do this year?

It’s a question with bigger implications than ever. According to the most recent registration statistics from the New Hampshire Secretary of State, undeclareds now comprise 44 percent of all voters in New Hampshire. That’s a four-point increase since the record-breaking 2008 cycle and double the figure from 1992. More of these undeclareds are younger voters, with shorter vote histories, making their behavior this cycle even harder to predict.

Of course, one way to anticipate what undeclareds may do (and whether they have decided) is to ask them. That’s what my organization, The MassINC Polling Group, did in our latest poll for WBUR, surveying undeclared voters only.

Here’s what we found: If you just take them at the word, around 55 percent of undeclareds plan to vote in the Republican primary next week, and 45 percent in the Democratic. This outcome would be unlike either 2000 or 2008, instead putting it somewhere in the middle.But New Hampshire undeclared have a maddening habit of making up their minds late, not only when choosing a candidate but even when settling on a primary in which to vote. And they seem ready to repeat their indecision this year, leaving plenty of possibilities as we close in in Primary Day.

Our poll found that one-third of undeclareds had yet to settle on which party’s ballot to pull. So it’s entirely possible that some late event could trigger a tidal wave of undeclareds into one primary at the expense of the other. To find out what would happen if voters flock to the left or right, we asked all the voters in our poll both the Democratic and Republican head-to-head candidate questions, and then ran scenarios showing the results with varying level of undeclared voter turnout on each side.

On the Democratic side, Sanders is consistently beating Clinton in every scenario with undeclared voters. This holds true whether you look at a low-turnout situation -- where only the most Democratic-leaning independents vote -- or a Democratic wave that includes even voters who were planning to pull a Republican ballot but changed their minds.

What this means for Sanders is that the more undeclared voters who choose to vote Democratic, the better for him, because he, like Bill Bradley, fares much worse with the registered Democrats who will make up the rest of the electorate.

On the Republican side, turnout does effect the outcome, at least among these undeclareds. In a low-turnout scenario, Donald Trump and Ted Cruz finish above the pack. But as more independent voters trickle in, establishment candidates like John Kasich and Jeb Bush start to rise. In the second highest turnout option we looked at, Kasich comes within 6 points of Trump with undeclared voters, and Bush closes to a near tie with Cruz.

For that to happen, though, a very high percentage (65 percent) of undeclared voters would have to choose the Republican primary – high but not unprecedented. In fact, a 65/35 split would roughly mirror the 2000 election.

If undeclared voters swarm to the Republican primary, expect both races to be close. If that happened, moderate Republican candidates would likely outperform expectations. And with fewer undeclareds voting Democratic, Sanders could find himself in a squeaker with Clinton.

These various scenarios illustrate the challenge of polling in New Hampshire. Many Granite State voters are independent, and none more so than those that decline to register with a political party. With relatively few and widely separated data points, and a quickly changing landscape, history has relatively little to offer in terms of projecting ballot choice this cycle. If independents break late and in large numbers toward one party, it could make for a very exciting Primary Night.