In other words, when money was added to the equation, questions about the economy became less like asking people which football team they thought was best, and more like asking them to place a wager. Even a little bit of cash gets people to think harder about the situation and answer more objectively.

“People are not telling you what they actually believe in ordinary surveys,” Mr. Bullock said. “With a payment, we’re eliciting not necessarily thoughtful responses, but more sincere responses.”

The effect was even more pronounced when respondents were rewarded for honestly answering “I don’t know” when they didn’t have enough information. Otherwise, it appears that people will respond objectively to questions when they know the answer, but revert to their partisan biases when they don’t.

The paper by Mr. Bullock, Alan S. Gerber, Seth J. Hill and Gregory A. Huber found that offering a $1 payment for a correct response and a 33-cent payment for an answer of “Don’t know” eliminated the entire partisan gap between Democrats and Republicans on questions about the economy.

Interestingly, in the paper by Mr. Prior, Gaurav Sood and Kabir Khanna, the cash payments became less effective at coaxing an accurate answer if the question mentioned the president by name. George W. Bush was president at the time of the survey, but by extension it appears that Americans can be more objective answering a question like “Is the unemployment rate lower or higher than it was seven years ago?” than a question like “Is the unemployment rate lower or higher than it was when Barack Obama became president?” even though as a factual matter those are the same question.

The research could have interesting parallels beyond the realm of opinion surveys. It calls to mind, for example, energy executives who might support politicians who deny that climate change is happening, but when doing their jobs with real money on the line, accept the scientific consensus that the planet is warming, and plan accordingly. Similarly, people who hate the Affordable Care Act and think it is a disastrous public policy will nonetheless take advantage of it to obtain health insurance.

The findings have some interesting implications for democracy, too, though depending on your inclination you could view it as good news or bad.