Why are dual-class stocks so popular these days (GOOG, FB, etc.)? Is this part of a building trend to entrench management against public shareholders? Why do shareholders put up with this?

These structures are desired, but to say they are popular is an overstatement.  The companies that have been able to do this (set up two classes of stock as a public company, with a class that allows certain early investors/employees/executives to have super-voting rights) are pretty rare. First you need to be pretty darned successful.  If you are begging for money as a private company this will never happen.

Then you need to show that even a fraction of ownership in your company will have tremendous value to public shares holders.

Then you need to show a history of fairly intelligent decisions (beyond your technical expertise) throughout your pre-IPO history.

These structures are popular because they allow a company to raise money through an IPO without giving up control of decisions. It is a rare company who can convince the world that this is a good idea.

Shareholders allow them because they want to make money.  That is why most investors invest (well...practically all investors). Giving up control of something that makes money is better than having control of something that doesn't.

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