Did higher levels of campaign spending buy George W. Bush the presidency in 2000 and 2004? And will all the money being spent on this year’s election move voters too?

That’s the conclusion of an intriguing new political science paper that estimates that between 1972 and 2004, 13.6 percent of voters “incorrectly” pulled the lever for Republicans in presidential elections, while 8.7 percent “incorrectly” voted Democratic.

Study author Sean Richey (a Georgia State University Professor) found that money was a factor. Republicans spend more of it, and that money often buys convincing and/or misleading ads.

“These results suggest that the Republicans’ financial advantage gave them the purchasing power to create persuasive campaigns that disproportionately brought incorrect votes to the Republican side,” wrote Richey. “As the Republican advantage in campaign resources grew, their share of incorrect voting grew.”

The paper is entitled “Random and Systematic Error in Voting in Presidential Elections” and is published in Political Research Quarterly. (Sadly, the paper does not include the 2008 election).

First, a word on “incorrect” voting. It may at first sound unfair some professor to decide whether somebody voted correctly or incorrectly. But the American National Election Studies does ask voters a barrage of questions on their political ideology. And based on these questions, political scientists Richard R. Lau and David P. Redlawsk have developed a formula to assess whether individual voters choose the candidate that better represents their politics. If they do, it means they are voting “correctly.”

Based on this formula, Richey went back over the ten presidential elections from 1972 to 2004. He estimated the percentage of votes cast incorrectly for both parties. His tallies are reproduced below. In addition to 2000 and 2004, He also estimates that had voters chosen “correctly,” Gerald Ford would have defeated Jimmy Carter in 1976.

While it might seem surprising to see on average roughly 20% of voters choosing the “incorrect” candidate, it’s worth keeping in mind that as of this August, only 60% of voters knew that Mitt Romney had been governor of Massachusetts, and only 40% of voters knew that Republicans held the majority in the U.S. House. In other words, many voters are not particularly well-informed.

This, argues Richey, creates an opportunity: If one campaign has the resources to do more persuasive manipulation than the other campaign, it could lead to a skew in voting. “Generally,” Richey wrote, “voters do not have the knowledge skills to overcome manipulation.”

And this is exactly what he found in a statistical analysis of the relationship between spending and incorrect voting (controlling for other factors).

“The greater skew in hard money spending by Republicans leads to greater incorrect voting for Republican candidates, as does Republican skew in soft money spending,” Richey wrote. “Greater skew in hard and soft money spending also decrease the likelihood of voting incorrectly for Democratic candidates, which further increases skew. These are large marginal effects.”

Certainly, there might be reasonable reasons why voters would support candidates even if they disagree with them on most of the issues (e.g., character, constituent service). And low-information voters might also have a poor handle on their political beliefs, rendering the idea of correct or incorrect voting somewhat meaningless.

But even if this were the case, one would still expect voting mistakes to be bipartisan. That voters incorrectly vote Republicans at a consistently higher rate suggests that something else is going on. And that this incorrect voting correlates with the amount of money being spent is intriguing (though 10 presidential elections is probably not enough to make a definitive case.)

This election cycle provides yet another test of this hypothesis. With more money being spent than ever before, we can see whether it adds up to anything. Will the side with more money persuade more voters to make the “incorrect” choice? Time will tell.