Are women set up to fail — by being appointed to positions of power only in hopeless situations?

Two British academics say so, and they claim to have proved it this year. In one study, they took 83 businesspeople — roughly half of them women — and described to them two companies, one that was steadily improving in profitability and another that was steadily declining. The subjects were told to pick a new financial director for the firm and were presented with three candidates: a man and a woman who were identical in experience and a lesser-qualified male. The subjects were slightly more likely to pick a man to lead the successful firm but were far more likely to pick the woman to lead the failing one. Two other experiments with similar designs yielded the same result: When presented with men and women to lead a company that’s going down the tubes, people pick the woman.

What’s going on? In a write-up of their experiments in The Leadership Quarterly in October, the academics, Michelle Ryan and Alex Haslam, called it “the glass cliff,” which they contend is an invisible form of prejudice. In other words, people will give women a position of power only when there’s a strong chance of failure. Why? “If someone has to be the scapegoat to take the fall, you’re not going to put your best man forward,” Ryan says. Women are thrust into desperate situations precisely because they’re likely to fail, generating “proof” that women can’t handle responsibility.

The theory has some historical evidence to back it up too. When the academics examined the performance of the 100 biggest firms in Britain, they found that women were disproportionately hired as C.E.O.’s only after their firms had been struggling for years. When firms were doing well, they rarely appointed women to lead.

Ryan and Haslam say the data also suggest the glass cliff applies to minorities. When you consider this year’s American presidential election, the glass-cliff theory becomes particularly tantalizing — because it might neatly explain the rise of Hillary Clinton and Barack Obama. Perhaps it was only during extremely hard times that America would finally consider a woman and a black man for the highest office.