I am familiar with the concept of the glass cliff, but when things are going smoothly, why would a company (which we already know are statistically mostly run by men) change leadership? If leadership mostly changes during times of turmoil, and the female population in leadership is growing, wouldn't the two correlate quite strongly irrespective of motive?
There may be something to that idea, but the Wikipedia article mentions several studies that cannot be explained that way. For example, the study discussed in "Origins" looked at companies who were adding new board members, and discovered that they were more likely to add a woman if the company had been performing poorly in the preceding months. If the glass cliff phenomenon is simply a result of increasing availability of women in leadership, then you would expect that study to show no difference between companies performing well and companies performing poorly.
Yahoo had a female CEO before Mayer, I think. Carol Bartz (from Autodesk) ran it from 2009-11.