>Or put another way, is Zuckerberg legally allowed to run the company into the ground if he felt like it?

It depends on how he runs the company into the ground, and his state of mind while doing it.

A CEO has a fiduciary duty to the shareholders - The CEO is supposed to act in a way he believes benefits the shareholders.

They also have duties of Care -

They must evaluate business decisions and agreements after taking into consideration information and input from shareholders/board/experts/employees etc

Loyalty -

They must act in the interests of the company and it's shareholders, putting this above decisions about their personal finances or outcome

and Disclosure -

They must inform the board and shareholders about challenges facing the company, or issues the company is having.

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That said... There's serious protection for the CEO in the "Business judgement rule" which says that as long as the CEO Fulfilled the above duties and acted openly and honestly - He's protected from any liability if the company loses money based on decisions he makes.

So if Zuckerberg stated: "I will kill Facebook by intentionally making terrible decisions" then no - he's not allowed to do that at all, and will likely face many shareholder lawsuits.

> A CEO has a fiduciary duty to the shareholders - The CEO is supposed to act in a way he believes benefits the shareholders.

To the shareholders or to the majority of the shareholders? If the latter, he can literally do whatever he wants (as he's the majority shareholder).

I don't think that's true. I think he holds fewer than 50% shares. He holds greater than 50% votes.

At some point if you extend that example far enough he could be sued for gross negligence or something like that- in the case you mention, someone having to slave in the proverbial gulag is gonna get hurt which would expose Zuck if he unilaterally issued those orders against the advice of everyone else. IANAL