It seems to me the best way to pick a CEO would be by soliciting bids from applicants. That way you get the cheapest one that is fully qualified. And you should repeat the process every two years whether the CEO is doing a good job or not.
You might find someone equally good who works cheaper. That’s capitalism. I find it hard to believe that a major company can’t get a perfectly functional CEO for a million dollars a year, or that the one who is willing to work for that amount is worse than the one who needs 40 million to do the same job.
Hiring the lowest bidder CEO can’t happen of course, because the boards of directors are comprised of CEOs of other companies, and supporting a bidding process would queer their own deals.
I think it would be interesting if someday a union went on strike and demanded a CEO bidding process as one small part of their agreement. They wouldn’t get it, but I’ll bet the CEO would be willing to settle the strike quicker to get that issue out of the public’s attention.
[Update: The prior version of this post was put up during some computer problems, now resolved. — Scott]