First, I've worked at a company that has undergone restructuring at a management level. From personal experience, small changes in strategic direction have a massive impact on people at the bottom of the "job-food" chain. It is easy to lose months, probably even years of work because someone above you made the wrong call. Since a CEO helps determine the strategic direction of the company, it seems reasonable to me that the pay of the CEO should scale with the sum pay of every other member of the company.
Second, there are a few studies which show a CEO's personal circumstances can have a percentage-point effect on a company's performance. A great example is a study of the effect on profit by a death in the immediate family of a CEO. Excerpt:
Sorting by the number of children we find the biggest effects on firm profitability in cases where the CEO only has one child. Specifically, one-child death shocks correlate with a 5 percentage point decline in firm profitability irrespective of the age of the child.The study goes on to show that the deaths of a spouse or child are significant events for a firm. I think the study underscores the importance of choosing the correct CEO. Though the study doesn't show the variation in profit during standard circumstances, to me it seems like a reasonable conclusion that variations in a CEO's ability to carry themselves through tough times will have a large effect on firm profit. For a company with hundreds of billions in profits per year, like an oil company, the CEO's personal circumstances could have an effect in the billion dollar range, meaning if the CEO themselves only received a fraction of this pay it would still be in the tens of millions range.
My math is a bit fuzzy here, but as always you're welcome to disagree in the comments and point out any mistakes I've made.
