In theory, boards of directors oversee CEOs, and can be sued by shareholders should they fail in that task. But in practice such failure is hard to prove, board members are often nominated by the CEO, and CEOs often put each other on their boards. In theory shareholders can dump the current board or CEO at annual meetings, but a commons greatly reduces the incentives for any one shareholder to mount an expensive campaign to find and convince other shareholders. In principle someone could buy out the whole company, dictate changes, and then sell the better-run company at a profit, but existing law and CEOS now lay many obstacles in this path.
The biggest problem with unaccountable CEOs is that they don't know when to step down and let someone else run the company. The value of companies often jump when such a CEO dies. So a recent "Just Vote No" campaign focuses on this problem, and proposes that dissatisfied shareholders withhold their vote in a certain way, in order to signal they think the current management should step down. The companies with the highest no votes are then publicized, to try and shame management into action.
The main proponent of this Vote No campaign thinks the following proposal of mine has promise. I propose to create, for each stock, a separate market in that stock for trades which are "called-off" if the CEO does not step down in the next year. The price of the stock in this market should indicate the market's expectation of the value of that company with a different CEO. If that stock price is consistently and significantly higher than the ordinary stock price, that should be a clear market signal, from informed traders, for the CEO to step down. (If there is no price, because there is no trading, then there is no signal.)
Ordinarily CEOs respond to statistics showing how poorly their company is fairing relative to similar companies by explaining how they are really different. And they respond to statistics of unhappy shareholders by pointing out how little incentives any one of them has to become well informed. These excuses should be blunted by my proposal, and board members may more plausibly fear legal action for ignoring these market signals.
This proposal is an example of a more general concept of policy markets.