To get past that, Iowa State University and WHO-TV, a local television station, polled likely caucus-goers not once but twice. By doing so, we learned a lot about the “why” behind changing poll numbers. (A note: Our numbers in this post will look slightly different than those in our official poll news release. That is because, in this analysis, we use all respondents — but the official release uses likely caucus-goers only.)

What’s happening among Iowa Democrats?

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In our January poll, undertaken January 5-22, we find former secretary of state Hillary Clinton leading Sen. Bernie Sanders among likely Democratic caucus-goers 51.4 to 39.5 — a lead of 11.9 points. But in November, taken November 2-15, the margin for Clinton was 49.5 to 27.8, giving her a lead of 21.7 points. While Clinton’s percentage of the vote increased by about two points, Sanders’s share increased by 12, and the undecideds dropped to less than 8 percent.

Why? We can think of three possible patterns of changes that could give us this result: (1) Sanders is drawing voters from Clinton; (2) Sanders is drawing more from previously undecided voters than Clinton is; or (3) the rate at which supporters of Clinton and Sanders answered the surveys changed — in other words, one group got more enthusiastic about their candidate and was more likely to answer our questions.

To see what happened, we created the figure below. The size of each oval (the small one says undecided) is proportional to the share of likely Democratic caucus-goers. We omitted former Maryland governor Martin O’Malley because his share is so much smaller than Clinton’s that it would be difficult to scale the figure. Each of the arrows represents the proportion of voters who were in each camp in November but switched in January. The darker the arrow, the higher the proportion who switched.

Here’s what we found. First, very few Clinton or Sanders voters have switched to undecided. If voters changed, they moved to the other candidate.

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Second, Clinton and Sanders attracted almost the same number of undecideds. Clinton now has the support of 30 percent of the voters who were undecided in November, and Sanders has the support of 29 percent. None moved to O’Malley. One November Clinton voter shifted to O’Malley; none came over to him from Sanders.

Third, Sanders attracted the support of 11.1 percent of those who, in November, said they supported Clinton. Clinton attracted 4.3 percent from Sanders. But since there were more Clinton voters than Sanders voters in November, he is getting a larger percentage of a larger group. We found no evidence that Sanders’s gains came because Clinton supporters opted out of the second survey.

In summary, Sanders gained because he converted more Clinton voters than Clinton converted Sanders voters. In other ways, the two candidates appear to be roughly even.

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What’s happening among Iowa Republicans?

Our topline results on the Republican race are in line with everyone else’s. In our January poll, we find that Sen. Ted Cruz (21.7 percent) and businessman Donald Trump (20.1 percent) are essentially tied for the lead, with Sen. Marco Rubio (18.6 percent) and retired neurosurgeon Ben Carson (10.9) next. Twelve percent of these Republicans are still undecided, and the remaining candidates split the other 16.7 percent.

What’s interesting is how their preferences changed between November and January. We have generated the same figure for the Republicans as we did for the Democrats. To make it easier to read, we have combined all of the candidates getting less than 5 percent into a single oval. Again, the size of the oval is based on the percentage of voters in each group, and the darkness of the arrows represents the proportion of people who were in that category in November but moved to the target group in January.

Carson is clearly losing support. Almost no one is moving toward him; many are moving away. Only 58 percent of those who said in November that they supported Carson have stayed with him into January.

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Those former Carson supporters, however, have moved pretty evenly into the other camps. The numbers heading from Carson to Cruz and Trump are almost identical, with just a shade fewer leaving for Rubio.

That means Cruz hasn’t taken the lead simply by becoming the candidate of choice for former Carson supporters. The actual pattern is more complicated, so we took a closer look, below.

You’ll see that Cruz has kept nearly all of his November supporters. While he does draw some from Carson, from undecideds and from the rest of the field, he gets a high percentage of former Trump supporters (22.8 percent) and former Rubio supporters (21.7 percent). In other words, more than one-fifth of people who supported Trump or Rubio in November switched to Cruz by January.

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Cruz hasn’t taken the lead by taking over Carson’s voters. He has done so by taking voters from Trump and Rubio, the other two candidates in our top three.

So how have Trump and Rubio managed to stay so high in the race when they are losing supporters to Cruz? By gaining even more supporters from the other camps. Let’s take a look, below.

Both Trump and Rubio lose a substantial number of supporters to Cruz but to no one else. Both draw relatively large numbers of supporters from Carson, undecided and the rest of the field.

Voter support in Iowa is much more fluid than polls make it appear. Rubio, for instance, had basically the same percentage in both waves of our survey, but fewer than two-thirds of his November supporters were still supporting him in January. While he lost a fifth of his support to Cruz, he made it up by drawing from the rest of the field. Cruz has pulled more voters away from Trump and Rubio than from Carson. Sanders is gaining on Clinton by winning over her former supporters.

Even when candidates’ standings in the polls don’t change much, there is still a surprising amount of movement in individual voters’ decisions.

David A. M. Peterson is a professor in the department of political science at Iowa State University and editor of Political Behavior.