There was one race in which Palin appears not to have been much help -- and, in fact, hurt the candidate. According to a 2010 study from researchers at Stanford University, noted by Brendan Nyhan, Palin's presence on the 2008 Republican presidential ticket cost John McCain 1.6 percentage points. In an election in which 131 million people voted, that's 2.1 million votes that McCain should have gotten but didn't.

The researchers set out to determine the extent to which voters made up their minds on presidential candidates or on the performance of the party that was currently in office. To answer that question, they tried to figure out how much of an influence the candidates in the election had on moving support one direction or the other.

Part of that process was to look at how candidate favorability ratings changed over the course of the campaign. Below is the chart they created to show Palin's favorability, from the moment she was announced as the vice presidential pick (and introduced to most Americans) to election day.

As the campaign progressed, fewer people said they didn't have an opinion on Palin. And as nearly all of those people formed an opinion on her, that opinion was a negative one. As the researchers put it, "Palin saw a sharp increase in negative evaluations as the fall campaign progressed. Looking at individual-level changes in favorability, we find that 34% of respondents downgraded their evaluations of Palin between September and Election Day, while just 12% became more favorable."

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To figure out the role that shift played, the researchers modeled elections in which Palin's favorability didn't plummet in the way that it did. The result? What they call the "Palin effect."

This counterfactual simulation finds that Palin’s declining favorability cost McCain 1.6 percentage points on Election Day. Since Obama actually won 53% of the popular vote, it suggests that Palin’s campaign performance did not necessarily change the election outcome, but was certainly large enough to be substantively meaningful.

We're looking at this now in light of Palin's endorsement of Donald Trump, of course, but it's important to set the context properly. We're not suggesting that this study means that Palin will have a deleterious effect on Trump in the primaries. On the contrary, Palin's endorsement likely helps solidify some support for Trump among conservative voters.

Instead, it's worth considering what happened with Palin in light of Trump's candidacy.

The study notes a 2008 Newsweek column which suggested that Palin "sent wavering Democrats, independents and moderate Republicans scurrying to Sen. Barack Obama." In a CNN/ORC poll released that November, Palin's net favorability among independents was plus-8 -- 47 percent viewing her favorably and 39 percent not. Obama's net favorability among independents was +54, Joe Biden's was +47 and McCain's was +31. In other words, the idea that independents were pushed to Obama (as stated in the column) is reinforced by the idea that people who looked at Palin negatively were less likely to vote for McCain -- and independents looked at her more negatively than any other candidate.

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If Trump wins the Republican nomination, there are conflicting theories about how voters react in the general election. Trump argues that he will turn out scads of new voters excited about his candidacy. (As we've noted before, if he wins the nomination, it's likely because he's proven he can do that.) Trump's opponents suggest that he will instead push moderate Republicans and independents away, given his unorthodox views. In other words, that he might experience a Palin effect of his own.