There’s an old saw—cribbed from Plato and popularized by Douglas Adams—that those most interested in leading others are least suited to the task. That’s not entirely accurate, yet new research has found a grain of truth in this idea: Many leaders have plenty of ambition to lead, but that’s no guarantee others think they’re effective.

“Our society assumes that there is a link between leadership ambition and leadership aptitude,” says Francis Flynn, a professor of organizational behavior at Stanford Graduate School of Business. People seeking power and success step up to take leadership roles, and how we select leaders rewards that ambition. “We largely rely on opt-in mechanisms to populate our pools of potential leaders—the people who apply to business schools like Stanford or seek a promotion to the next level in their organizations,” Flynn says. “That assumes implicitly that those people who want to lead are the ones who should lead. But is that assumption valid?”

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