In Facebook’s case we aren’t talking about any new information that would affect the stock price. The dual-class nature of the stock is well-known. Individual investors may not have known, and they may have bought the stock based on wrong information. But for the most part “Zuckerberg still has supermajority voting control” isn’t an actual headline. The only new information is that we now have one datapoint about what Zuckerberg will do when he disagrees with investors. I don’t think that changes the value of the stock in any meaningful way.
The end result is that there’s no reason to believe that upset investors selling off their shares would have any long-term effect on the stock’s price: the moment the price drops, other investors will bid it back up. If Zuckerberg loses any sleep, it will be for less than a week and he wouldn’t need to make any changes (he wouldn’t have time to!).