Update: An earlier version of this article referenced a study by two political scientists, Kyle Kopko and Christopher Devine, on whether Green Party presidential candidate Jill Stein’s voters could have swung the election to Hillary Clinton. That study was based on incomplete data: Vote totals for Pennsylvania weren’t yet final, and the final tally showed that Clinton could have won the state if she’d had all of Stein’s votes as well as her own. This article has been updated to reflect the final results in Pennsylvania and elsewhere.

Democrats are searching for a why in how Hillary Clinton lost the presidential election — an extremely close race claimed by small margins in battleground states, a race that defied almost every poll and projection.

When the reality set in that Clinton actually won the popular vote, likely by more than 2 million votes, Democrats started revisiting the haunts of the 2000 election. That year, Green Party candidate Ralph Nader’s performance in Florida arguably swung the election to George W. Bush, who claimed the presidency with Florida’s electoral votes by less than 600 ballots. (Nader won 97,488 votes in Florida that year.)

Now, the question lives once more. Did third-party voters lose the election for Clinton as they did for Gore almost two decades ago?

Two political scientists, Kyle Kopko from Elizabethtown College, and Christopher Devine with the University of Dayton, have tried to answer this question. Their conclusion: While the third-party vote could have made a difference in some key states, including Michigan, it’s more complicated than that.

“The 2000 election came down to one state in particular,” Devine said, referring to Florida. “It was very clear that if Green Party voters had voted for Gore, Bush wouldn’t have won. We don’t have as clear cut a story this time around.” In 2016, the election was decided by more than one battleground state — and the importance of the third-party’s performance in those states varied.

A Vox analysis of third-party voter turnout in battleground states in 2016 compared with 2012 does highlight an impressive improvement for third-party candidates this year. That suggests that this year’s major-party candidates were more disliked than Obama and Romney, but it doesn’t mean third parties shaped the election — unless Democrats disproportionately defected from Clinton in all the important states. And that doesn’t appear to be the case.

The third-party voter effect on the election: Here’s the math.

In Michigan, Wisconsin and Pennsylvania, one could plausibly blame third parties for the outcome. In Michigan, Clinton lost by less than a percentage point, a deficit she could have recovered from with half of Stein’s votes. Again in Wisconsin and Pennsylvania, where Clinton lost by one point, Jill Stein’s votes would have covered her loss. Had Clinton won all three states, she would have won the election.

Kopko and Devine’s analysis took two approaches to examining the third-party question: First, they projected the outcomes in battleground states if Clinton got all of Libertarian candidate Gary Johnson and Green Party candidate Jill Stein’s votes. Second, they explored exit polling that asked voters to decide between Clinton and Trump in a two-person race. Both approaches suggested that third parties didn’t make the difference. (To be sure, both approaches have caveats: Exit polling is fallible, for example.)

According to Kopko and Devine’s analysis, if Clinton were given all of Stein and Johnson’s votes, Trump still would have won Iowa, Ohio, Georgia, and North Carolina. But Clinton would have won Florida, Pennsylvania, Wisconsin, and Michigan — enough to win her the election. Kopko and Devine’s analysis was completed before all votes were counted.

The final totals revealed that, in fact, Stein’s total voters exceeded Clinton’s margin of victory. In other words, if every Stein voter had voted for Clinton instead, she could have won Pennsylvania, Michigan, Wisconsin and the presidency.

Time to blame those idealistic third-party voters? Not quite. Obviously, not all Stein and Johnson voters were disaffected Democrats — some would have voted for Trump, written in candidates, or not voted at all.

This is very different from Florida in 2000, where only a small fraction of Florida voters for Nader — about half of a percent — would have needed to vote Gore to give Gore the election.

And that’s what exit polling that asked people how they would have voted in a two-party race — with the third option of not voting — finds. Under that scenario she would have won Michigan, still lost Florida, and Wisconsin and Pennsylvania would have been a 48 to 48 percent toss-up. Clinton would have needed to win both of those states to reach 270 electoral votes. So even in the artificial world of that exit poll that erased Stein and Johnson, Clinton seemed likely to lose.

This isn’t the 2000 election — but third parties did increase their support

That being said, interest in third parties should not be understated this election. In 2012, Gary Johnson attracted 1 percent of the national vote. This year he pulled just more than 3 percent. Jill Stein got 1 percent of the vote this year, compared with less than half a point in 2012. Basically, minor-party candidates tripled their support this year.

That translates to a lot of ballots in battleground states, according to Vox’s analysis. Florida saw an increase of 185,000 votes for minor parties between 2012 and 2016. In Wisconsin, there was an increase of 105,202 votes this year, relative to the last election cycle.

We can’t know for sure where those votes would have gone if not for third parties, but it does indicate that Trump and Clinton were unfavorable enough candidates that people were willing to knowingly sacrifice their vote for candidates that had no chance of winning the election (or even one state).

Johnson had a lot of hype this election. He didn’t really live up to it.

While Stein’s polling numbers were negligible throughout the election cycle, political scientists were more bullish with Johnson, who consistently polled higher than the typical minor-party candidates, and maintained his relatively high poll numbers late into the summer: He was drawing 8.5 percent of the vote in August.

He was able to get national attention, even without participating in the general election debates. In late August, FiveThirtyEight’s Harry Enten even wrote that Johnson had the chance to win 7.1 percent of the national vote:

Most third-party candidates didn’t lose that much support between late summer and Election Day … The average drop-off is about 2 percentage points … Johnson was projected to finish with 6.5 percent of the vote in mid-July when he was polling slightly higher than he is today.

That didn’t happen. His numbers dropped to around 4 percent by Election Day.

“Libertarians and the Greens can claim improvement” since 2012, Devine said. “That’s true, but it’s a limited celebration. Especially in a year with historically unpopular candidates, rising frustration with politics and Washington D.C., it’s not that impressive a showing.”

Instead Johnson and Stein reflected the hard truth with minor-party candidates: They don’t usually do as well as the polls may suggest. Once people get into the voting booth they recognize the stake of the election.

Third-party support always fades. This election was no different.

"Third parties tend to lose, their poll numbers tend to decrease over time, and they perform worse on Election Day," John Sides, a political scientist with George Washington University, tells me.

Take Ross Perot’s unprecedented run in 1992, the most successful modern-day minor-party candidate to date. Perot, a wealthy Texan businessman who ran as an independent with a plan to eliminate the deficit, led both Bill Clinton and incumbent former President George H.W. Bush in the polls for three months leading up to the conventions.

Then Perot began to fade. "The conventions remind regular voters why they are Democrats or Republicans," Georgetown University political scientist Jonathan Ladd said of Perot’s decline in support.

Perot temporarily suspended his campaign in July of 1992, and restarted it again in October. On Election Day, Perot won 19 percent of the vote behind Clinton and Bush — 1 point less than polling projections. He didn’t win a single state. As president, Clinton eventually took on eliminating the deficit, absorbing the policy idea that made Perot so popular.

Overall, Perot’s trajectory is consistent with other minor-party campaigns. (The New York Times has a good visualization of this.) In 1968, third-party candidate George Wallace, who ran on a segregationist platform, won 14 percent of the vote on Election Day, despite polling around 17 percent a few months prior. It’s a "pattern of third-party support fading as people face the prospect of a wasted vote," Dartmouth College political scientist Brendan Nyhan tells me.

In other words, as Election Day nears, the reality of a presidential vote dawns on American voters who had once expressed support for third-party candidates.

In a Trump-Clinton race, notably, there was a substantial increase in third-party voters’ interest — but not enough to definitively swing the race.

Sarah Frostenson contributed reporting to this story.