Power is a force that needs an object: To have power, a person has to have it over something, or someone.

One would think that this would be the appeal of power—to be able to control things, to change them to fit your vision of reality. (This can obviously be good or bad, depending on who’s in power and what their vision is.) But a new study suggests that people who desire power are mostly looking to control one thing—themselves.

The study authors, from the University of Cologne, the University of Groningen, and Columbia University, present two different conceptions of power—power as influence and power as autonomy. “Power as influence is expressed in having control over others, which could involve responsibility for others,” they write. “In contrast, power as autonomy is a form of power that allows one person to ignore and resist the influence of others and thus to shape one’s own destiny.” Their question: Which of those things, influence or autonomy, would satisfy people’s desire for power?

In the first part of the study, 100 participants took an online survey asking them to imagine that they’d been offered a promotion at work. Some participants were told that the promotion gave them more influence over subordinates but less autonomy; others were told they had more autonomy to set their own goals but less influence. Neither scenario included a salary bump, and in either case, their boss would be equally happy whether they said yes or no. When asked if they’d accept their new role, 62 percent of people in the higher-autonomy group took the promotion, while only 26 percent in the higher-influence group did the same. The numbers were similar in a repeat survey in which all participants were offered both promotions.

For the next experiment, 40 Dutch undergrads did some BLARPing, or office role-playing, with some participants playing managers and others assigned to be assistants. The participants were told that they would have to complete a list of tasks—some fun, some boring—and that the managers could choose who did what between themselves and their assistants. In an after-the-fact the survey, assistants reported that they were less happy, experienced less autonomy and less influence, and had a higher desire for power than managers did. But within the assistants, those who felt that lack of autonomy most strongly were more likely to desire power. Feeling the lack of influence didn’t have the same effect.

Next, in a group of priming studies—two with Americans and one with Indians—participants were asked to recall a time when they had power over other people, or when someone else had power over them (or what happened yesterday, as a control). Afterwards they answered questions about whether they were satisfied with the level of power and control they had in the situation.

In all three studies, the researchers wrote, feeling “autonomy quenches the desire for additional power—but influence does not (or much less).”

And finally, the researchers did a survey of 986 readers of a Dutch magazine “aimed at professionals,” in which readers indicated how much power they had at their jobs (measured by where they fell in their company’s hierarchy), then completed surveys on the autonomy their positions afforded, their influence, and how much they desired more power. Top managers felt they had a lot of autonomy and didn’t indicate a strong desire for power, while middle managers, lower managers, and non-managers all desired power more than the top managers, at pretty similar levels.

All told, this research indicates that the desire for power may be somewhat misplaced: Generally, when people say they want power, what they really want is autonomy. And when they get that autonomy, they tend to stop wanting power.

That people would value autonomy over influence jives with self-determination theory, a psychological theory that suggests autonomy is one of humans’ basic psychological needs, along with relatedness and competence. Influence is not a need under this theory. Another study suggests that while striving for power lowers people’s well-being, once they have power, they really are happier, because they feel more authentic—the power makes them feel like the circumstances of their lives are more in line with who they feel they are inside. That may be because the power gives them the freedom to make their own decisions, and their sense of well-being grows when they do what they want.

The researchers on the new study suggest that influence may seem more important to people just because it’s more visible. It’s easier to see how people control others than it is to see them feeling autonomous. The study references real leaders like Napoleon, Caesar, Obama, and Putin, and fictional ones like Darth Vader and Sauron, and says, “The sense of autonomy of these powerful individuals is not as visible: It is reflected in the absence of constraint, plans not being thwarted, and ambitions not being frustrated—an absence which remains unobserved.”

“This,” they concluded, “can easily lead to a false understanding of what drives the desire for power.”