It was her six-minute mile that did it. Or her youth. That’s the assumption about the choice by David Petraeus, America’s most-revered military statesman, to pursue an extramarital affair with Paula Broadwell, who co-wrote a biography of him.

After the announcement last week from Petraeus that he would resign his post as director of central intelligence because of the relationship, television and the Internet have been alive with descriptions of the physical allure of Broadwell, who is 20 years younger than Petraeus.

But a woman’s age or the time in which she runs a mile are probably not the primary explanations for Petraeus’s actions, just as they weren’t necessarily the main reasons that John Edwards or Jack Welch, for example, pursued their affairs. Age or looks matter, yet only secondarily. The force driving all these gents is probably something stronger than sex. What drives them is narcissism.

To label someone as noble as Petraeus with psycho-jargon would be tacky if this particular psycho-jargon didn’t capture so much. In myth, Narcissus was the hunter so beautiful that he fell in love with his own reflection. Narcissism occurs in modern life when an individual suffers from a need for affirmation of his or her own importance.

Flattery Addiction

There are levels of narcissism -- all successful people nurse some vanities. But like gambling, narcissism can go from a habit to an obsession. To a serious narcissist, flattery becomes crucial to survival. He will therefore be drawn to anyone who makes him like what he sees in the mirror: a younger, attractive partner suggests that he himself is young and attractive. Narcissists gravitate especially toward anyone who supplies that flattery reliably or, even better, assures the narcissistic feed, providing something that elicits praise from others.

“All In,” Broadwell’s adulatory biography of Petraeus, was a media event that delivered not a single but multiple moments of gratification.

Edwards’s choice of a mistress was a video maker who was filming his presidential campaign, Rielle Hunter.

Welch chose business editor Suzy Wetlaufer. She could help Welch spread Welch, the brand, post-General Electric Co., better than anyone. These women aren’t arm candy. They are mirrors or cameras.

Scholars have discerned reliable ways to identify narcissists. One is as simple as the size of signature -- the more of a John Hancock, the more self-centered the signer. In the case of chief executive officers, the prominence of their photos and names in news releases relative to those of colleagues is a giveaway, as is the length of an executive’s “Who’s Who” entry.

Many theorists these days find some benefit in narcissistic leadership. Narcissists don’t have to be unfaithful. And they are often notable for great talent. Their desperation to produce the work that wins mega-recognition can pull forward a whole company. In “The Productive Narcissist,” author Michael Maccoby argues that the egotism of executives such as Welch helps them undertake great projects and make their companies advance. Translate Maccoby’s concept over to the military, and the theory fits as well: Petraeus’s self-esteem gave him the courage to wage the controversial surge of troops in Iraq.

“Why do we all go along for the ride with narcissistic leaders?” Maccoby asked. “Because the upside is enormous.”

Exploiting Narcissism

Related benefits of narcissism were found by scholars Arijit Chatterjee and Donald Hambrick. In an article in Administrative Science Quarterly, they noted that narcissism in CEOs correlated positively to “strategic dynamism and grandiosity.” Corporate boards do their part to reinforce narcissism by approving payments to media consultants and other handlers in the name of improving the performance of their management stars. At business schools, teachers often console students who have been exploited by self-centered bosses by noting that these bosses are relatively easy for juniors to manipulate: You just take the subject of discussion back to them.

But narcissism has a dark side: It skews the judgment of the narcissist. With the news of his little affair, against the rules of soldiering, Petraeus has already tarnished his incredible feats. It is this poor wager, and not the affair itself, that so many Petraeus fans resent.

There is evidence that similar damage can be wrought by narcissists in business. The presence of a narcissistic CEO tends to mean a company enjoys a lower return on assets than others, according to scholars Charles Ham, Nicholas Seybert and Sean Wang. Companies led by narcissists pay lower dividends to shareholders. They acquire too many companies due to the leader’s vain assumption that he or she can add value. The silent tragedy at many companies is the growth forgone due to the vanity of chief executives and another mirror, the board of directors.

Again: to categorize someone who has achieved as much as Petraeus has feels wrong. Yet it isn’t a bad idea to try to understand narcissism, or vanity, the Victorian label many of us prefer. Although most of us hesitate to diminish our heroes with labels, we can be assured that others, and not merely benign personal coaches or clever deputies, quickly pick up the vulnerability of the narcissist and won’t hesitate to exploit it. At the CIA or in the corner office, the boss who doesn’t recognize his own narcissism and combat it is ceasing to be worthy of his rank. He is a project of the human-resources people and the consultants and the psychiatrists. He is a leader on his way to becoming just another case.

(Amity Shlaes is a Bloomberg View columnist and the director of the Four Percent Growth Project at the Bush Institute. The opinions expressed are her own.)

To contact the writer of this article: Amity Shlaes at amityshlaes@hotmail.com.

To contact the editor responsible for this article: Katy Roberts at kroberts29@bloomberg.net.