The men were also less aware that they had used a risky strategy. In the last few minutes of the game, Dr. Preston interrupted each person immediately after he or she had just lost money. She asked people to rate how risky each of their possible choices had been, including the unsuccessful one they had just made. Women were more likely to rate their losing strategy as a poor one.

In one interesting study, a team led by Livia Tomova and Claus Lamm, of the University of Vienna, found through three experiments that under stressful conditions, women became more attuned to others. In one, people reached through a curtain and touched something pleasant, like a feather or a cotton ball, or something unpleasant, like a slimy mushroom or a plastic slug. Each person could see a picture of what he or she was touching, and what another person was touching a few feet away, and had to rate the pleasantness of their respective experiences. Typically, people merge the other person’s experience with their own — if I’m touching something pleasant, then I’ll rate your slug-touching experience as nicer than I ordinarily would.

WHEN women were stressed, however, from having to give a public speech, they actually found it easier than usual to empathize and take the other person’s perspective. Just the opposite happened for the stressed men — they became more egocentric. If I’m stroking a piece of silk, that cow tongue you’re touching can’t be all that bad.

Of course, just because it works this way in a lab doesn’t mean the same thing happens in the messy real world. Do organizations with women in charge actually make less risky and more empathetic decisions in stressful circumstances?

Some evidence suggests they do. Credit Suisse examined almost 2,400 global corporations from 2005 to 2011 — including the years directly preceding and following the financial crisis — and found that large-cap companies with at least one woman on their boards outperformed comparable companies with all-male boards by 26 percent.

Some might assume that there was a cost to this as well, that boards with women must have been excessively cautious before the financial crisis of 2008, as was the case with the balloon experiment. Not so. From 2005 to 2007, Credit Suisse also found, the stock performance of companies with women on their boards essentially matched performance of companies with all-male boards. Nothing lost, but much gained.

If we want our organizations to make the best decisions, we need to notice who is deciding and how tightly they’re gritting their teeth.