Do the smartest presidents make the best presidents? This question invariably emerges as a topic of spirited debate when the U.S. presidential election approaches. In 2004, former New York Times Executive Editor Howell Raines asked, “Does anyone in America doubt that Kerry has a higher IQ than Bush?” Citing Bush’s and Kerry’s scores on the Armed Services Vocational Aptitude Battery—an IQ-like test that the military uses to determine whether a recruit is qualified for enlistment—the conservative pundit Steve Sailer countered that there was no doubt that, in fact, Bush had the higher IQ. And the chatter about IQ has begun for next November’s election. Democratic frontrunner Hillary Clinton is “smart enough to handle the job” and “may have a higher IQ than Bill”, while among Republican hopefuls, Jeb Bush is the “smart brother” and Ted Cruz “towers as the smartest presidential candidate”. Wisconsin governor Scott Walker may not be the smartest candidate but “our most intelligent presidents have often been our worst presidents” anyway.

There are three basic views on the relationship between IQ and success in the Oval Office. The first view says the smarter the president, the better. In line with this view, Gary Hart, the retired U.S. Senator and one-time presidential hopeful, argued that although a big part of success as president is picking smart people for key positions, “it takes a pretty keen mind, honed by study, travel, experience, and exposure to competing ideas, to form good judgment and to know whom to trust on complex substantive issues.” The second view holds that you only have to be smart enough to be president. The idea behind this view is that IQ is a “threshold” variable, which loses its predictive power beyond a certain level. Malcolm Gladwell explained this idea in his book Outliers:“The relationship between success and IQ works only up to a point. Once someone has reached an IQ of somewhere around 120, having additional IQ points doesn’t seem to translate into any measureable real-world advantage.” (The average IQ for the general population is 100; an IQ of 120 is at about the 91st percentile.) The final view is that the president can actually be too smart—because, for example, he or she may be unable to communicate on a level that less-intelligent colleagues and constituents can understand. According to one analysis, this is President Obama’s problem: “President Obama is too intelligent for Republicans to understand.” This view puts greater emphasis on interpersonal skills than intelligence. The president is someone you should want to have a beer with, or maybe go bowling with.

What does science say? For obvious reasons, it is not possible to have the 43 U.S. Presidents sit for an IQ test. Thus, in a 2006 study, the University of California Davis psychologist Dean Keith Simonton used a historiometric research approach to estimate the correlation between IQ and presidential success. In the conventional approach to measuring IQ, a person is given a standardized test, such as the Wechsler Adult Intelligence Scale, and their score on the test is assumed to reflect their level of intelligence (with some amount of random error). By contrast, in the historiometric approach, a person’s IQ is quantitatively estimated based on variables having known correlations with IQ, such as highest level of education, academic honors, scores on college admissions exams, occupation, and preferences. In his study, Simonton found that IQ estimates for the first 42 presidents (Washington to G. W. Bush) ranged from 118—around the average for a college graduate—to a stratospheric 165—well beyond the conventional cutoff for “genius.” (The three lowest, from the bottom, were Ulysses S. Grant, Warren Harding, and James Monroe. The three highest, from the top, were John Quincy Adams, Thomas Jefferson, and John F. Kennedy.) What’s more, IQ correlated positively with a measure of “presidential greatness” based on multiple rankings and ratings of presidents’ leadership ability—and the relationship went in a straight line. The smarter the president, the better, roughly speaking. Simonton’s IQ estimates also correlate positively with a ranking of presidential performance compiled by statistician and FiveThirtyEight.com founder Nate Silver.

This finding agrees with results of large-scale meta-analyses by the University of Iowa industrial psychologist Frank Schmidt demonstrating that general cognitive ability—the psychological trait underlying IQ—is the single best predictor of performance in the workplace. It is also consistent with findings from research that has directly tested the idea that IQ is a threshold variable. In a project known as the Study of Mathematically Precocious Youth, Vanderbilt psychologists David Lubinski, Camilla Benbow, and their colleagues found that, even among a sample of intellectually gifted people, a higher level of cognitive ability in childhood forecasted great accomplishment later in life, both in school and beyond. In another study, using four data sets with sample sizes in the thousands, a team of researchers led by the University of Minnesota psychologist Paul Sackett investigated the relationship between cognitive ability and both academic and work performance. In all cases, the relationship was positive and linear—the higher the level of cognitive ability, the better the performance. There was no evidence to support the threshold hypothesis, that there is a “smart enough.”

There is also evidence that IQ is an important predictor of acquiring expertise in specific domains. For example, in a study of 90 Austrian tournament chess players, the psychologist Roland Grabner and his colleagues found that IQ correlated positively with tournament chess rating. (As it happens, over half of U.S. presidents reportedly played chess, and one—Jimmy Carter—aspired to become a chess master after leaving office.) Similarly, in a re-analysis of results of a previous study, my colleague Brooke Macnamara and I found that fluid intelligence—the general ability to reason and think logically—was a strong positive predictor of skill in the board game GO, as measured by a laboratory task that was specially designed to measure a GO player’s ability to evaluate game situations and select optimal moves. In turn, performance in this task was strongly related to a player’s tournament GO rating.

The job of president of the United States calls on a wide range of knowledge, skills, and abilities. The president must acquire vast amounts of knowledge about a dizzying array of topics, consider competing points-of-view and ideas in making decisions, and solve complex problems of all sorts. It goes without saying that IQ isn’t the only predictor of success in this job. Many other factors matter, including experience, personality, motivation, interpersonal skill, and perhaps above all else, luck. Yet, what science tells us is that a high level of intellectual ability translates into a measureable advantage in the Oval Office. As Gary Hart noted, “The Constitution imposes no IQ test”—and it seems safe to assume that it never will. All the same, we should want smart people to run for president, and then we should wish the winner all the luck in the world.